Network Science: Theory, Modeling and Applications

Network Science: Theory, Modeling and Applications

Madhav V. Marathe

Dept. of Computer Science & Network Dynamics and Simulation Science Laboratory

Virginia Bioinformatics Institute Virginia Tech

NDSSL TR-10-148

Supported by Grants from NIH MIDAS, NSF HSD, NSF CNS, CDC COE, and DoD.

Network Dynamics & Simulation Science Laboratory

Where: LLNL, Livermore,

Dates: December 1st to December 15th 2010

Hosts: Dr. David Brown and Dr. Celeste Matarazzo

Time: 10.00 am to 11.30 am (OfMice hours as needed afterwards)

Lecturer: Madhav Marathe, Virginia Tech ([email protected])

Guest Lectures: Christopher Kuhlman (VT), Goran Konjevod (Staff Scientist, LLNL), Anil Vullikanti (Asst Prof. VT and DOE Career award recipient)


Complex Networks are pervasive in our society. Realistic biological, information, social and technical networks share a number of unique features that distinguish them from physical networks. Examples of such features include: irregularity, time-‐varying structure, heterogeneity among individual components, and selMish/cooperative game-‐like behavior by individual components and co-‐evolution. The size and heterogeneity of these networks, their co-‐evolving nature and the technical difMiculties in applying dimension reduction techniques commonly used to analyze physical systems makes reasoning, prediction and controlling of these networks even more challenging. Recent quantitative changes in high performance and pervasive computing including faster machines, distributed sensors and service-‐oriented software have created new opportunities for collecting, integrating, analyzing and accessing information related to such large complex networks. The advances in network and information science that build on this new capability provide entirely new ways for reasoning and controlling these networks. Together, they enhance our ability to formulate, analyze and realize novel public policies pertaining to these complex networks. The course will cover the mathematical and computational aspects of Network Science. It will provide a broad overview of the area and then will focus on • Mathematical aspects, including structure theorems, existence proofs, • Computational aspects, including, provable lower as well as upper bounds on the computational resources, efMicient algorithms for computing the structure and dynamics over complex networks, • Developing high performance computing based computational models and modeling environments for supporting Network Science. Practical applications arising in the context of infrastructure planning, energy systems, national security and integrated communication systems will be used to illustrate the applicability of the concepts.

Course Synopsis


Work funded in part by NIGMS, NIH MIDAS program, CDC, Center of Excellence in Medical Informatics, DTRA CNIMS, NSF, NeTs, NECO and OCI program, VT Foundation.


•  Lada Adamic: For graciously sharing her course notes •  NDSSL Laboratory members who are in reality coauthors of this. •  Other places that I have borrowed the material includes:

• Tim Roughgarden’s lectures on Games • David Kempe’s Lectures on Networks • Henning Mortveit’s lectures on SDS • Bogdan Oporowski’s lecture on Graph theory • Michael Kearns lectures on Networks and Games • … and many more

• Books • Fernando Vega-‐Redondo, Complex Social Networks, Econometric Society Monographs, , Cambridge University Press, 2007 • D. Easley, J. Kleinberg. Networks, Crowds, and Markets: reasoning about a Highly Connected World, Cambridge University Press, 2010. • J. Kleinberg, E. Tardos. Algorithm Design. Addison Wesley, 2005. Matthew Jackson, Social and Economic Networks, Princeton University Press, 2010 • … and many more

Acknowledgements for Course Material

What is a Network? History, Broad Research Questions, Illustrative

Applications


What is a network ?

  Although no formal accepted deMinition, there appears to be a consensus that all network comprise of the following attributes:   A set of agents (entities): agents can be simple, game like, adaptive …

  Interaction among the entities governed by a graph (binary or in general k-‐ary relationship)   Graph itself can change, co-‐evolve with the entities

  Entities modify their local states and behavior by interacting with their neighbors

Blogosphere (datamining.typepad.com)

points lines vertices edges, arcs math nodes links computer science sites bonds physics actors ties, relations sociology

node

edge

Images of Various Networks


Social Networks: Facebook has over 500Million individuals!

http://www.smrfoundation.org/category/industry/companies/facebook/


High School Dating Network (Discovery Magazine 2007)


Router-level network based on ISPs


Delta Airlines Routes (airline routes maps.com


EU rail network


Biological Networks

Institute of biology and technology - Saclay (iBiTec-S)/ Unités/ Department of Integrative Biology and Molecular Genetics (SBiGeM)/ Integrative biology laboratory (LBI)/ Dynamics of Biological Network (J. Labarre)

http://djpowell.wordpress.com/

http://www.leonelmoura.com/tree.html


In real world Networks are layered and coupled


Growth of network science as measured by publications

#papers with “complex networks” in the title [National Academy of Science Report, 2007]

Journal special issues on Network Science


Even appears in main stream publications YESTERDAY !


