GMap: Drawing Graphs as Maps Emden R. Gansner, Yifan Hu, and Stephen G. Kobourov AT&T Research Labs, Florham Park, NJ, {erg,yifanhu,skobourov}@research.att.com Abstract. Information visualization is essential in making sense out of large data sets. Often, high-dimensional data are visualized as a collection of points in 2-dimensional space through dimensionality reduction techniques. However, these traditional methods often do not capture well the underlying structural information, clustering, and neigh- borhoods. In this paper, we describe GMap: a practical tool for visualizing relational data with geographic-like maps. We illustrate the effectiveness of this approach with examples from several domains All the maps referenced in this paper can be found in www.research.att.com/ ∼ yifanhu/GMap. 1 Introduction Graphs capture relationships between objects and graph drawing allows us to visualize such relationships. Typically vertices are placed as points in two or three dimensional space, and edges are represented as lines between the corresponding vertices. The layout optimizes some aesthetic criteria, for example, minimal edge length and edge crossings. While such point-and- line representation are most commonly used, other representations have also been considered. For example, treemaps [27] use a recursive space filling approach to represent trees. There is also a large body of work on representing planar graphs as contact graphs [7, 12, 19], where vertices are embodied by geometrical objects and edges are shown by two objects touching in some specified fashion. Koebe’s theorem [16] shows that all planar graphs can be represented by touching disks. Similar representation is possible with triangles, where two adjacent vertices correspond to vertex-to-side touching pair of triangles, as shown by de Fraysseix et al. [7]. If vertices are represented by rectilinear regions and edges correspond to side-to-side contact between paired regions, He [12] has shown that all planar graphs have such drawings. Graph representations of side-to-side touching regions tend to be visually appealing and have the added advantage that they suggest the familiar metaphor of a geographical map. In this paper we describe GMap, an algorithm to represent general graphs as maps. Clearly, there are theoretical limitations to what graphs can be represented exactly by touching poly- gons, even when allowing for non-convexity. However, our aim here is practical rather than graph theoretical. We do not insist that the created map be an exact representation of the graph but that it captures the underlying relationships well. With this in mind, we do not insist that all vertices are represented by individual polygons either. In fact, we group closely connected vertices into regions. If we would like to show all of the relationships, we can superimpose a graph drawing on top of the map. Our overall goal is to create a representation which makes the underlying data understand- able and visually appealing. Our map representation is especially effective when the underlying graph contains structural information such as clusters and/or hierarchy. The traditional line- and-point representation of graphs often requires considerable effort to comprehend, and often puts off general users. On the other hand, a map representation is more intuitive, as most people are very familiar with maps and even enjoy carefully examining maps. Given that we do not insist on the map to be an exact representation for the graph, at first it may seem trivial to generate a map. For example, one can start with a “good” graph drawing arXiv:0907.2585v1 [cs.CG] 15 Jul 2009
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GMap: Drawing Graphs as Maps
Emden R. Gansner, Yifan Hu, and Stephen G. Kobourov
AT&T Research Labs, Florham Park, NJ, {erg,yifanhu,skobourov}@research.att.com
Abstract. Information visualization is essential in making sense out of large data sets.Often, high-dimensional data are visualized as a collection of points in 2-dimensionalspace through dimensionality reduction techniques. However, these traditional methodsoften do not capture well the underlying structural information, clustering, and neigh-borhoods. In this paper, we describe GMap: a practical tool for visualizing relationaldata with geographic-like maps. We illustrate the e!ectiveness of this approach withexamples from several domains All the maps referenced in this paper can be found inwww.research.att.com/!yifanhu/GMap.
1 Introduction
Graphs capture relationships between objects and graph drawing allows us to visualize suchrelationships. Typically vertices are placed as points in two or three dimensional space, andedges are represented as lines between the corresponding vertices. The layout optimizes someaesthetic criteria, for example, minimal edge length and edge crossings. While such point-and-line representation are most commonly used, other representations have also been considered.For example, treemaps [27] use a recursive space filling approach to represent trees. There isalso a large body of work on representing planar graphs as contact graphs [7, 12, 19], wherevertices are embodied by geometrical objects and edges are shown by two objects touching insome specified fashion. Koebe’s theorem [16] shows that all planar graphs can be representedby touching disks. Similar representation is possible with triangles, where two adjacent verticescorrespond to vertex-to-side touching pair of triangles, as shown by de Fraysseix et al. [7].If vertices are represented by rectilinear regions and edges correspond to side-to-side contactbetween paired regions, He [12] has shown that all planar graphs have such drawings. Graphrepresentations of side-to-side touching regions tend to be visually appealing and have theadded advantage that they suggest the familiar metaphor of a geographical map.
In this paper we describe GMap, an algorithm to represent general graphs as maps. Clearly,there are theoretical limitations to what graphs can be represented exactly by touching poly-gons, even when allowing for non-convexity. However, our aim here is practical rather thangraph theoretical. We do not insist that the created map be an exact representation of thegraph but that it captures the underlying relationships well. With this in mind, we do notinsist that all vertices are represented by individual polygons either. In fact, we group closelyconnected vertices into regions. If we would like to show all of the relationships, we cansuperimpose a graph drawing on top of the map.
Our overall goal is to create a representation which makes the underlying data understand-able and visually appealing. Our map representation is especially e!ective when the underlyinggraph contains structural information such as clusters and/or hierarchy. The traditional line-and-point representation of graphs often requires considerable e!ort to comprehend, and oftenputs o! general users. On the other hand, a map representation is more intuitive, as mostpeople are very familiar with maps and even enjoy carefully examining maps.
Given that we do not insist on the map to be an exact representation for the graph, at firstit may seem trivial to generate a map. For example, one can start with a “good” graph drawing
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and build a Voronoi diagram of the vertices along with the four corners of the bounding boxfor the drawing. However, the results are visually unappealing as maps, with straight bordersbetween “countries” and jagged, angular overall appearance. Our GMap algorithm takes asinput a graph and produces a map with a “natural” look, outer boundaries that follow theoutline of the vertex sets, and inner boundaries having the twists and turns found in realmaps. Our maps also can have lakes, islands, and peninsulas, similar to those found in realgeographic maps; see Figures 3-5.1
2 Related Work
There is little previous work on generating map representations of graphs. Most related workdeals with accurately and appealingly representing a given geographic region, or on re-drawingan existing map subject to additional constraints. Examples of the first kind of problem arefound in traditional cartography, e.g., the 1569 Mercator projection of the sphere into 2DEuclidean space. Examples of the second kind of problem are found in cartograms, where thegoal is to redraw a map so that the country areas are proportional to some metric, an ideawhich dates back to 1934 [25] and is still popular today (e.g., the New York Times red-bluemaps of the US, showing the presidential election results in 2000 and 2004 with states drawnproportional to population).
The map of science [4] uses vertex coloring in a graph drawing to provide an overviewof the scientific landscape, based on citations of journal articles. Treemaps [27], squarifiedtreemaps [6] and the more recent newsmaps [30] represent hierarchical information by meansof space-filling tilings, allocating area proportional to some important metric.
Representing imagined places on a map as if they were real countries also has a longhistory, e.g., the 1930’s Map of Middle Earth by Tolkien [29] and the Bucherlandes map byWoelfle from the same period [1]. More recent popular maps include xkcd’s Map of OnlineCommunities [2]. While most such maps are generated in an ad hoc manner and are notstrictly based on underlying data, they are often visually appealing.
Generating synthetic geography has a large literature, connected to its use in computergames and movies. Most of the work (e.g., [20, 22]) relies on variations of a fractal model.Although these techniques could provide additional photorealism, it is unclear how they couldbe used with the position and size constraints attached to the maps we consider here.
3 The Mapping Algorithm
The input to our algorithm is a relational data set from which we extract a graph G = (V,E).The set of vertices V corresponds to the objects in the data, e.g., authors in the graphdrawing community, and the set of edges E corresponds to the relationship between pairsof objects, e.g., co-authoring a paper. In its full generality, the graph is vertex-weighted andedge-weighted, with vertex weights corresponding to some notion of the importance of a vertexand edge weights corresponding to some notion of the distance between a pair of vertices.
The first step in our GMap algorithm is to embed the graph in the plane. Possibleembedding algorithms include principal component analysis [15], multidimensional scaling(MDS) [17], force-directed algorithm [10], or non-linear dimensionality reduction such asLLE [26] and Isomap [28].
1 This paper contains zoom-able high resolution images; all the images are also available at www.research.att.com/!yifanhu/GMap.
2
The second step is a cluster analysis of the underlying graph or the embedded pointsetfrom step one. In this step, it is important to match the clustering algorithm to the embeddingalgorithm. For example, a geometric clustering algorithm such as k-means [21] may be suitablefor an embedding derived from MDS, as the latter tends to place similar vertices in thesame geometric region with good separation between clusters. On the other hand, with anembedding derived from a force-directed algorithm [10], a modularity based clustering [23]could be a better fit. The two algorithms are strongly related, as pointed out in the recentfindings by Noack et al. [24], and therefore we can expect vertices that are in the same clusterto also be geometrically close to each other in the embedding.
In the third step the two-dimensional embedding together with the clustering are usedto create the map. Using the embedding information, a Voronoi diagram of the vertices iscreated. A naive approach would be to form the Voronoi diagram of the vertices, togetherwith fours points on the four corners of the bounding box; see Fig. 1(a). This would result inaesthetically unappealing maps with unnatural outer boundaries and sharp corners. A morenatural appearance can be obtained by placing some random points. A random point is onlyaccepted, if its distance from any of the real points is more than r (a preset threshold) away.This leads to more rounded boundaries. The randomness of the points on the outskirts alsogives rise to some randomness of the outer boundaries, thus making them more realistic andnatural; see Fig. 1(b). Furthermore, depending on the value of r, this step can also resultin the creation of lakes (e.g., Fig. 5) in areas where vertices are far apart from each other.Nevertheless, some inner boundaries remain artificially straight.
(a) (b) (c) (d)
Fig. 1. (a) Voronoi diagram of vertices and corners of bounding box; (b) better construction of outerboundaries through placement of random points; (c) Voronoi diagram of vertices and points insertedaround the bounding boxes of the labels; (d) the final map.
Another undesirable feature is that the three “countries” all have more or less equalarea, whereas we might often want some areas to be larger than the others, perhaps due toimportance of the entities them represent. As an illustration, in Fig. 1, we assume that thearea corresponding to “node 1” is more important than the other two areas, and use a largerlabel for that area. To make areas proportional to the label size, we first generate artificialpoints along the bounding boxes of the labels; see Fig. 1(c). To make the inner boundariesmore realistic, we perturb these points randomly instead of running strictly along the rectanglebounding boxes. Here Voronoi cells that belong to the same vertex are colored in the samecolor, and cells that correspond to the random points on the outskirt are not shown. Cells ofthe same color are then merged to give the final map in Fig. 1(d). Note that instead of the
3
bounding boxes of labels, we could use any 2D shapes, e.g., the outlines of real countries, inorder to obtain a desired look and proportion of area, as long as these shapes do not overlap.
When mapping vertices that contain cluster information, in addition to merging cells thatbelong to the same vertex, we also merge cells that belong to the same cluster, thus formingregions of complicated shapes, with multiple vertices and labels in each region. At this pointwe can add more geographic components to strengthen the map metaphor. For instance, inplaces where there is significant space between vertices in neighboring clusters, we can addlakes, rivers, or mountain ranges to the map to indicate the distance. These structures canall be formed by similar insertion of random points in places where vertices are far away fromeach other.
In terms of complexity, the algorithm is scalable and has a time complexity of O(|V | log |V |).We first add na artificial points along the bounding boxes of the labels, typically na = 40|V |.We then insert nr random points of distance r away from any vertices and artificial points,usually nr is set to between |V | to 40|V |, depending on the size of the graph. This step iscarried out by first forming a quadtree of the vertices and artificial points, which takes timeO(|V | log |V |), then testing whether a random point is within distance r of the set of ver-tices and artificial points. Each test takes O(log |V |) time, thus overall O(|V | log |V |). We firstcompute a Delaunay triangulation of the points, which can be done in time O(|V | log |V |) [9].Then we create the corresponding Voronoi diagram of all points and merge Voronoi cells thatbelongs to the same cluster. This step requires O(|V |) and thus the overall complexity ofGMap is O(|V | log |V |), with a relatively large coe"cient due to the large number of arti-ficial and random points. As a reference point, all maps in this paper were generated in afew seconds. Mapping a larger graph with |V | = 440, 000, nr = |V | and na = 40|V | took 4minutes2.
4 GMap Maps
In this section we examine several maps produced by our algorithm. The underlying datacomes from di!erent domains and the corresponding graphs are structurally di!erent and ofvarying sizes.
