An Introduction to Social Network Analysis

An Introduction to Social An Introduction to Social Network AnalysisNetwork AnalysisFulvio D’Antonio

NARG: Network Analysis Research GroupDII - Dipartimento di Ingegneria dell'InformazioneUniversità Politecnica delle Marche

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OutlineOutlineWhat is a social network?

A little history…

Modelling social networks with random graphs

Link prediction

Content-based social networks

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What is a Social Network?What is a Social Network?

Networks in which nodes and ties model social phenomena.

Generally represented using graphs

Different kind of relationships:◦Static (kinship, friendship, similarity,…)◦Dynamic (information flow, material

flow,…)

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HistoryHistory In the 19th century Durkheim introduces

the concept of “social facts”

◦ phenomena that are created by the interactions of individuals, yet constitute a reality that is independent of any individual actor.

In the 1930s, Moreno:◦ the systematic recording and analysis of social

interaction in small groups, especially classrooms and work groups (sociometry)

◦ He invents the “sociogram” (graphical representation of interpersonal relationships)

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History (2):History (2):Milgram’s experiment Milgram’s experiment (1960s)(1960s)

People in Nebraska, were each given a letter addressed to a target person in Boston, Massachusetts, along with demographic information (name, address, profession) on this person.

They were asked to send the letter to the target person, by forwarding it to other people

Average number of hops to get the letter to the target: 6

◦ “six degrees of separation”

History (3):History (3):The Strength of Weak TiesThe Strength of Weak Ties

Granovetter◦“The Strength of Weak Ties” (1973)

considered one of the most important sociology papers written in recent decades

◦He argued that “weak ties” could actually be more advantageous in politics or in seeking employment than “strong ties”

◦Some reasons: They allows you to reach a vaster audience. Information coming from weak ties is “fresh”

Understanding Networks Understanding Networks with Random Graphswith Random Graphs A random graph is a graph that is generated by

some random process

The objective is to study the properties of random graphs (e.g. diameter, clustering coefficient, mean degree)

Are generated graphs compatible with actual social networks?

Different approaches:◦ Erdős–Rényi Graphs◦ Small-World model◦ Barabasi-albert model

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Random GraphsRandom GraphsStudied by P. Erdös A. Rényi in 1960s

How to build a random graph◦ Take n vertices◦ Connect each pair of vertices with an edge with some probability p

There are n(n1)/2 possible edges

The mean number of edges per vertex is

( 1)( 1)

n n pz n p np

n

Degree DistributionDegree DistributionProbability that a vertex of has degree k

follows binomial distribution

In the limit of n >> kz, Poisson distribution

◦ z is the mean

11(1 )k n k

k

np p p

k

!

k z

k

z ep

k

CharacteristicsCharacteristics

Small-world effect (Milgram 60s)• Diameter (Bollobas)• Average vertex-vertex distance• Grows slowly (logarithmically with the size)

Doesn’t fit real-world networks

• Degree distribution (not Poisson!)

• Clustering (Network transitivity) Random graphs: small clustering

coefficient social networks, biological networks in nature,

artificial networks – power grid, WWW: significantly higher

ClusteringClustering

If A is connected to B, and B is connected to C, then it is likely that A is connected to C

“A friend of your friend is your friend”

The average fraction of a node’s neighbor pairs that are also neighbors each other

6*( )

( 2)

number of triangles on a graphC

number of paths of length

Small-World ModelSmall-World Model Watts-Strogatz (1998) first introduced small

world model Mixture of regular and random networks

• Regular Graphs have a high clustering coefficient, but also a high diameter

• Random Graphs have a low clustering coefficient, but a low diameter

Characteristic of the small-world model• The length of the shortest chain connecting two

vertices grow very slowly, i.e., in general logarithmically, with the size of the network

• Higher clustering or network transitivity

Small-World Model (2)Small-World Model (2)

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•Construct a regular ring lattice . Each node has degree k

•For every node take every edge (a,b) with i < j, and rewire it with probability β

Scale-Free NetworkScale-Free Network

A small proportion of the nodes in a scale-free network have high degree of connection

Power law distribution • A given node has k connections to other nodes with

probability as the power law distribution with exponent ~ [2, 3]

Examples of known scale-free networks:• Communication Network - Internet• Ecosystems and Cellular Systems• Social network responsible for spread of disease

Barabasi-Albert NetworksBarabasi-Albert Networks Start from a small number of node, add a new

node with m links

Preferential Attachment • Probability of these links to connect to existing

nodes is proportional to the node’s degree

• “The rich gets richer”

This creates ‘hubs’: few nodes with very large degrees

( ) ii

jj

kk

k

Link PredictionLink PredictionWho will be connected in the next future

(present or past)?

Why link prediction?

◦ Eliciting hidden or Incomplete link information Missing links from data collection (criminal networks)

◦ Recommendation Friends, groups in social networks Product, Book, Movie, Music on e-commerce site Articles on content site Who should one collaborate?

◦ ….

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Ok, this was about the Ok, this was about the structure…. but structure…. but what what about the content?about the content?

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Content-based social Content-based social networksnetworksA special kind of Social Networks

The actors (nodes) of the network produce documents◦ They can be produced by more than one

actor co-authorship relationship

Similarity relationship between any 2 actors A and B of the network can be estimated using a function on the set of documents produced Doc(A) and Doc(B)

◦ Sim: DOC(A) DOC(B) [0,1]19

Automatically detecting Automatically detecting content-based social content-based social networksnetworksNLP Methodology*:

1. Choose a set of actors and gather related documents; 2. Pre-process textual data to extract raw text; 3. Process raw text with a part-of-speech tagger; 4. Extract candidate annotating terms by using a set of

part-of-speech patterns5. Rank candidates, possibly filter them choosing a

threshold; 6. Output a set of weighted vectors V of annotating

terms for each documents; 7. Group the vectors by actor and construct a centroid

(i.e. a mean vector) with such groups. This centroid roughly represents the actor main interests.

8. Build a graph by computing a similarity function for each pair of centroids.

*Cooperation with university of Rome 20

Reducing Information Reducing Information Dimensionality:Dimensionality:Clustering / Community findingClustering / Community findingdividing a set of data-points into subsets

(called clusters) so that points in the same cluster are similar in some sense ◦ Crisp/Fuzzy clustering◦ Partitive/Non partitive clustering

K-means, repeated bisection, graph partitioning,…

Cohesive subgroups detection:◦ Cliques◦ K-Cliques◦ K-Plex◦ Density based subgraphs

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Experiments: Research Experiments: Research NetworksNetworksINTEROP NoE (6FP):•Domain Ontology expressed using OWL (Ontology Web Language) in the Interoperability of Software Application domain•INTEROP partners’ corpus•2 types of edges:

•Coauthorship•Similarity

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Evaluation: predictive power Evaluation: predictive power of the modelof the model  We evaluated how many of the possible opportunities

computed for year 2003 have been exploited in the rest of the project (2004-2007).

Perc. of opportunities for year 2003 realized in the rest of the project (2004-2007)

Perc. of opportunities for year 2004 realized in the rest of the project (2005-2007)

Year Perc. realized

In 2004 20%

In 2005 33%

After 2005 57%

Year Perc. realized

In 2005 54%

After 2005 75%24

Experiments: Patent Experiments: Patent NetworksNetworks

The European Patent Office (EPO):web-services to access to information about European patents that have been registered; • the date of presentation•the applicant name and mission,•the address of the applicant• textual description of the patent.

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Thank you…..Thank you…..

Questions?!?!?!Questions?!?!?!

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