The Emerging Network Science?

  Newman, Barabasi, Watts: The Structure and Dynamics of Networks: “We argue that the science of networks that has been taking shape over the last few years is distinguished from preceding work on networks in three important ways:   (1) by focusing on the properties of real-‐world networks, it is concerned with

empirical as well as theoretical questions;   (2) it frequently takes the view that networks are not static, but evolve in time

according to various dynamical rules; and   (3) it aims, ultimately at least, to understand networks not just as topological

objects, but also as the framework upon which distributed dynamical systems are built.”

  Kearns: An Emerging Science:   Examine apparent similarities (and differences) between many social, economic, information, biological and technological networks

  Importance of network effects in such systems   How things are connected matters greatly   Details of interaction matter greatly

  Qualitative and quantitative; can be very subtle   A revolution of measurement, theory, and breadth of vision


Science of Networks: A personal (and likely biased) viewpoint 1:

  Real World Networks:   Extremely important but ..   Folks in social sciences, transportation, electrical systems, VLSI, … all have been studying real world networks

  We need to seriously revisit the use of simple random graph models as a way to explain a phenomenon: the mathematics is elegant but often means very little in the real world

  Real world networks are dynamic, coupled and co-‐evolve   Ability to collect data that is diverse (spatially, demographically), process it, store it and reason about it very fast   New data should be utilized in developing network models

New and realistic models of real world networks. Models should represent coupling and co-evolution


Accessibility of Network Science: Pervasive Computing Environment

  High performance computing (larger machines, data intensive systems, distributed systems …)

  Software as a service; delivering results to specialist who is not interested in becoming a computer scientist

  Ability to collect data that is diverse (spatially, demographically), process it, store it and reason about it very fast

Develop Pervasive computing technology to deliver Network Science technology to domain specialists and

others who are not computing experts


Science of Networks: Centrality of Computing and Information Science

  From analytical results to algorithmic viewpoint: this is the essence of new science in my opinion if one has to do deal with real networks

  Questions that become important are:   How can we design certain networks   How can we measure distributed networks   What is a certain set of distributed agents computing: interaction based computing and

social cognition

  Models are not monolithic or federated anymore but really a way to synthesize information by interacting with various components – Milner’s in_luential idea on interactionism

Algorithmic Viewpoint provide the foundational basis HPC computing provide the underlying technology


Inter and intra-discipline interactions – Emergence of a Giant Component !

  We have reached critical point wherein researchers from diverse disciplines are starting to share their ideas and interact (Gladwell’s Tipping point)   Beautiful convergence of ideas and view points in CS, Engineering, Economics, Mathematics, Physics, Social Science, Biology…. (convergence of several events, world becoming smaller, funding agencies pushing to do joint work!, global problems, problems that were being solved by disciplinary viewpoints)

  Economic drivers: Information economy, distributed logisitics, global markets, mobile labor force, funding shortfalls

  Measurement technologies and technologies for developing and sustaining diverse organizations and ecosystems have taken hold

Multi-disciplinary view important: from real research social networks !


Culmination of diverse _ields: Viewpoints are different and interesting

Engineers • Understand how infrastructure networks work • Design and control of these networks

Computer Scientists • Understand and design complex, distributed networks •  algorithmic view: design of a system and inferring its semantics

Social Scientists, Behavioral Psychologists, Economists • Understand human behavior in “simple” settings • Revised views of economic rationality in humans

Biologists • Neural networks, gene regulatory networks,… • Understanding the evolution of networks

Physicists and Mathematicians • Interest and methods in complex systems • Theories of macroscopic behavior (phase transitions)

Scientists forming co-evolving

networks World


Proposed Components of a Research Program in Network Science and Engineering

Structural Analysis of Complex Networks

Dynamics on Complex Networks

Co-‐evolution of dynamics, network

and individual behavior

Measurement and Inference

Networks Science in Real

World


Key Research Challenges (NA report on Network Science)

1.  Dynamics: Better understanding between structure and function

2.  Modeling and Analysis of large networks: Tools, abstractions, approximations

3.  Design and Synthesis of Networks 4.  Increasing level of rigor and mathematical structure 5.  Abstracting common concepts across Mields 6.  Better experiments and measurements of network

structure 7.  Robustness and Security

Motivating examples/applications


Application 1 (1736): First Use of Graphs Seven Bridges of Königsberg

  Seven Bridges of Königsberg – one of the Mirst problems in graph theory

  Is there a route that crosses each bridge only once and returns to the starting point?