4.1 Collaboration Graph
This graph has authors as vertices and collaborations as edges. That is, there is an edgebetween two authors if they have collaborated on a paper. The graph has 509 vertices and1517 edges. The largest component has 275 vertices and 784 edges, and thus contains about54% of all authors. The data comes from the first 10 years of the Symposium on GraphDrawing, 1994-2004. We look at the first eight largest connected components. This graph iscumulative, in the sense that two authors are connected with an edge if they have writtenat least one joint paper in the first ten years of the symposium. Even when drawn with ahigh-quality scalable force-directed algorithm [13] and after applying a node-overlap removalstep, the resulting graph looks more like a hairball than anything else; see Fig. 2.
On the other hand, the corresponding map, as shown in Fig. 3, seems much more ”read-able”. The map shows one continent corresponding to the largest connected component andseven islands, corresponding to the seven largest remaining connected components. The con-tinent contains about a dozen “countries” determined by the collaboration patterns. The size2 Using a single thread on a Linux machine with 16 Intel Xeon processors, each with 4 cores running
at 2.4 GHz, with 16 GB memory per processor.
4
Tamassia
TollisBattista
Goodrich
Liotta Bridgeman
Fanto
Garg
VismaraBrandes
Wagner
Eades
Didimo
Gelfand
Vargiu
TassinariParise
Kosaraju
Shubina
Chan
Dogrusoz
Madden
Castello
Mili
Biedl
Kakoulis
Six
Xia
Papakostas
Brandenburg
Marks
MutzelJunger
Kobourov
Bachl
Edachery
Sen
SchreiberHimsolt
Forster
Raitner
Eppstein
Himsholt
Rohrer
PickBachmaier
NorthMarshall
Dobkin
GansnerKoutsofios
EllsonWoodhull
Whitesides
Bose
Demetrescu
Finocchi
PatrignaniPizzonia
Lenhart
LubiwBertolazzi
Buti
Carmignani
Matera Marcandalli
Lillo
Vernacotola
Barbagallo
Boyer
Cortese
Mariani
SymvonisWood
Alt
Godau
Houle
Wismath
ElGindy
Meijer
Dujmovic
Fellows
Hallett
Kitching
McCartin
Nishimura
Ragde
RosamondSuderman
Shermer
Ryall
Fekete
Lesh
AndalmanRuml
Shieber
Kruja
Blair
Waters
Leipert
Lee
Odenthal
Gutwenger
Buchheim
Ziegler
Klau
Klein Barth
Kupke
Weiskircher
Percan
Hundack
Pouchkarev
Thome
Brockenauer
Fialko
KrugerNaher
Alberts
AmbrasKoch
Cheng
Duncan
Gajer
Efrat
Wenk
Erten
Harding
WamplerYee
Pitta
Le
Navabi
Tanenbaum
Scheinerman
Wagner
DickersonMeng
Lynn
Thiele
JohansenMorin
Madden
Genc
Kikusts
Freivalds
Frick
Bertault
Feng
Fosmeier
Grigorescu
Powers
Chrobak Nakano
Nishizeki
TokuyamaWatanabe
Miura
Yoshikawa
Rahman
Uno
Dean
Hutchinson
RamosMcAllister
Snoeyink
Gomez
Toussaint
SablowskiBrus
Keskin
Vogelmann
Ludwig
Mehldau
Jourdan
Rival Zaguia
Hashemi
Kisielewicz
Alzohairi
Barouni
Jaoua
Chen
Lu
YenLiao
Chuang
Lin
Roxborough
Italiano
Giacomo
Felsner
Binucci
NonatoCruz
Rusu
Chanda
Lozada
Neto
Rosi
Stolfi
Miller
Kaufmann
Hes
Kant
SteckelbachBubeck
Ritt
Rosenstiel
Cornelsen
Kenis
Dwyer
Kopf
Herman
BaurBenkert
Gaertler Lerner
EiglspergerSchank
Kuchem
Miyazawa
Ghosh
Naznin
Egi
Asano
Shahrokhi
Sykora
Szekely
Vrto
Newton
Munoz
Unger
Djidjev
Pach
Toth
Tardos
Wenger
Agarwal
Aronov
Pollack
Sharir
Pinchasi
Eckersley
Hong
Quigley
Sugiyama
Lee
AbelsonTaylorMaeda
Lin LinCohen
Huang Feng
WebberRuskey
Garvan
Friedrich
Nascimento
Murray
Vince
Kanne
Trumbach
Skodinis
Eschbach Gunther
Drechsler Becker
Schonfeld
Molitor
Bretscher
AbellanasGarcia!Lopez
Hernandez!Penver
Noy
Hurtado
Marquez
CastroCobos
Dana
GarciaHernando
Tejel
Purchase
Allder
Carrington
James
ScottChow
Leonforte
Closson
Gartshore
Dyck
JoevenazzoNickle
Wilsdon
Iturriaga
Fernau
Wiese
CarpendaleCowperthwaite
Fracchia
Matuszewski
MelanconRuiter
Delest
Lambe
Twarog
Rucevskis
Cerny
Kral
Nyklova
Pangrac
Dvorak
Jelinek
Kara
Babilon
Vondrak
MateosGarrido
Aggarwal
Pop
Misue
SanderVasiliu
Diguglielmo
DurocherKaplan
Alt
Ferdinand
Wilhelm
Baudel
Haible
DillencourtHirschberg
Matousek
Maxova
Valtr
Fig. 2. Author collaboration graph for the GD conference, 1994-2004.
of each label is determined by the logarithm of the number of publications and the edgethickness is similarly proportional to the number of collaborations. However, node weightsand edge weights are not used in the layout calculations.
It is easy to see that European authors dominate the main continent. Several well-definedGerman groups can be seen on the west and southwest coasts. A largely Italian cluster occupiesthe center, with an adjacent Spanish peninsula in the east. The northwest contains a mostlyAustralasian cluster. Two North American clusters are to be found in the southeast and in thesouthwest, the latter one made up of three distinct components. A combinatorial geometrycluster forms the northernmost point of the main continent. Most Canadian researchers can befound in the central Italian cluster and the Spanish peninsula. Northeast of the mainland liesa large Japanese island and southeast of the mainland there is a large Czech island. Northwestof the mainland is a Crossings Number island.
4.2 TradeLand
Fig. 4 is a map visualizing the trade relations between all countries. Bilateral trade databetween each of the 209 countries and its top trading partners were acquired from Mathe-matica’s CountryData package. The font size of a label is proportional to the logarithm ofthe total trade volume of the country, and the color of a label reflects whether a country hasa trade surplus (black) or deficit (red).
The label color gives an easy way to spot the oil-rich countries with large surpluses, whichare distributed all over the world as well as in our map: Middle East (Saudi Arabia, Kuwait),Europe (Russia), South America (Venezuela), Africa (Nigeria, Equatorial Guinea). On the
5
Tamassia
TollisBattista
Goodrich
Liotta Bridgeman
Fanto
Garg
VismaraBrandes
Wagner
Eades
Didimo
Gelfand
Vargiu
TassinariParise
Kosaraju
Shubina
Chan
Dogrusoz
Madden
Castello
Mili
Biedl
Kakoulis
Six
Xia
Papakostas
Brandenburg
Marks
MutzelJunger
Kobourov
Bachl
Edachery
Sen
SchreiberHimsolt
Forster
Raitner
Eppstein
Himsholt
Rohrer
PickBachmaier
NorthMarshall
Dobkin
GansnerKoutsofios
EllsonWoodhull
Whitesides
Bose
Demetrescu
Finocchi
PatrignaniPizzonia
Lenhart
LubiwBertolazzi
Buti
Carmignani
MateraMarcandalli
Lillo
Vernacotola
Barbagallo
Boyer
Cortese
Mariani
SymvonisWood
AltGodau
Houle
Wismath
ElGindy
Meijer
Dujmovic
Fellows
Hallett
Kitching
McCartin
Nishimura
Ragde
RosamondSuderman
Shermer
Ryall
Fekete
Lesh
AndalmanRuml
ShieberKruja
Blair
Waters
Leipert
Lee
Odenthal
Gutwenger
Buchheim
Ziegler
Klau
Klein Barth
Kupke
Weiskircher
Percan
Hundack
Pouchkarev
Thome
Brockenauer
Fialko
KrugerNaher
Alberts
AmbrasKoch
Cheng
Duncan
Gajer
Efrat
Wenk
Erten
Harding
WamplerYee
Pitta
Le
Navabi
Tanenbaum
Scheinerman
Wagner
DickersonMeng
Lynn
Thiele
JohansenMorin
Madden
Genc
Kikusts
Freivalds
Frick
Bertault
Feng
Fosmeier
Grigorescu
Powers
Chrobak Nakano
Nishizeki
TokuyamaWatanabe
Miura
Yoshikawa
Rahman
Uno
Dean
Hutchinson
RamosMcAllister
Snoeyink
Gomez
Toussaint
SablowskiBrus
Keskin
Vogelmann
Ludwig
Mehldau
Jourdan
Rival Zaguia
Hashemi
Kisielewicz
Alzohairi
Barouni
Jaoua
Chen
Lu
YenLiao
Chuang
Lin
Roxborough
Italiano
Giacomo
Felsner
Binucci
NonatoCruz
Rusu
Chanda
Lozada
Neto
Rosi
Stolfi
Miller
Kaufmann
Hes
Kant
SteckelbachBubeck
Ritt
Rosenstiel
Cornelsen
Kenis
Dwyer
Kopf
Herman
BaurBenkert
Gaertler Lerner
EiglspergerSchank
Kuchem
Miyazawa
Ghosh
Naznin
Egi
Asano
Shahrokhi
Sykora
Szekely
Vrto
Newton
Munoz
Unger
Djidjev
Pach
Toth
Tardos
Wenger
Agarwal
Aronov
Pollack
Sharir
Pinchasi
Eckersley
Hong
Quigley
Sugiyama
Lee
AbelsonTaylorMaeda
Lin LinCohen
Huang Feng
WebberRuskey
Garvan
Friedrich
Nascimento
Murray
Vince
Kanne
Trumbach
Skodinis
Eschbach Gunther
Drechsler Becker
Schonfeld
Molitor
Bretscher
AbellanasGarcia!Lopez
Hernandez!Penver
Noy
Hurtado
Marquez
CastroCobos
Dana
GarciaHernando
Tejel
Purchase
Allder
Carrington
James
ScottChow
Leonforte
Closson
Gartshore
Dyck
JoevenazzoNickle
Wilsdon
Iturriaga
Fernau
Wiese
CarpendaleCowperthwaite
Fracchia
Matuszewski
Melancon Ruiter
Delest
Lambe
Twarog
Rucevskis
Cerny
Kral
Nyklova
Pangrac
Dvorak
Jelinek
Kara
Babilon
Vondrak
Mateos
Garrido
Aggarwal
Pop
Misue
SanderVasiliu
Diguglielmo
DurocherKaplanAlt
Ferdinand
Wilhelm
Baudel
Haible
DillencourtHirschberg
Matousek
Maxova
Valtr
Fig. 3. Author collaboration map for the GD conference, 1994-2004.
other hand, the countries with huge deficits are mostly in Africa (Sierra Leone, Senegal,Ethiopia) with the United States, the clear outlier.
Many countries in close geographic proximity end up close in our map, e.g, Central Amer-ican countries like Honduras, El Salvador, Nicaragua, Guatemala and Costa Rica are closeto each other in the northeast. Similarly the three Baltic republics, Latvia, Lithuania andEstonia, are close to each other in the northwest. This is easily explained by noting that geo-graphically close countries tend to trade with each other. There are easy to spot exceptions:North Korea is not near South Korea, Israel is not particularly close to Jordan or Syria.
The G8 countries (Canada, France, Germany, Italy, Japan, Russia, United Kingdom, andthe United States) are all in close proximity to each other in the center of the map. Two ofthe largest and closest countries in our map are China and the United States. Clearly, theproximity is due to the very large trade volume rather than geographic closeness. All thesecountries are in the largest cluster which is dominated by European countries in the west,Asian countries in the east, and Middle Eastern countries in the south. African countriesare distributed in several clusters in close proximity to China (a major trading partner tomany African countries), the United States (trading less with Africa these days), and aroundformer colonizers (e.g., Togo, Cameroon and Senegal, which are all close to France). SouthAmerican and Central American countries form several clusters in the north of the map. Onthe periphery of the map are small countries from around the world, and countries with fewtrading partners.
6
Fig. 4. A map of trade relations between countries.
4.3 BookLand Maps
Many e-commerce websites provide recommendations to allow for exploration of related items.Traditionally this is done in the form of a flat list. For example, Amazon typically lists around5-6 books under “Customers Who Bought This Item Also Bought”, with a clickable arrow toallow a customer to see further related items.
Instead of a flat list, which provides a very limited view of the neighborhood, there havebeen attempts to convey the underlining connectivity of the products through graph visu-alization. For example, TouchGraph, a New Jersey-based company, has an Amazon browser(http://www.touchgraph.com/TGAmazonBrowser.html) which essentially lays out a graphtaken from a small neighborhood surrounding the book of concern. None of the existingapproaches, however, gives a comprehensive view of the relationship and the clustering struc-tures.
Using our GMap algorithm, we obtained the map in Fig. 5. The underlying data is obtainedwith a breadth-first traversal following Amazon’s “Customers Who Bought This Item AlsoBought” links, starting from the George Orwell’s 1984. All books in the map are at most 9hops away from the source node. We further merge nodes that represent the same book, butwith di!erent publishers or di!erent bindings. This reduces the number of vertices by 1-4%.As can be seen by the 5 versions of Chinua Achebe’s Things Fall Apart in the central cluster,we are not always successful. The underlying graph for this map contains 913 vertices and3410 edges. With an average degree of nearly eight, peripheral vertices in this map have onlya handful of edges while central vertices have more than 20 immediate neighbors. We next
7
1984
Fahrenheit 451
Brave NewWorld
Catch!22
The Catcher inthe Rye Slaughterhouse!Five: A
Novel
Animal Farm
A ClockworkOrange
The GreatGatsby
Of Mice andMen
Lord of theFlies
Cat's Cradle:A Novel
Breakfast of Champions:A Novel
To Killa Mockingbird
One Flew Over theCuckoo's Nest:
The Adventures ofHuckleberry Finn
Their Eyes WereWatching God
The Grapes ofWrath
Death of aSalesman
The Sirens of Titan:A Novel
Mother Night:A Novel
Welcome to the MonkeyHouse: Stories
The ScarletLetter
The Crucible
Invisible ManThe ThingsThey Carried
East ofEden
The GlassMenagerie
A StreetcarNamed Desire
A Raisin inthe Sun
Player Piano
God Bless You
BelovedNative Son
Their Eyes Were WatchingGod CD
Fitzgerald's The GreatGatsby
Cannery Row:
Anna Karenina
Long Day's Journeyinto Night
Who's Afraid ofVirginia Woolf?
A Mercy
Song ofSolomon
Black Boy
Their Eyes Were WatchingGod Literature Guide
The GreatGatsby CD
Hawthorne's The ScarletLetter
Sweet Thursday
The Winter of OurDiscontent
The BrothersKaramazov
Crime andPunishment
Love in the Timeof Cholera
Waiting for Godot: ATragicomedy in Two Acts
The IcemanCometh
Glengarry Glen Ross:A Play
The White Tiger: ANovel
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The Hour I FirstBelieved: A Novel
Unaccustomed Earth:Stories
The Story of EdgarSawtelle: A Novel
Paradise
Golding's the Lord ofthe Flies
Zora Neale Hurston's Their Eyes WereWatching God: A Casebook
New Essays on Their EyesWere Watching God
Romeo andJuliet
Tortilla Flat
The WaywardBus
The LongValley
In DubiousBattle
Travels with Charley inSearch of America:
The Idiot
Notes fromUnderground
The Stranger
Heart ofDarkness
Demons
The Pillars of theEarth
Eat
One Hundred Years ofSolitude
Middlesex: ANovel
Atonement
No Exit and ThreeOther Plays
Things Fall Apart:A Novel
Hamlet
A Moon forthe Misbegotten
Sam Shepard : SevenPlays
American Buffalo
Glengarry GlenRoss
The Brief Wondrous Lifeof Oscar Wao
The Girl with theDragon Tattoo
Sea of Poppies:A Novel
The Guernsey Literary and PotatoPeel Pie Society
The Savage Detectives:A Novel
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Testimony: ANovel
Couldn't Keep It to Myself: Wally Lamband the Women of York Correctional Institution
I Know This Much IsTrue: A Novel
Interpreter ofMaladies
Olive Kitteridge:Fiction
The Art of Racingin the Rain
Dewey: The Small!Town Library CatWho Touched the World
Love: ANovel
JazzTar Baby
The InvisibleMan
In OurTime Quicksand and
Passing
Zora Neale Hurston: ALife in Letters
Night
In Search of History !SalemWitch Trials
The Odyssey
Of Mice& Men
Once There Was aWar
To a GodUnknown
War andPeace
The Myth of Sisyphus:And Other Essays
The Plague
Siddhartha
The Fall
Jane Eyre
Wuthering Heights
The Awakening
Madame Bovary
War AndPeace
The Adolescent
The Double andThe Gambler
World WithoutEnd
A DangerousFortune
Eye ofthe Needle
The Keyto Rebecca
Choose To Be Happy: AGuide to Total Happiness
Pilgrims
Stern Men
The LastAmerican Man
The Unbearable Lightness ofBeing: A Novel
Collected Stories
Memories of MyMelancholy Whores
Chronicle of aDeath Foretold
Water for Elephants:A Novel
The Virgin Suicides:A Novel
The Glass Castle:A Memoir
The Other BoleynGirl
On ChesilBeach
No Country for OldMen
Nausea
Being AndNothingness
Things FallApart
All Quiet on theWestern Front
Rosencrantz and GuildensternAre Dead
Othello
King Lear
Fool for Love andOther Plays
August: OsageCounty
The Clean House andOther Plays
Speed!the!Plow
Topdog!underdog
Drown
Out Stealing Horses:A Novel
The Girl Who Playedwith Fire
The Brass Verdict:A Novel
A Fraction ofthe Whole
The SecretScripture
The NorthernClemency
Loving Frank:A Novel
The Help
Then We Came tothe End: A Novel
Tree of Smoke:A Novel
Lush Life:A Novel
Handle with Care:A Novel
The Associate
I'll Fly Away: Further Testimonies fromthe Women of York Prison
She's ComeUndone
Sickened: The True Storyof a Lost Childhood
Drowning Ruth: ANovel
Black andBlue
The Namesake:A Novel
The God of SmallThings: A Novel
A FineBalance
The Elegance ofthe Hedgehog
Merle's Door: Lessons froma Freethinking Dog
Amazing Gracie: ADog's Tale
Wesley the Owl: The Remarkable Love Storyof an Owl and His Girl
Alex & Me: How a Scientist and a Parrot Uncovered a HiddenWorld of Animal Intelligence!!and Formed a Deep Bond in the Process
Letter toMy Daughter
The BluestEye
Cultural Contexts for Ralph Ellison's InvisibleMan: A Bedford Documentary Companion
Spark NotesInvisible Man
A FarewellTo Arms
The SunAlso Rises
CanePlum Bun: A NovelWithout a Moral
Wrapped in Rainbows: The Life ofZora Neale Hurston
Every Tongue Got to Confess: NegroFolk!tales from the Gulf States
The CompleteStories
Zora Neale Hurston : Folklore
Dust Tracks on aRoad: An Autobiography
The Odyssey: TheFitzgerald Translation
Julius Caesar
Romeo &Juliet
A Midsummer Night'sDream
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The MoonIs Down
The Pastures ofHeaven
The Rest Is Noise: Listeningto the Twentieth Century
The Rebel: An Essayon Man in Revolt
The Alchemist
Steppenwolf: ANovel
Narcissus andGoldmund
Pride andPrejudice
Wide Sargasso Sea:A Novel
Emma
Great Expectations
Favorite Jane Austen Novels: Pride and Prejudice
The Host:A Novel
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Stone Cold
People of the Book:A Novel
Playing forPizza
A PlaceCalled Freedom
Night OverWater
The Man FromSt. Petersburg
On My Own: The Art ofBeing a Woman Alone
A New Earth: Awakening toYour Life's Purpose
Happy for No Reason: 7 Steps toBeing Happy from the Inside Out
The Self!esteem Companion: Simple Exercises to Help You ChallengeYour Inner Critic & Celebrate Your Personal Strengths
Three Cups of Tea: One Man's Mission to Promote Peace. . . One School at a Time
A Writer's Workbook: Daily Exercisesfor the Writing Life
Stern Men:A Novel
Still Life with Chickens: Starting Overin a House by the Sea
Into theWild
The Book of Laughterand Forgetting
A HeartbreakingWork ofStaggering Genius
The Unbearable Lightness ofBeing
Of Love and OtherDemons
The Autumn of thePatriarch
Snow Flower and theSecret Fan: A Novel
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The MemoryKeeper's Daughter
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Prozac Nation
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The Queen's Fool: ANovel
The Virgin'sLover
The Six Wives ofHenry VIII
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The Gathering
DivisaderoBridge of Sighs: A
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Blood Meridian: Or the EveningRedness in the West
All thePretty Horses The Border Trilogy: All the Pretty Horses
Oil"
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Being andTime
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One Day in the Lifeof Ivan Denisovich
Rosencrantz & GuildensternAre Dead
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The Tempest
The Merchant ofVenice
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Angels in America: A Gay Fantasia on National Themes:Part One: Millennium Approaches Part Two: Perestroika
Doubt
The Seafarer
Rock 'n' Roll: ANew Play
Dead Man'sCell Phone Rabbit Hole
Sarah Kane:Complete Plays
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Sexual Perversity in Chicago and theDuck Variations: Two Plays
How I Learnedto Drive
Anna InThe Tropics
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The LostSymbol
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Heat Lightning
Extreme Measures: AThriller
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Man Gone Down:A Novel
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Rescuing Sprite: A Dog Lover's Storyof Joy and Anguish
Ralph Ellison's Invisible Man:A Casebook
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New Essays on InvisibleMan A Historical Guide to
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Nineteen Eighty!Four
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For Whom theBell Tolls
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Home ToHarlem
The Blacker theBerry
I Love Myself When I Am Laughing... AndThen Again: A Zora Neale Hurston Reader
Zora Neale Hurston: ALiterary Biography
Mules andMen
Zora Neale Hurston : Novels and Stories : Jonah's Gourd Vine ! Their Eyes Were WatchingGod !Moses
Tell My Horse: Voodoo and Lifein Haiti and Jamaica
The Iliad
The Aeneid
Mythology
The Three ThebanPlaysThe Iliad
of Homer
Twelfth Night
Olivier Messiaen: Quartet forthe End of Time
The Nine: Inside the Secret Worldof the Supreme Court
This Is Your Brain on Music:The Science of a Human Obsession
Resistance
Warrior of the Light:A Manual
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By the River Piedra I Sat Down andWept: A Novel of Forgiveness
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Beneath theWheel
Pride &Prejudice
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A Passageto India
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Twilight: The Complete IllustratedMovie Companion
Betrayed
Run: ANovel
The Maytrees:A Novel
Heidegger's Being And Time:A Reader's Guide
Phenomenology ofPerception
Introduction toMetaphysics
Phenomenology ofSpirit Basic Writings
The EthicsOf Ambiguity
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Achebe's Things Fall Apart:A Reader's Guide
Spark Notes ThingsFall Apart
Chinua Achebe's Things FallApart: A Casebook
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Cancer Ward
The Masterand Margarita
Beowulf: A New VerseTranslation
Beowulf
Manchild in thePromised Land
Bodega Dreams:A Novel
Dreaming inCuban
How the Garcia GirlsLost Their Accents
The Boy In theStriped Pajamas
I Amthe Messenger
A ThousandSplendid Suns
The Satanic Verses:A Novel
The Moor'sLast Sigh
Liberty and Tyranny: AConservative Manifesto
My Grandfather's Son:A Memoir
Men in Black: How the SupremeCourt Is Destroying America
An Inconvenient Book: Real Solutions tothe World's Biggest Problems The Christmas
Sweater
The Collected Essays ofRalph Ellison
The Cambridge Companion toRalph Ellison
Juneteenth: ANovel
Flying Home: andOther Stories
Ralph Ellison: Emergenceof Genius
Steinbeck's the Grapes ofWrath
Spark Notes TheGreat Gatsby
Brave NewWorld andBrave New World Revisited
Frankenstein
The Complete Short Stories of ErnestHemingway: The Finca Vigia Edition
To Have andHave Not
The Oresteia: Agamemnon; The LibationBearers; The Eumenides
The Histories
The DivineComedy
Mythology: Timeless Tales ofGods and Heroes
How to Read Literature Like a Professor: A Livelyand Entertaining Guide to Reading Between the Lines
Plato: Republic
The Trial and Deathof Socrates
The Inferno
Livy: The Early History ofRome
The Odysseyof Homer
Aeschylus I: Oresteia: AgamemnonSophocles I: Oedipus The King
The History of the PeloponnesianWar: Revised Edition
The Winter'sTale
Twelfth Night: or
Henry IV
Legacy of Ashes: TheHistory of the CIA
The Age of Turbulence: Adventuresin a NewWorld
The Coldest Winter: Americaand the Korean War
The Brethren: Inside theSupreme Court
American Creation: Triumphs and Tragedies inthe Founding of the Republic
The World in Six Songs: Howthe Musical Brain Created Human Nature
Music
Music andthe Mind
The Singing Neanderthals: The Origins ofMusic
The FirstMan
The FifthMountain
The Valkyries
Brida: ANovel
Eleven Minutes: ANovel
The Zahir: A Novelof Obsession
The Servant!Leader Within: ATransformative Path
Focus on Leadership: Servant!Leadershipfor the 21st Century
Moral Intelligence: Enhancing Business Performanceand Leadership Success
The Congruent Life: Following the Inward Pathto FulfillingWork and Inspired Leadership
Gertrude: ANovel
To theLighthouse
A Room ofOne's Own
A Portrait of the Artist asa Young Man
On Beauty
The Remains ofthe Day
A Tale of TwoCities
David Copperfield
Bleak House
Twilight: Director's Notebook: The Story of HowWe Made theMovie Based on the Novel by Stephenie Meyer
Twilight: TheScore
The TwilightSaga Collection
Chosen
Untamed
Hunted
Vampire Academy
Fyodor Dostoevsky's Crime andPunishment
The Marx!EngelsReader:
No Longerat EaseChinua Achebe's Things Fall
Apart
Understanding Things Fall Apart:Selected Essays and Criticisms
Warning tothe West
The Gulag Archipelago 1918!1956 Abridged: AnExperiment in Literary Investigation
The Gulag Archipelago: 1918!1956
Gulag: AHistory
In the First Circle:A Novel
Heart ofa Dog
We
The Collected Tales ofNikolai Gogol
The CanterburyTales
Sir Gawain and the GreenKnight
Sir Gawain and theGreen Knight
The Enchantress of Florence:A Novel
Shalimar the Clown:A Novel
Shame: ANovel
Infidel
The Ground Beneath HerFeet: A Novel
The 5000 Year Leap: A MiracleThat Changed the World
Atlas Shrugged
The Real GeorgeWashington
Common Sense
Power tothe People
If Democrats Had AnyBrains
Surrender Is Not an Option: DefendingAmerica at the United Nations
The Forgotten Man: A New Historyof the Great Depression
Guilty: Liberal Victims andTheir Assault on America
Liberal Fascism: The Secret History of the AmericanLeft
Grace: ANovel
Do the Right Thing: Inside the Movement That'sBringing Common Sense Back to America
Trading Twelves: The Selected Letters ofRalph Ellison and Albert Murray
Living with Music: RalphEllison's Jazz Writings
Shadow andAct
Going tothe Territory
Spark Notes The Adventuresof Huckleberry Finn
Spark Notes TheScarlet Letter
Animal Farmand 1984
Island
The Short Stories of F. ScottFitzgerald: A New Collection
Islands in the Stream: A Novel
The Annals of ImperialRome
Metamorphoses
The Epic of Gilgamesh: An EnglishVerison with an Introduction
Theogony
Medea and OtherPlays
Plutarch's Lives Volume1
Plutarch's Lives
Paradise Lost and ParadiseRegained
The Prince
The Dore Illustrations forDante's Divine Comedy
A Modern Reader's Guide toDante's the Divine Comedy
Heroes
The Dictionary ofClassical Mythology
The Complete World ofGreek Mythology
D'Aulaires' Book ofGreek Myths
How to Read Novels Like a Professor: AJaunty Exploration of the World's Favorite Literary Form
Voice Lessons: Classroom Activities to TeachDiction
Reading Like a Writer: A Guide for People Who LoveBooks and for Those Who Want to Write Them
Politics
The CommunistManifesto
Nicomachean Ethics
The Wealth ofNations
Leviathan
The Daodejingof Laozi
Meditations on First Philosophy: In Which the Existence of God andthe Distinction of the Soul from the Body Are Demonstrated
Introductory Lectureson Psychoanalysis
The Epic ofGilgamesh
Paradise Purgatorio
St. AugustineConfessions
Paradiso
The War with Hannibal: The History of Romefrom Its Foundation
The TwelveCaesars
The Rise of theRoman Empire
The Fall of the RomanRepublic: Six Lives
Rome and the Mediterranean: Books XXXI!XLV of theHistory of Rome from its Foundation
Euripides I: Alcestis
Euripides V: Electra
Aeschylus II: The Suppliant Maidens and The Persians
Greek Tragedies
Sophocles II: Ajax
The Last Days ofSocrates
All's Well That EndsWell
Hamlet
A Midsummer Night'sDream
Spark Notes No FearShakespeare Othello
King LearKing Henry IV
Ulysses
The SecondSex
The FeminineMystique
Moments ofBeing
Dubliners
Finnegans Wake
Never LetMe Go
Howards End
The History of Love:A Novel
Saturday
The EnglishPatient
Bronte's WutheringHeights
CliffsNotes JaneEyre
Little Dorrit
Our MutualFriend
Middlemarch
The PickwickPapers
Dombey andSon
Frostbite
Shadow Kiss
A Hero of OurTime
Spark Notes Crimeand Punishment
Writing Fiction: A Guideto Narrative Craft
The Art of Fiction: Notes onCraft for Young Writers
Bird by Bird: Some Instructionson Writing and Life
Half of aYellow Sun
Howl and OtherPoems
On theRoad
The Electric Kool!AidAcid Test
Leaves of Grass: TheOriginal 1855 Edition
Junky: The Definitive Textof Junk
Female Chauvinist Pigs: Women and theRise of Raunch Culture
The Beauty Myth: How Images ofBeauty Are Used Against Women
Feminism Is for Everybody:Passionate Politics
Getting Off: Pornography andthe End of Masculinity
Pornified: How Pornography Is Damaging OurLives
The Division of Laborin Society
From Max Weber: Essaysin Sociology
Basic PoliticalWritings
Second Treatiseof Government
Discipline & Punish: TheBirth of the Prison
Arrow ofGod
A Man ofthe People
Anthills ofthe Savannah
Girls atWar
The GoodEarth
The Solzhenitsyn Reader: Newand Essential Writings
We Never Make Mistakes:Two Short Novels
The Gulag Archipelago
The Gulag Archipelago1918!1956 I!II
Man Is Wolf toMan: Surviving the Gulag
Stalin: The Court ofthe Red Tsar
Khrushchev: The Man andHis Era
August 1914
White Guard
The TwelveChairs
Journey into theWhirlwind
Stories ofAnton Chekhov
Dead Souls:A Novel
Paradise Lost
The Song ofRoland
Beowulf: ANew Telling
Le Morte D'Arthur: TheWinchester Manuscript
Haroun and the Seaof Stories
The Caged Virgin: An Emancipation Proclamationfor Women and Islam
While Europe Slept: How Radical Islamis Destroying the West fromWithin
The Fountainhead
The Real BenjaminFranklinThe Real Thomas
Jefferson
The FederalistPapers
The Constitution of the United States of America
Fleeced: How Barack Obama
Godless: The Churchof Liberalism
A Slobbering Love Affair:The True
A Bold Fresh Pieceof Humanity
Economic Factsand Fallacies
Lenin
The Doors of Perception andHeaven and Hell
The PerennialPhilosophy
Dr. Jekyll & Mr.Hyde
The Essential Homer: Selections from theIliad and the Odyssey
The BhagavadGita
Homeric Hymns
Bacchae and Other Plays: Iphigenia among the Taurians;Bacchae; Iphigenia at Aulis; Rhesus
Lysistrata and OtherPlays
Copenhagen
Narrative of the Lifeof Frederick Douglass
The Landmark Herodotus:The Histories
Gilgamesh: A New Renderingin English Verse
Plutarch: Lives of NobleGrecians and Romans
The Conquest ofGaul
The Divine Comedy: Inferno;Purgatorio; Paradiso
The ArtOf War
The Artof War
The DoreBible Illustrations Dante's Divine Comedy: Hell
Divine Comedy:Inferno
The Cambridge Companion toDante
Greek Gods andHeroes
The LastOlympian
The Library of GreekMythology
Bulfinch's Greek and Roman Mythology: TheAge of Fable
Iliad and Odysseyboxed set
D'Aulaires' Book ofNorse Myths
Classic Myths to Read Aloud: The Great Stories of Greek and RomanMythology
Black Ships Before Troy: TheStory of 'The Iliad'
The Gods and Goddessesof Olympus
Greek Myths for YoungChildren
Discovering Voice: Voice Lessons forMiddle and High School
How FictionWorks
5 Steps to a 5 on the AP:Writing the AP English Essay
Grammar for High School: ASentence!Composing Approach!!!A Student Worktext
Sentence Composing for High School: AWorktext on Sentence Variety and Maturity
On Writing
The Republic Of Plato:Second Edition
The SocialContract
Civilization andIts Discontents
Grounding for the Metaphysics of Morals: With on aSupposed Right to Lie Because of Philanthropic Concerns
Kant: Groundwork of theMetaphysics of Morals
Five Dialogues
Capitalism and Freedom: FortiethAnniversary Edition
The General Theory ofEmployment
Free to Choose: APersonal Statement
Theban Plays
The Bhagavad!Gita : Krishna's Counsel inTime of War
An Enquiry ConcerningHuman Understanding
Dialogues Concerning Natural Religion: The Posthumous Essays ofthe Immortality of the Soul and of Suicide
New Introductory Lectures onPsycho!Analysis:
Myths from Mesopotamia: Creation
Purgatory
Inferno
The Consolation of Philosophy:Revised Edition
Pseudo Dionysius: The CompleteWorks
Don Quixote
The Decameron
Montaigne: Essays
City ofGod
The Aeneid ofVirgil
Rome and Italy: Books VI!X of the Historyof Rome from its Foundation
Makers of Rome: NineLives
The Jugurthine War ! TheConspiracy of Catiline
The CivilWars
Euripides III: HecubaEuripides II: The Cyclops and Heracles
Euripides IV: Rhesus
Greek Tragedies
As You LikeIt
Cymbeline
The Merry Wives ofWindsor
The Taming of theShrew
The Taming of theShrew
Macbeth
Twelfth Night
The TempestKing RichardII
King HenryV
Henry V
Between theActs
The Years
Jacob's Room
Ulysses Annotated: Notes for James Joyce'sUlysses "Revised and Expanded Edition#
The New Bloomsday Book:A Guide Through Ulysses
Gender Trouble: Feminism and theSubversion of Identity
Black Skin The History of Sexuality
Backlash: The UndeclaredWarAgainst American Women
Full Frontal Feminism: A Young Woman'sGuide to Why FeminismMatters
A Reader's Guide toFinnegans Wake
Amsterdam: ANovel
Enduring Love:A Novel
The Innocent:A Novel
In the Skin ofa Lion
Catharine: and OtherWritings
A Tale of TwoCities: 150th Anniversary
Wuthering Heights
Wuthering Heights
The Old CuriosityShop
Martin ChuzzlewitBarnaby Rudge
The Mill on theFloss
Daniel Deronda The Woman inWhite
Vanity Fair
Eugene Onegin: A Novelin Verse
Oblomov
The Hours
Orlando
The Battle of theLabyrinth
The DemigodFiles
Percy Jackson and the OlympiansPaperback Boxed Set
The Titan'sCurse
The Elements of Style
On Becominga Novelist
Aspects ofthe Novel
Writing Down the Bones:Freeing the Writer Within
Traveling Mercies: Some Thoughtson Faith
Grace
On Writing Well
Fear and Loathing in Las Vegas: A SavageJourney to the Heart of the American DreamNaked Lunch: The
Restored Text
Hell's Angels: A Strangeand Terrible Saga
Self!Reliance and OtherEssays Walden; Or
Civil Disobedience and OtherEssays
101 Great AmericanPoems
The Essential Writings ofRalph Waldo Emerson
Queer: ANovel
The Body Project: An IntimateHistory of American Girls
Can't Buy My Love: How Advertising Changesthe Way We Think and Feel
The End of America: Letter ofWarning to a Young Patriot
Discourse on Method and Meditations onFirst Philosophy
Leviathan: With Selected Variants from theLatin Edition of 1668
On Liberty
Madness and Civilization: A History ofInsanity in the Age of Reason
Power!Knowledge: Selected Interviews andOther Writings
Imagined Communities: Reflections on the Originand Spread of Nationalism
The Order of Things: An Archaeologyof the Human Sciences
Orientalism
The Ego and theId
The Future ofan Illusion
Beyond the PleasurePrinciple
On the Genealogy ofMorals and Ecce Homo
Home andExile
God's Bits ofWood
A Tree Grows inBrooklyn
The Soul and Barbed Wire:An Introduction to Solzhenitsyn
Solzhenitsyn: A Soulin Exile
The Gulag Archipelago 1918!1956
Kolyma Tales
The Harvest of Sorrow: SovietCollectivization and the Terror!Famine Execution by Hunger: The
Hidden Holocaust
Potemkin: Catherine the Great'sImperial Partner
The Whisperers: Private Lifein Stalin's Russia
Stalin and His Hangmen: The Tyrantand Those Who Killed for Him
Sashenka: ANovel
Khrushchev's Cold War: The Inside Storyof an American Adversary
American Prometheus: The Triumph and Tragedyof J. Robert Oppenheimer
Truman
One Hell of a Gamble: Khrushchev
The FatalEggs
Red Cavalry
A Dead Man's Memoir:A Theatrical Novel
Ilf and Petrov's American Road Trip: The1935 Travelogue of Two Soviet Writers
The Life and Extraordinary Adventures ofPrivate Ivan Chonkin
Twelve ChairsEnvy
Within theWhirlwind
Survival InAuschwitz
The Soviet Experiment: Russia
Utopia
The History of theKings of BritainEcclesiastical History of the
English People
Rule of Saint Benedictin English
Saint George andthe DragonShakespeare Stories
One Thousand and OneArabian Nights
The Adventures of RobinHood
The Once andFuture King
Idylls of theKing
The Virtue ofSelfishness
We theLiving
AnthemCapitalism: TheUnknown Ideal
The Anti!Federalist Papers and theConstitutional Convention Debates
The Obama Nation: Leftist Politics andthe Cult of Personality
Real Change: From the World ThatFails to the World That Works
The Case Against Barack Obama: The Unlikely Riseand Unexamined Agenda of the Media's Favorite Candidate
Culture Warrior
Basic Economics 3rd Ed: A CommonSense Guide to the Economy
Climate Confusion: How Global Warming Hysteria Leads to Bad Science
Ever Wonder Why? AndOther Controversial Essays
American Progressivism:A Reader
The Psychedelic Experience: A Manual Based on theTibetan Book of the Dead
DMT: The Spirit Molecule: A Doctor's Revolutionary Researchinto the Biology of Near!Death and Mystical Experiences
Your BrainIs God
Huxley andGod: Essays
Moksha: Aldous Huxley's Classic Writings onPsychedelics and the Visionary Experience
The InvisibleMan
The Picture of DorianGray ! Oscar Wilde
The Annals: The Reigns of Tiberius
The CivilWar
The Penguin Historical Atlasof Ancient Rome
The EssentialAeneid
Oresteia
Ten Playsby Euripides
The DhammapadaThe Koran
The Analects Tao TeChing
The Yoga Sutras of Patanjali: Commentary on theRaja Yoga Sutras by Sri Swami Satchidananda
Anthology Of Classical Myth: Primary Sources in Translation : with Additional Translations by OtherScholars and an Appendix on\
Linear B sources by Thomas G. Palaima
Classical Mythology
Hesiod's Theogony
Greek Tragedies
Electra and OtherPlays
Eichmann in Jerusalem: A Report onthe Banality of Evil
The Making of theAtomic Bomb
Michael Frayn's Copenhagen in Debate: Historical Essays and Documents onthe 1941 Meeting Between Niels Bohr and Werner Heisenberg
Arcadia: APlay
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The Autobiography of BenjaminFranklin
Incidents in the Life ofa Slave Girl
The LandmarkThucydides
Travels withHerodotus
A History of Histories: Epics
The Landmark Thucydides: A Comprehensive Guideto the PeloponnesianWar
Gulliver's Travels
Selected Works
The Campaigns ofAlexander
The 48 Lawsof Power
Sun Tzu: The Art of Warfor Managers; 50 Strategic Rules
The Book ofFive Rings
The Artof Seduction
Dore's Illustrations for ParadiseLost
Dore's Illustrations of theCrusades
Dore's Angels
The Dore Gallery: His120 Greatest Illustrations
Dore's Dragons
Milton's ParadiseLost
The Aeneid
The Divine Comedy:Purgatorio
Vita Nuova
The Greek Myths:Complete Edition
This Countryof Ours
Poor Richard
D'Aulaires' Book ofTrolls
The Children of Odin: TheBook of Northern Myths
D'Aulaires' Book ofAnimals Leif the
Lucky
Classics to Read Aloud to Your Children: Selections from Shakespeare
Aesop's Fables: A ClassicIllustrated Edition
Archimedes and the Doorof Science
The Children's Homer: The Adventures ofOdysseus and the Tale of Troy
The GoldenGoblet
In Search of a Homeland: TheStory of the Aeneid
The Odyssey
DK Readers: TrojanHorse
Aesop's Fables
Stories from Around theWorld
Grammar for Middle School: ASentence!Composing Approach!!A Student Worktext
Sentence Composing for Middle School: AWorktext on Sentence Variety and Maturity
Mechanically Inclined: Building Grammar
Nothing to BeFrightened Of
Home: ANovel
5 Steps to a 5: APEnglish Literature
CliffsAP English Language andComposition
AP English Literature &Composition
Sentence Composing for College: A Worktexton Sentence Variety and Maturity
Plot &Structure:
The Elements ofStyle
The First Five Pages: A Writer's Guide toStaying Out of the Rejection Pile
Four Texts on Socrates: Plato's Euthyphro
On War
The Elements ofMoral Philosophy
Aristotle: NicomacheanEthics
Utilitarianism
The Road to Serfdom: Text andDocuments!!The Definitive Edition
Why Government Is theProblem
Capitalism
The Return of Depression Economics andthe Crisis of 2008
Economics in One Lesson: The Shortest andSurest Way to Understand Basic Economics
Four Plays: Medea
An Introduction toHinduism
What the Buddha Taught: Revised and Expanded Editionwith Texts from Suttas and Dhammapada
The World's Religions: OurGreat Wisdom Traditions
Descartes: Meditations on First Philosophy: With Selectionsfrom the Objections and Replies
Prolegomena to Any Future Metaphysics That Will Be Able to Come Forward As ScienceWith Kant's Letter to Marcus Herz
Memories
The Interpretationof Dreams
Faces in a Cloud:Intersubjectivity in Personality Theory
Fantasies ofFlight
Sumerian Mythology: A Study of Spiritual and LiteraryAchievement in the Third Millennium B.C.Gods
Ancient Iraq: ThirdEdition
Stories fromAncient Canaan
Ironies of Faith: The Laughter atthe Heart of Christian Literature
Anselm of Canterbury: TheMajor Works
Gregory of Nyssa: TheLife of Moses
Origen: An Exortation to Martyrdom
Maximus Confessor: SelectedWritings
Bernard of Clairvaux: SelectedWorks
Augustine of Hippo: ABiography
Confessions
The Roman History: TheReign of Augustus
Four Plays by Aristophanes: The Birds;The Clouds; The Frogs; Lysistrata
The HomericHymns
Americana
VictorianaTransylvania
Thespia Coelholand
Cliffsnotistan
Oprahland
Selfhelpistania
KFCRussiana
Graecoromania
Mythium
Shakespearea
Fringistan
Feministan
Fig. 5. A map of books related to “1984”
examine several of the “countries” in the map in more detail. More countries are examinedin the Appendix, where we also show several close-ups from the map.
Americana: Somewhat surprisingly, George Orwell’s 1984 along with Animal Farm endedup in the west corner of a region populated mostly by American writers. Britain is alsorepresented by William Golding’s The Lord of the Flies and Aldous Huxley’s Brave NewWorld along with Anthony Burgess’s Clockwork Orange, which connect the British corner ofthe region to the main part dominated by 20th century American classics. Ray Bradbury’sFahrenheit 451 and Salinger’s Catcher in the Rye provide a transition to a variety of well-known novels: Steinbeck’s Grapes of Wrath and Of Mice and Men, Ernest Hemingway’s ForWhom the Bell Tolls and The Old Man and the Sea, F. Scot Fitzgerald’s Great Gatsby,Harper Lee’s To Kill a Mockingbird and Ralph Ellison’s Invisible Man, Joseph Heller’s Catch22, Kurt Vonnegut’s Slaughterhouse Five, Ken Kesey’s One Flew Over a Cuckoo’s Nest. Some19th century novels can also be found here: Nathaniel Hawthorne’s Scarlet Letter and MarkTwain’s Adventures of Huckleberry Finn.
Victoriana: To the southwest of Americana is a region dominated by Dickens, Austenand Bronte novels. Starting with A Tale of Two Cities, Great Expectations and Oliver Twistin the north and going through Jane Eyre, Pride and Prejudice, Sense and Sensibility andWuthering Heights in the middle, the region ends with more Dickens’ books in the southwest(The Pickwick Papers) and George Elliot novels in the southeast (Middlemarch).
Russiana: To the north of Americana lies one of the largest countries in BookLand, dom-inated by Russian literature and history. The core contains classic novels by Dostoyevsky(Crime and Punishment, The Brothers Karamazov), Tolstoy (War and Peace, Anna Karen-ina), and Solzhenitsyn (The Gulag Archipelago, Cancer Ward). In the northern part of theregion is a collection of books about Russia and Russian history: Stalin: The Court of theRed Tsar, Khrushchev: The Man and His Era and Potemkin: Catherine the Great’s Imperial
8
Partner. In the west there is a cluster of Albert Camus books (The Stranger, The Plague,The Fall), all well connected with the Russian classics.
Graecoromania: Another large region to the west of Americana contains a diverse collec-tion of Graeco-Roman books. History books by Thucydides, Plutarch, Livy, Suetonius, Salustshare the region with philosophy by St. Augustine, Plato, Socrates, and Aristotle. Greektheater is represented by Aristophanes, Aeschylus, Euripides, Sophocles and epic poetry byHomer and Virgil.
Mythium: Close to Graecoromania, on the southwest coast, lies the the legendary landof Mythium. Aesop’s Fables, Greek Myths for Young Children and The Gods and Goddessesof Olympus are next door to D’Aulaires’ Book of Trolls, D’Aulaires’ Book of Animals andD’Aulaires’ Book of Norse Myths.
Shakespearea: Very centrally located, neighboring Victoriana, Americana, Russiana,Graecoromania, and Mythium lies the land of Shakespeare. It is not surprising that nearlyall tragedies, comedies and histories are present but it is interesting to observe what non-Shakespeare books are in this region: Chaucer’s Canterbury Tales, Tennyson’s Idyls of theKing, Dante’s Divine Comedy, One Thousand and One Arabian Nights, Beowulf and TheAdventures of Robin Hood.
5 The Map Coloring Algorithm
In this section we consider the problem of assigning good colors to the countries in our maps.The Four Color Theorem states that only four colors are needed to color any map so that noneighboring countries share the same color. It is implicitly assumed that each country formsa contiguous region. However, this result is of limited use to us because countries in our mapsare often not contiguous. For instance, a group of North American researchers are placed ina cluster made from three disjoint regions in light orange color in the southwest corner of themain continent; see Fig. 3. In cases where one cluster is represented by several disjoint regionswe must use the same color for all regions to avoid ambiguity. Thus, four colors (or even fiveor six) are not enough.
In GMap we start with a coloring scheme from ColorBrewer [5], which typically has 5 easyto di!erentiate base colors, and generate as many as the number of countries by blending thebase colors. As a result our color space is linear and discrete. Because of the blending, anytwo consecutive colors in the linear array of colors are similar to each other. When applyingthese colors to the map, we want to avoid coloring neighboring countries with such pairs ofcolors. With this in mind, we define the country graph, Gc = {Vc, Ec}, to be the undirectedgraph where countries are vertices, and two countries are connected by an edge if they sharea non-trivial boundary. We then consider the problem of assigning colors to nodes of Gc sothat the color distance between nodes that share an edge is maximized.
More formally, let C be the color space, i.e., a set of colors; let c : Vc ! C be a function thatassigns a color to every vertex; and let wij " 0 be weights associated with edges {i, j} # Ec.Let d : C $ C ! R be a color distance function. Define the vector of color distances alongedges to be
v(c) = {wi,j d(c(i), c(j)) | {i, j} # Ec}.
Then we are looking for a color function that maximizes this vector with respect to some costfunction. Two natural cost functions are:
maxc!C
{!
{i,j}!Ec
wi,j d(c(i), c(j))2} (2-norm), or maxc!C
{ min{i,j}!Ec
wi,j d(c(i), c(j))} (MaxMin)
9
Dillencourt et al. [8] investigated the case where all colors in the color spectrum areavailable. They proposed a force directed model aimed at selecting |Vc| colors as far apartas possible in the color space. However in our map coloring problem, for aesthetic reasons,we are limited to “map-like” colors, and our color space is discrete. Therefore we model ourcoloring problem as one of vertex labeling, where our color space is C = {1, 2, . . . , |Vc|}, andthe color function we are looking for is a permutation that maximizes the labeling di!erencesalong the edges. The cost functions we consider are
max!
{i,j}!Ec
wi,j(ci % cj)2, c is a permutation of {1, 2, . . . , |Vc|} (2-norm) (1)
and
max min{i,j}!Ec
wi,j |ci % cj |, c is a permutation of {1, 2, . . . , |Vc|} (MaxMin)
where ci is the i-th element of the vector c.The complementary problem of finding a permutation that minimizes the labeling di!er-
ences along the edges is well-studied. For example, in the context of minimum bandwidth orwavefront reduction ordering for sparse matrices, it is known that the problem is NP-hard,and a number of heuristics [14,18],were proposed. One such heuristic is to order vertices usingthe Fiedler vector. Motivated by this approach, we approximate (1) by
max!
{i,j}!Ec
wi,j(ci % cj)2, subject to!
k!Vc
ck = 1 (2)
where c # R|Vc|. This continuous problem is solved when c is the eigenvector corresponding tothe largest eigenvalue of the weighted Laplacian of the country graph, while the Fiedler vector(the eigenvector corresponding to the second smallest eigenvalue) minimizes the objectivefunction above. Once (2) is solved, we use the ordering of the eigenvector as an approximatesolution for (1). We call this algorithm SPECTRAL.
Fig. 6. Coloring schemes RANDOM, SPECTRAL, and SPECTRAL+GREEDY. Each node is colored bythe color index shown as the node label. Edge labels are the absolute di!erence of the endpoint labels.
Fig. 6 illustrates three coloring schemes on a 4-4 unweighted grid graph given 16 colors inthe Blue-Yellow spectrum. A random assignment of colors, RANDOM, does reasonably well,but has one edge with a color di!erence of 2. SPECTRAL performs better, with the minimumcolor di!erence of 4. However there are still 2 edges with a color di!erence of only 4. It is easyto see that SPECTRAL can be improved (e.g., swapping colors 6 and 2 would improve themeasurements according to both cost functions). With this in mind we developed GREEDY, agreedy refinement algorithm based on repeatedly swapping pairs of vertices, provided that the
10
swap improves the coloring scheme according to one of the two cost functions. Starting froma coloring scheme obtained by SPECTRAL and applying GREEDY often leads to significantimprovements.
The GREEDY algorithm has a high computational complexity as we consider all possibleO(|Vc|2) pairs of vertices for potential swapping. Since recomputing the cost functions can bedone in time proportional to the sum of degrees of the pair on nodes considered for swapping,the overall complexity of GREEDY is O(|Vc|2 + |Ec|2). Because the country graph GC istypically much smaller than the underlying graph G, GREEDY is still quite fast and all mapsin this paper were colored using SPECTRAL+GREEDY.
6 Conclusion and Future Work
In this paper we described GMap, an e"cient algorithm for drawing graphs as geographicmaps. Using a number of structurally di!erent graphs and graphs of di!erent sizes, we il-lustrated the aesthetic appeal of the map metaphor for displaying underlying structures andclustering information. While the approach of visualizing relational information with the aid ofgeographical maps is general, here we showed one particular implementation where a scalableforce-directed layout algorithm was coupled with a modularity-based clustering algorithm.Exploring di!erent combinations of layout and clustering algorithms is one clear direction forfuture work.
While our algorithm is e"cient and can handle large graphs, the resulting maps look beston large wall-sized posters and display walls. To make such maps more useful for interactiveexploration of large underlying data sets we plan to incorporate topological clustering whichwould allow us to show the map in varying level of detail. We can leverage previous workon large graph visualization such as topological fisheye views [11] and the related compoundfisheye views [3].
We plan to explore the map coloring problem further through the use of weighted graphsto promote color di!erences not only between neighboring countries, but also non-neighboringcountries that are geographically close. In addition, the algorithm in [8] may be adapted forthis problem by using a 1D color space; at the same time it would be interesting to usethe spectral algorithm with three largest eigenvectors as an approximate solution for thecontinuous color assignment problem in 3D as studied in [8].
There are practical and theoretical obstacles to obtaining “perfect” maps, that is, mapsthat do not omit or distort the underlying information. However, a similar drawback plaguesany 2-dimensional representation of data that is not 2-dimensional, including the standardgeographical maps of Earth. Clearly, in dense graphs it is impossible to realize all graph ad-jacencies as neighboring countries. For example, with 8 countries we can have at most 18pairwise neighbors (from Euler’s formula for planar graphs), possibly forming some unavoid-able “false negative associations”. It is easier to deal with “false positive associations”. Suchan association between two countries can be formed if they are physically adjacent in themap but there is no strong relationship between the objects in the two countries One way toalleviate such a problem is to add “rivers” or “fords” along such borders near the coasts and“mountain ranges” inland, to convey that the two sides are close but not strongly connected.
Acknowledgments
We would like to thank Stephen North for helpful discussions. We thank Michael Junger forthe 1994-2008 GD author collaboration data used in Fig. 11.
11
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views and treemaps. In 12th Symposium on Graph Drawing (GD), pages 431–441, 2004.4. K. Boyack, R. Klavans, and K. Borner. Mapping the backbone of science. Scientometrics,
64(3):351–374, 2005.5. C. Brewer. Colorbrewer - selecting good color schemes for maps. http://www.colorbrewer.org.6. M. Bruls, K. Huizing, and J. van Wijk. Squarified treemaps. In Joint Eurographics and IEEE
TCVG Symposium on Visualization, pages 33–42. Press, 1999.7. H. de Fraysseix, P. O. de Mendez, and P. Rosenstiehl. On triangle contact graphs. Combinatorics,
Probability and Computing, 3:233–246, 1994.8. M. B. Dillencourt, D. Eppstein, and M. T. Goodrich. Choosing colors for geometric graphs via
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10. T. M. J. Fruchterman and E. M. Reingold. Graph drawing by force directed placement. Software- Practice and Experience, 21:1129–1164, 1991.
11. E. R. Gansner, Y. Koren, and S. North. Topological fisheye views for visualizing large graphs.IEEE Transactions on Visualization and Computer Graphics, 11:457–468, 2005.
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71, 2005.14. Y. F. Hu and J. A. Scott. A multilevel algorithm for wavefront reduction. SIAM Journal on
Scientific Computing, 23:1352–1375, 2001.15. I. T. Jolli!e. Principal Component Analysis. Springer, second edition, October 2002.16. P. Koebe. Kontaktprobleme der konformen Abbildung. Berichte uber die Verhandlungen der
Sachsischen Akademie der Wissenschaften zu Leipzig. Math.-Phys. Klasse, 88:141–164, 1936.17. J. B. Kruskal and M. Wish. Multidimensional Scaling. Sage Press, 1978.18. G. Kumfert and A. Pothen. Two improved algorithms for envelope and wavefront reduction.
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image. Computer Vision and Image Understanding, pages 227–243, 2008.21. S. Lloyd. Last square quantization in pcm. IEEE Transactions on Information Theory, 28:129–
137, 1982.22. F. K. Musgrave. Methods for Realistic Landscape Imaging. PhD thesis, Yale Univeristy, 1993.23. M. E. J. Newman. Modularity and community structure in networks. Proc. Natl. Acad. Sci.
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7 Appendix
In this section we provide more maps obtained with our algorithm, as well as close-up imagesfrom some of the earlier maps.
7.1 BookLand cont.
Figures 7-8 show close-ups of some of the large countries of Americana, Victoriana, Russiana,Graecoromania, Mythium, and Shakespearea discussed earlier. Fig. 9 shows close-ups of someof the other interesting countries in BookLand, some of which we consider in more detailbelow.
Transylvania: As with all books in this map, there is a fairly short path from 1984 toTwilight, the teenage favorite vampire series by Stephenie Meyers. In this case, the path goesthrough Victoriana via Pride and Prejudice and Wuthering Heights. The other main cluster inthis region is made of novels in the House of Night series by Cast and Cast (Hunted, Betrayed,Marked, Chosen, etc).
Fig. 7. Close-up images of various countries in BookLand’
13
Fig. 8. Close-up images of various countries in BookLand’
Thespia: In the south, adjacent to Transylvania but mainly connected to Americana,sits a region nearly exclusively containing American Plays, from 20th century mainstays suchas Tennessee Williams’ Streetcar Named Desire and Arthur Miller’s Death of a Salesman,through the more modern plays by David Mammet like American Bu!alo and GlengarryGlen Ross, to the 2008 Broadway hit August: Osage County.
Coelholand: The very popular Brazilian writer Paulo Coelho occupies another southernregion with his bestsellers The Alchemist, Brida, etc.
Cli!snotistan: The southeast coast of BookLand contains a collection of books aboutwriting. Classics like Strunk’s Elements of Style and Zinnser’s On Writing Well share theregion with books such as Sentence Composing for High School: A Worktext on SentenceVariety and Maturity. Several Cli!’s Notes books such as 5 Steps to a 5 on the AP and Cli! ’sAP English Language and Composition, give this region its name.
Oprahland: A large cluster of mainly 21st century popular literature contains several“club selections” of Oprah’s Book Club: She’s Come Undone, Drowning Ruth, Black andBlue. Recent bestsellers in this region include The Brief Wondrous Life of Oscar Wao, WhiteTiger, The Guernsey Literary and Potato Peel Pie Society. Connection with Americana isthrough the Salman Rushdie’s Satanic Verses and Arundhati Roy’s The God of Small Things.
Selfhelpistania: An odd region, nearly contained in Oprahland, has a focus on self-helpwith books like Choose to Be Happy and The Self-Esteem Companion: Simple Exercises to
14
Fig. 9. Close-up images of various countries in BookLand’
Help You Challenge Your Inner Critic and Celebrate Your Personal Strengths. A relatedcluster of Elizabeth Gilbert books is in the same region: Pilgrims, Last American Man andStern Men.
KFC: The Ken Follett Club, located to the northwest of Selfhelpistania contains some ofFollett’s British thrillers, Eye of the Needle, The Man from St. Petersburg and some of hishistorical fiction, The Pillars of the Earth, Night Over Water and A Place Called Freedom.
Fringistan: This region in the north is represented by arguably fringe work such as Men inBlack: How the Supreme Court is Destroying America, The Case Against Barack Obama: TheUnlikely Rise and Unexamined Agenda of the Media’s Favorite Candidate and Bill O’Reilly’s ABold Fresh Piece of Humanity. Not surprisingly, the connection to the main-stream literatureis through Ayn Rand’s Atlas Shrugged.
Feministan: Next to Fringistan is similarly controversial cluster of books: from NaomiWolf’s The Beauty Myth through Ariel Levy’s Female Chauvinist Pig: Women and the Riseof Raunch Culture to Jessica Valenti’s Full Frontal Feminism: A Young Woman’s Guide toWhy Feminism Matters.
7.2 PotterLand
As further examples, Fig. 10 shows the continent of PotterLand, a map related to “HarryPotter and the Sorcerer’s Stone”. It is notable that here the clustering structure matches
15
Harry Potter and theSorcerer's Stone
Harry Potter and thePrisoner of Azkaban
Harry Potter and theGoblet of Fire
Harry Potter and the Orderof the Phoenix
Harry Potter and theHalf!Blood Prince
Harry Potter Schoolbooks: Fantastic Beasts and Where toFind Them ! Quidditch Through the Ages
Harry Potter and theChamber of Secrets
The Tales of Beedlethe Bard
The Tales of Beedle theBard
Harry
Harry Potter BoxsetBooks 1!7
The Sorcerer's Companion: A Guide tothe Magical World of Harry Potter
Inkdeath
The Magician: The Secrets ofthe Immortal Nicholas Flamel
The Alchemyst: The Secrets ofthe Immortal Nicholas Flamel
The Deathly Hallows Lectures: The Hogwarts ProfessorExplains the Final Harry Potter Adventure
The Book of Harry PotterTrifles
Harry Potter Years 1!5Limited Edition Gift Set
FactThe Hidden Myths in Harry Potter:SpellbindingMap and Book of Secrets
The Magical Worlds ofHarry Potter
Unlocking Harry Potter: Five Keysfor the Serious Reader
Inkheart
Brisingr
The TimeParadox
The LastOlympian
The Battle of theLabyrinth
The Sorceress
The MysteriousBenedict Society
How Harry Cast His Spell: The Meaning Behindthe Mania for J. K. Rowling's Bestselling Books
20Q HarryPotter
Field Guide toHarry Potter
Muggles and Magic: An Unofficial Guide to J.k.Rowling and the Harry Potter Phenomenon
Looking for God inHarry Potter
Inkspell
The ThiefLord
Dragon Rider
Diary of a WimpyKid: The Last Straw
Eldest
Eragon
The LostColony
Artemis Fowl: TheOpal Deception
Queste
The DemigodFiles
Percy Jackson and the OlympiansPaperback Boxed Set
The Titan'sCurse
The Sea ofMonsters
The LightningThief
Fablehaven: Secrets of theDragon Sanctuary
The Mysterious Benedict Societyand the Perilous Journey
The Invention ofHugo Cabret
Diary of aWimpy Kid
The 39Clues
The Seeker's Guide toHarry Potter
The Complete Idiot's Guide to theWorld of Harry Potter
The Gospel According to Harry Potter: Spirituality inthe Stories of the World's Most Famous Seeker
The Wisdom of Harry Potter: What Our FavoriteHero Teaches Us About Moral Choices
What's a Christian toDo with Harry Potter?
Igraine theBrave
Diary of a WimpyKid Do!It!Yourself Book
Diary of a WimpyKid: Rodrick Rules
Lawn Boy
The EternityCode
The ArcticIncident
Artemis Fowl
Artemis Fowl: LostColony
Physik
Septimus Heap
Demigods and Monsters: Your Favorite Authors on RickRiordan's Percy Jackson and the Olympians Series
The 39 Clues: TheSword Thief
Fablehaven: Grip of theShadow Plague
Rise of the EveningStar
Fablehaven
Grip of the ShadowPlague
The Penderwicks onGardam Street
The Willoughbys
Good Masters" Sweet Ladies" Voicesfrom a Medieval Village
The WednesdayWars
39 Clues: OneFalse Note
The 39 Clues: CardPack
The Gospel According to Harry Potter:Leader's Guide for Group Study
The Gospel According to the Simpsons
God
Harry Potter and Philosophy:If Aristotle Ran Hogwarts
The Psychology of Harry Potter: An Unauthorized Examinationof the Boy Who Lived
Harry Potter and the Bible :The Menace Behind the Magick
A Charmed Life: TheSpirituality of Potterworld
Emmy and the IncredibleShrinking Rat
The LemonadeWar
Stink and the World'sWorst Super!Stinky Sneakers
No Talking
Artemis Fowl Book1
Artemis FowlFiles
Magyk
Septimus Heap Box Set:Books 1 and 2
Flyte
The 39 Clues: Beyondthe Grave
The CandyShop War
The Penderwicks: A Summer Tale of Four Sisters
The GraveyardBook
The Underneath
Elijah OfBuxton
Feathers
The Wall: Growing Up Behindthe Iron Curtain
The Absolutely True Diaryof a Part!Time Indian
The 39 Clues: The Card Pack2: Branch vs. BranchThe Gospel according to The Simpsons:
Leader's Guide for Group Study
The Simpsons and Philosophy: TheD'oh" of Homer
The Psychology of TheSimpsons: D'oh"
Religions of theWorld
What's Science Ever Done For Us: What the Simpsons CanTeach Us About Physics
The World According to The Simpsons: What Our Favorite TV Family Saysabout Life
Star Wars andPhilosophy
Mapping the World ofthe Sorcerer's Apprentice
Brendan Buckley's Universe andEverything in It
A Crooked Kindof Perfect
The Fabled Fourth Gradersof Aesop Elementary School
Punished
The Puzzling World ofWinston Breen
Night of theHowling Dogs
The Year ofthe Dog
Stink
Stink and the GreatGuinea Pig Express
The HomeworkMachine
Frindle
Artemis Fowl: TheGraphic Novel
The 39Clues #5
Leven Thumps and the Eyesof the Want
The Tale of Despereaux: Being the Story of a Mouse
The Miraculous Journey ofEdward Tulane
From the Mixed!Up Files ofMrs. Basil E. Frankweiler
Coraline
The House inthe Night
Nation
Neverwhere: ANovel
Savvy
How ILearned Geography
Chains
Henry's FreedomBox
First theEgg
American BornChinese
The Lone Ranger andTonto Fistfight in Heaven
The Arrival
The BookThief
The Gospel According toDr. Seuss
Seinfeld and Philosophy: A Bookabout Everything and Nothing
The Matrix and Philosophy: Welcome tothe Desert of the Real
Planet Simpson: How a CartoonMasterpiece Defined a Generation
History of the World'sReligions
Comparative Religions
Publication Manual of theAmerican Psychological Association
Classics ofWestern Philosophy
Life's UltimateQuestions
Insultingly Stupid Movie Physics: Hollywood's Best Mistakes
The SimpsonsMovie
The Simpsons Handbook: Secret Tipsfrom the Pros
Leaving Springfield: The Simpsons and thePossibility of Oppositional Culture
The Dharma ofStar Wars
Superheroes and Philosophy: Truth Batman and Philosophy: The Dark Knightof the Soul
The Tao ofStar Wars
Who Killed Albus Dumbledore?: What Really Happened in Harry Potter and theHalf!Blood Prince? Six Expert Harry Potter Detectives\
Examine the Evidence.
The Middleof Somewhere
Stink and the IncredibleSuper!Galactic Jawbreaker
Judy Moody & Stink:The Holly Joliday
Stink: The Super!Incredible Collection:Books 1!3
Roxie andthe Hooligans
Rules
Clementine
Lunch Money
The LandryNews
The ReportCard
Airman
Redwall: TheGraphic Novel
The 39Clues #6
Leven Thumps and theWrath of Ezra
Leven Thumps and theGateway to Foo
Professor Winsnicker's Book of Proper Etiquettefor Well!mannered Sycophants
Because ofWinn!Dixie
The TigerRising
Great Joy
The PhantomTollboothHarriet the
Spy
A Wrinklein Time
The Cricket in TimesSquare
Number theStarsStardust
American Gods:A Novel
Good Omens: The Nice and AccurateProphecies of Agnes Nutter
Anansi Boys
A Couple of Boys Havethe Best Week Ever
A River of Words: The Storyof William Carlos Williams
Hogfather
Making MoneyThe HungerGames
Wintersmith
After Tupac and DFoster
What I Saw AndHow I Lied
Wintergirls
Moses: When Harriet Tubman Led HerPeople to Freedom
Not a Box FlotsamA Visitorfor Bear
The RedBook
Knuffle Bunny Too: ACase of Mistaken Identity
Persepolis: The Story ofa Childhood
Fun Home: AFamily Tragicomic
Monster
Speak
Ceremony:
Reservation Blues
Smoke Signals
The Toughest Indian inthe World
The LostThing
The Guernsey Literary and PotatoPeel Pie Society
Loving Frank:A Novel
The Boy In theStriped Pajamas
I Amthe Messenger
People of the Book:A Novel
The Gospel According toPeanuts
The Gospel According to Disney: Faith
Seuss!isms: Wise and Witty Prescriptions forLiving from the Good Doctor
Short Meditations on theBible and Peanuts
The Parables ofDr. Seuss
HowWell Do You Know Jerry. . .and His Friends?: A Trivia Book
Seinlanguage
Seinology: The Sociologyof Seinfeld
Jerry Seinfeld Live on Broadway: I'mTelling You for the Last Time
Like a Splinter in Your Mind:The Philosophy Behind the Matrix Trilogy
The Lord of the Rings and Philosophy: OneBook to Rule Them All
Philosophers ExploreThe Matrix
Introducing Religion: From Insideand Outside
Women and WorldReligions
History of AsiaThe World's Wisdom: Sacred Texts
of the World's Religions
DSST Introduction to WorldReligions
Philosophy
English Grammar andPunctuation
Weights andMeasures
Essays and TermPapers
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Looking Out
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The Universe Next Door:A Basic Worldview Catalog
Hollywood Science: Movies
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The Simpsons ! TheComplete Tenth Season
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Star Wars Jesus ! A spiritual commentaryon the reality of the Force
The Journey of Luke Skywalker: AnAnalysis of Modern Myth and Symbol
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Comic Book Nation: The Transformation ofYouth Culture in America
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Wisdom from the Batcave: How toLive a Super
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Judy Moody: Around the World in8 1!2 Days
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Judy Moody's Double!Rare Way!Not!Boring Book ofFun Stuff to Do
Phineas L. MacGuire . . .Erupts": The First Experiment The Ghost's
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Dexter theTough
Penny fromHeaven
Clementine's Letter
Talented Clementine
The Janitor'sBoy
A Week inthe Woods
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Treasure Island: The GraphicNovel
Doomwyte: A Novelof Redwall
Call of theWild
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The 39 Clues:Book 7
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Maniac Magee
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The LittleYellow Leaf
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Going Postal
The Wit and Wisdomof Discworld
Graceling
The Host:A Novel
Catching Fire
The Twilight Saga: TheOfficial Guide
A Hat Full of Sky: The Continuing Adventuresof Tiffany Aching and the Wee Free Men
The Amazing Maurice andHis Educated Rodents
The Surrender Tree: Poems ofCuba's Struggle for Freedom
Disreputable History of FrankieLandau!Banks
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The Higher Powerof Lucky
Not aStick
What Do You Do with aTail Like This?
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Big Words forLittle People
Dirt onMy Shirt
Ten Little Fingers andTen Little Toes
Smash" Crash"
Zen Shorts
Kitten's FirstFull Moon
Knuffle Bunny: A CautionaryTale
The Pigeon Wantsa Puppy
There Is a BirdOn Your Head"Don't Let the Pigeon
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Persepolis 2: The Storyof a Return
Maus I: A Survivor's Tale:My Father Bleeds History
The Complete Maus: ASurvivor's Tale
Understanding Comics: TheInvisible Art
Blankets
Jimmy Corrigan: The SmartestKid on Earth
The ChocolateWar
The FirstPart Last
Cut
The Perks of Beinga Wallflower
Thirteen ReasonsWhy
Tracks
House Madeof Dawn
Beloved
Fools Crow
The Woman Warrior: Memoirs ofa Girlhood Among Ghosts
Flight: ANovel
Indian Killer
Ten LittleIndians
The Rabbits
The RedTreeThe Viewer
Tales FromOuter Suburbia
The Story of EdgarSawtelle: A Novel
The Girl with theDragon Tattoo
The Help
Dewey: The Small!Town Library CatWho Touched the World
The White Tiger: ANovel
Out Stealing Horses:A Novel
The Boy in theStriped Pajamas
Yellow Star
The Reader
Getting TheGirl
Year ofWonders
The Zookeeper's Wife: AWar Story
Peanuts GuideTo Life
From Mouse to Mermaid: The Politicsof Film
The Mouse that Roared: Disney andthe End of Innocence
Seuss!isms forSuccess
You're Only Old Once" ABook for Obsolete Children
Oh
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Happy Birthday toYou"
The Parablesof PeanutsThe Shack
Mattel Scene it? SeinfeldDVD Game
The DarkKnight
Comedian
Scene It?Seinfeld
Seinfeld !Season 9
Seinfeld
Simpsonology: There's a Little Bit ofSpringfield in All of Us
Philosophy forDummies
Love Your God with All Your Mind: The Roleof Reason in the Life of the Soul
More Matrix and Philosophy: Revolutionsand Reloaded Decoded
The Chronicles of Narnia and Philosophy: The Lion
Introduction to Philosophy: Classicaland Contemporary Readings
The Ultimate MatrixCollection
God the Evidence : The Reconciliation of Faithand Reason in a Postsecular World
Paths ofFaith
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Zen in the Artof Archery
The World's Religions: OurGreat Wisdom Traditions
Exploring Religion
The Concise Oxford Dictionaryof World Religions
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Still LifeWith Rice
The 47Ronin Story
Train toPakistan
Classics ofEastern Thought
The Illustrated World's Religions: A Guideto Our Wisdom Traditions
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World Religions: The GreatFaiths Explored & Explained
The Ten Challenges: Spiritual Lessons from the Ten Commandments forCreating Meaning
DSST Here's to YourHealth
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DSST The Official TestPreparation Guide
DSST Principles of PublicSpeaking
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Algebraic EquationsPeriodic Table
Apa!mla Guidelines
Futuring: The Exploration ofthe Future
The Elements of Style
The Extreme Future: The Top Trends That WillReshape the World in the Next 20 Years
DSM!IV Made Easy: TheClinician's Guide to Diagnosis
Kaplan and Sadock's Synopsis ofPsychiatry: Behavioral Sciences!Clinical Psychiatry
Theory and Practice ofGroup Psychotherapy
Interview Guide for Evaluating Dsm!IV PsychiatricDisorders and the Mental Status Examination
Pocket Companion for PhysicalExamination & Health Assessment
Davis's Drug Guide for Nurses
Nursing Diagnosis Handbook: An Evidence!BasedGuide to Planning Care
Taber's Cyclopedic Medical Dictionary
Qualitative Inquiry and Research Design:Choosing Among Five Approaches
Doing a Literature Review: Releasing theSocial Science Research Imagination
Writing Your Dissertation in Fifteen Minutes a Day: A Guideto Starting Qualitative Research &
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Bookmarks: A Guide toResearch and Writing
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Case Studies in Interpersonal Communication:Processes and Problems
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What the Buddha Taught: Revised and Expanded Editionwith Texts from Suttas and Dhammapada
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The Bhagavad!Gita : Krishna's Counsel inTime of War
The Cambridge Illustrated Historyof China
A Source Book inChinese Philosophy
The Arizona ConstitutionStudy Guide
Historical Survey of theOld Testament
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Philosophy of Religion: AGuide and Anthology
How to Read the Biblefor All Its Worth
Grasping God's Word: A Hands!On Approach toReading
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The Reason for God: Belief inan Age of Skepticism
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Ten Moments That Shook the Sports World: One Sportswriter's Eyewitness Accounts ofthe Most Incredible Sporting Events of the Past\
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Aristotle and an AardvarkGo to Washington Poker and Philosophy: Pocket Rockets and
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Bridge toTerabithia
Stinkville
Whangdoodleland
Potterland
Riordiania
Teenland IndianaKinderland
Psychland
TVLand
BatmanlandStarwarsland
Graphicland
TweenlandWest Tweenland
Reliregion
North Reliregion
Literary Reliregion
Fig. 10. A map of books related to “Harry Potter and the Sorcerer’s Stone”
the layout very well, with fewer fractured countries and mostly contiguous territories. It isworth mentioning that the books and their connections in this map reflect American readingpreferences (as opposed to say European or World preferences). Even the title of the the firstHarry Potter book was “translated” from British English where it was Harry Potter and thePhilosopher’s Stone to American English Harry Potter and the Sorcerer’s Stone3 Once again,we look at some of the countries around PotterLand.
Stinkville: In the west is a cluster of books for 4-6 year old kids. Megan McDonald’s booksdominate the region with Stink and the Great Guinea Pig Express, Stink and the IncredibleSuper-Galactic Jawbreaker, Stink and the World’s Super-Stinky Sneakers and the Judy Moodyseries by the same author. Andrew Clements’ kids books, Lunch Money, The Report Cardand Frindle, occupy the southern end of this region.
Whangdoodleland: Below Stinkville are books targeted at the 9-12 year old kids. Clas-sics of the genre in this area include Katherine Paterson’s Bridge to Terabithia, MadelineL’Engle’s A Wrinkle in Time, Norton Juster’s Phantom Tollbooth, E. L. Konigsburg’s Fromthe Mixed-Up Files of Mrs. Basil E. Frankweiler, Julie Andrews Edward’s The Last of theReally Great Whangdoodles
PotterLand: The main cluster in this map is the one containing works by the Britishwriter, J. K. Rowling. In addition to the seven books in the Harry Potter saga, there are adozens of books about the Harry Potter books in the western part. To the east is the relatedcluster of the six books in the Irish writer Eoin Colfer’s Artemis Fowl series: Artemis Fowl,The Arctic Incident, Eternity Code, Opal Deception, Lost Colony, Time Paradox. Directlysouth is the Septimus Heap series by the British writer Angie Sage: Flyte, Queste, Physik,Magyk. Finally, in the south is German writer Cornelia Funke’s Inkworld Trilogy: Inkheart,Inkspell, Inkdeath.
Riordiania: Several fantasy series form the cluster to the southeast of PotterLand. Themain books are Rick Riordan’s Percy Jackson and the Olympians series: The Lightning Thief,The Sea of Monsters, The Titan’s Curse, as well as a number of 39 Clues books, another
3 While “philosopher’s stone” is an ancient concept sought after by alchemists and scientist alike, a“sorcerer’s stone” is quite meaningless without the context.
16
popular Riordan series. Other books in this cluster include Obert Skye’s Leven Thumps seriesand Brandon Mull’s Fablehaven series.
Batmanland, Starwarsland, Startrekland, Graphicland: Directly south of Potter-Land is a cluster of Batman-related books. To the southwest is a large cluster of Star Warsbooks and books about Star Wars. Further south is a smaller but similar cluster of Star Trekbooks. Nearby is a cluster of Saun Tan’s illustrated tales Tales From Outer Suburbia, TheArrival, The Lost Thing, etc.
Tweenland and West Tweenland: There are a couple of diverse clusters with contem-porary books aimed at pre-teenagers. Brian Selznik’s The Invention of Hugo Cabret, TrentonLee Stewart’s The Mysterious Benedict Society, and Cynthia Lord’s Rules anchor Tweenland.Next door is West Tweenland with Neil Gayman’s Graveyard Book, Anansi Boys, Coralineand books about vampires Twilight Saga, The Host, The Hunger Games.
Teenland: On the southern coast is a cluster of more mainstream books which appeal toteenagers and Oprah’s Book Club. Typical examples are White Tiger, The Guernsey Literaryand Potato Peel Pie Society, People of the Book, The Story of Edgar Sawtelle, The BookThief.
Indiana: This is a cluster of books by Sherman Alexie, focusing on Native Americantopics The Lone Ranger and Tonto Fistfight in Heaven, Indian Killer, The Absolutely TrueDiary of a Part-Time Indian.
Kinderland: On the southeast coast is a collection of books targeted at the kindergartenaudience: Kitten’s First Full Moon, The Pigeon Wants a Puppy and the Knu"e Bunny series.
PsychLand: The west contains a large and diverse cluster of mostly psychological texts,anchored by Publication Manual of the American Psychological Association.
Reliregion, North Reliregion, and Literary Reliregion: the southwest coast is pop-ulated with books dealing with religion, from Christianity (The Ten Challenges: SpiritualLessons from the Ten Commandments for Creating Meaning) to Buddhism (What the Bud-dha Taught: Revised and Explained Edition with Texts from Suttas and Dhammapada). In thenorthwest is the smaller North Reliregion cluster with books about Christianity. Immediatelyadjacent to PotterLand is the Literary Reliregion, dealing with religion in literature: Lookingfor God in Harry Potter, Harry Potter and the Bible: The Menace Behind the Magic, What’sa Christian to Do with Harry Potter. Next to it is a related cluster of several themed booksby Mark Pinsky: The Gospel According to the Simpsons, The Gospel According to Disney,and similarly titled books by other authors, The Gospel According to Peanuts, The GospelAccording to Dr. Seuss, The Gospel According to Harry Potter.
TVland: Surrounded by religious-themed areas in the north lies a cluster of books aboutthe popular TV shows the Simpsons and Seinfeld.
7.3 GDLand
Fig. 11 shows a map centered at Graph Drawing: Algorithms for the Visualization of Graphs.Here each vertex has a distance of 6 or less to that book. It is interesting to see how thesubject quickly goes outside Mathematics and Computer Science. For example, the orangecluster in the far left contains books largely unrelated to Mathematics or Computer Science,but connected to such books via books on Game Theory.
7.4 GD Collaboration 1994-2008
Fig. 3 presented a map based on GD author collaboration up to 2004. More recent data fromhttp://gdea.informatik.uni-koeln.de/, kindly provided to us by Michael Junger, gives
17
Fig. 11. A map of books related to Graph Drawing: Algorithms for the Visualization of Graphs
author collaboration information extending to 2008. This graph has 670 vertices and 1517edges with a largest component of 464 nodes and 1313 edges. A map of the eight largestcomponents in the graph is shown in Fig. 12.
Due to the di!erent origins of the two data sets it is di"cult to perfectly match authorsin the two graphs, and therefore provide a stable mental map. Nevertheless, when comparingthese two maps of the GD community, we can observe several interesting changes. The totalnumber of GD auhtors has grown from 508 in 2004 to 670 in 2008, or about 32%. The largestconnected component has grown from 54% of all the authors in 2004 to 68% of all the authorsin 2008. One of the large islands populated by Czech authors in 2004 has become part of themainland in 2008. Similarly, the large island populated by Japanese authors has also joinedthe mainland, creating the peninsula on the east coast.
18
LeeRobertsonBederson
Nachmanson
Tóth
Kyncl
Pinchasi CernKeszegh
PálvölgyiPach Tardos
Thiele
Finocchi Pizzonia
Di Battista
Patrignani Liotta
ThomePouchkarev
Mutzel
Hundack
Ahmed
ForsterHong
Murray
Dwyer
Taib
Nikolov
Fu
Ho
KoschutzkiTarassov
McAllister
Bose
Purchase
Cohen
Görg
Hoggan
Allder
James
Felsner DangelmayrZickfeld
MassowBonichon
Mosbah
Vargiu Di Giacomo
Goodrich
Didimo
Meijer
Wood
Rosamond
Garg
van Kreveld
ElGindy Lubiw
Fellows
Ragde
Kobourov
TassinariParise
BinucciGiordano
NonatoEverett
Dujmovic
Tamassia
Lazard
Eppstein
Brandenburg
Nishimura
Speckmann
Lenhart
McCartin
Whitesides
Buti
Bridgeman
SnoeyinkCarmignani
Barbagallo
Vyskocil
Kára
Tanenbaum
Scheinerman
Madden
Madden
Powers
Grigorescu
Himsolt
Laison
SafariTrotterEvans
Dean
Marriott
Stuckey
WybrowHe
Koren
Newton
S koraUzovic
Wagner Benkert
KaufmannLerner
BaurGaertler
Kenis
Görke
de Berg
Plaisant
Sims Parr
BubeckRosenstiel
Ritt
Fößmeier
Steckelbach
Vondrák
Nyklová
Babilon
Krug
Andalman
Ryall
Dickerson
Meng
Rosi
de Mendonça Neto
Harel
Agarwal
Sharir
Kaplan
Vasiliu Diguglielmo
Sander
Ellson
Koutsofios
Woodhull
North
Gansner
Ju
Park
Gudmundsson
Matera
ChrobakNakano
Joevenazzo
Wilsdon
Wampler HardingErten
NavabiForrester
Yee
Alzohairi
Rival
Such
JelínkováPergel
Kratochvíl
Nöllenburg
Atienza
Garrido
Moreno
Hernández
Grima
Kroll
ValenzuelaPortillo
Haverkort
Villar
Cortés
Reyes
Wolff
Gassner
SchaeferSchulz
Estrella!Balderrama
Eades
Lee
HuangLin
do Nascimento
Feng
Huang
Trümbach
Schreiber
de Castro
Márquez
Dana
DuncanWenk
Cheng
Bachmaier
Raitner
Geyer
Vrt'o
Wilhelm
Alt
Kikusts
Dogrusoz
Rucevskis
KumarAbello
Dyck
GiralCivril
Demir
Le
Edachery
Sen
Aloupis
Morin
Maeda
Sugiyama
Garcìa
Ramos
KochFialko
Leipert
Jünger
Gutwenger
Alberts
Ambras
Ziegler
Abellanas
Noy
Ferran
Johansen
Shermer
Gartshore
Closson
Siebenhaller
KeskinVogelmann
Frick
BoyerCortese
Aronov
Pollack
Hurtado
Mateos
Hernando
Tejel
García
Melançon
Herman
Delest
de Ruiter
Mariani
Frati
Lesh
Roxborough
Tsiaras
Triantafilou
Tollis
Kisielewicz
Chow
Ruskey
Pohl
Deng
BrandesBachl
PickRohrer
Cudjoe
Manning
WieseEiglsperger
Kupke
Miyazawa
Nishizeki
Miura
HallettKitching
Suderman
Fanto
Valtr
Devillers
Pentcheva
CarpendaleFracchia
Cowperthwaite
Bocek!Rivele
Magdon!Ismail
SchankCornelsen
GomezNickle
Six Papakostas
Kakoulis
Vince
Houle
Jourdan
Zaguia
Rappaport
Hirsch
Munoz
Unger
Wenger
Yildiz
Barth
Gotsman
Székely
Shahrokhi
Torok
Djidjev
Matsuno
Hashemi
Diehl
Birke
Bruß
Ludwig
Chanda
Marcandalli
Yusufov
DrechslerGünther
BeckerEschbach
Doerr
Papamanthou
Goaoc
Okamoto
Holleis
Goldberg
SkienaShannon
Berry
Dean
Boitmanis
Shubina
Puppe
Pich
Gelfand
FinkelChan
Molitor
SchönfeldMatuszewski
Dobkin
Proskurowski
Fiala
Dvorák
Taylor
Abelson
Durocher
Brunner König
Maxová
MatousekMisue
Hutchinson
Bretscher
Blair
Kruja
Waters
Tóth
GhoshRahman
Xu
Kuchem
Jeong
Byun
Pop
Aggarwal
Kanne
PittaRuml
Sablowski
Pangrác
Král
Vismara
Heß
Sun
Trotta Wismath
Skodinis
Marcus
Pacheco
Atallah
Liao
Yen Lu
Chen
Xia
Bekos
PotikaJelínek
Cruz
LambeTwarog
Carmel
Nakano
Telle
Lynn
Merrick
Leonforte
Pór
Gethner
Lueker
Grilli
Asano
LandisKöpf
Rusu
PelsmajerStefankovicSchmidt
ChimaniLee
Lin
Weiskircher
Buchheim
Percan
Dhandapani
Basu
Schlieper
Friedrich
Lillo
Stolfi
Lozada
Näher
KrügerBrockenauer
Marshall
Mili
Castelló
AltGodau
Fox
Biedl Aziza
Spriggs
Lozito
Iturriaga
Haible Baudel
Yoshikawa
Healy
HarriganLynch Kuusik
Uno
Symvonis
Murtagh
Ferdinand
Przytycka
Feng
Lin
Chuang
Zhu
ShieberCappos
Odenthal
Carrington
Han
Demetrescu
Freivalds
Jaoua
Efrat
Garvan
Azuma
Fekete
Marks
Bertolazzi
Fleischer
Naznin
Quigley
Cobos
Vernacotola
Kant
Eckersley
Shin
Wagner
Sykora
Klau
Ebner
Barouni
Webber
Scott
Klein
Fowler
Dillencourt
Hirschberg
Egi
Hachul
Tokuyama
Watanabe
Kosaraju
Gajer
Mumford
ToussaintCarlson
Cetintas
Italiano
Hui
Wagner
Bertault
Miller
Fernau
Genc
Mehldau
Fig. 12. Author collaboration map for the GD conference, 1994-2008.
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