We will see how this problem can be solved by modeling it as a graph theory problem later


Application 2 (1850s): Cholera Pandemic: John Snow

First Cholera Pandemic

Second Cholera Pandemic

  During this time germ theory of diseases was not widely accepted.

 During John Snow's life time there were three pandemics of Asiatic cholera (1817-‐23, 1826-‐37 and 1846-‐63), two of which reached the British isles.

  The epidemic in 1848 to 1849, killed between 50,000 and 70,000 in England and Wales. A third outbreak in 1854 left over 30,000 people dead in London alone.

 Vibrio cholerae: Toxin alters sodium pump in intestinal cells Mluid loss

 Entry: oral Colonization: small intestine Symptoms: nausea, diarrhea, muscle cramps, shock

http://www.ph.ucla.edu/epi/snow.html


Application 3 (1950-60) Segregation (Schelling): Micromotives to Macrobehavior

  Duncan and Duncan’s (1957) study of Chicago   1940-‐1950 Census tracts, mixed neighborhoods all segregate

  Placed pennies and dimes on a chess board and moved them around according to various rules.   Board = city, Square = Housing lot, agent: at a location   Pennies and dimes = agents representing two groups in society,

e.g. boys and girls, smokers and non-‐smokers, etc.   Neighborhood =adjacent locations on the board   Happy if (neighbors of same type > threshold)   If Unhappy then move to a random location that is happy

  Result: Many basic conMigurations produce segregation   relate decisions about where to live (micro) to patterns of

segregation (macro)   No obvious relationship between individual behavior and

aggregate outcomes.   Behavior is interdependent. Individuals’ behaviors depend on

social context (micro)   Individual behaviors collectively change social context (long

term, macro)

http://cs.gmu.edu/~eclab/projects/mason/projects/schelling/


Application 4: Power grids and cascading failures

  Vast system of electricity generation, transmission & distribution is essentially a single network

  Power Mlows through all paths from source to sink (Mlow calculations are important for other networks, even social ones)

  All AC lines within an interconnect must be in sync

  If frequency varies too much (as line approaches capacity), a circuit breaker takes the generator out of the system

  Larger Mlows are sent to neighboring parts of the grid – triggering a cascading failure


Application 4: Blackout of 2003:

  Electrical Infrastructure Affected   Area of 50 million people in eight US states and two provinces in Canada

  Approximately61,800Megawatts(MW)oMload

  Most cascaded happen extremely rapidly from 4.10 pm to 4.13 pm

  Human and information system error also contributed to the cascade

  Other Infrastructures including water, communication, and most notably transportation (rail, road and air) were affected

  TV and radio stations also affected


Timeline for 2003 Blackout: Need for Multi-level networks

The 2003 blackout wasn't just about fallen trees and broken transmission lines. As this timeline from the Department of Energy report shows, it resulted from a combination of many grid events,

computer glitches, and human interaction.


Blackout of 2003:Time Line – The Initial Phase   12:15 p.m. Incorrect telemetry data renders inoperative the state estimator, a power Mlow

monitoring tool operated by the Indiana-‐basedMidwest Independent Transmission System Operator (MISO). An operator corrects the telemetry problem but forgets to restart the monitoring tool.

  1:31 p.m. The Eastlake, Ohio generating plant shuts down. The plant is owned by FirstEnergy, an Akron, Ohio-‐based company that had experienced extensive recent maintenance problems.

  2:02 p.m. The Mirst of several 345 kV overhead transmission lines in northeast Ohio fails due to contact with a tree in Walton Hills, Ohio.

  2:14 p.m. An alarm system fails at FirstEnergy's control room and is not repaired.   3:05 p.m. A 345 kV transmission line known as the Chamberlain-‐Harding line fails in Parma, south

of Cleveland, due to a tree.   3:17 p.m. Voltage dips temporarily on the Ohio portion of the grid. Controllers take no action.   3:32 p.m. Power shifted by the Mirst failure onto another 345 kV power line, the Hanna-‐Juniper

interconnection, causes it to sag into a tree, bringing it ofMline as well. While MISO and FirstEnergy controllers concentrate on understanding the failures, they fail to inform system controllers in nearby states.

  3:39 p.m. A FirstEnergy 138 kV line fails in northern Ohio.   3:41 p.m. A circuit breaker connecting FirstEnergy's grid with that of American Electric Power is

tripped as a 345 kV power line (Star-‐South Canton interconnection) and Mifteen 138 kV lines fail in rapid succession in northern Ohio.

http://en.wikipedia.org/wiki/Northeast_Blackout_of_2003


Blackout of 2003: Timeline -- the cascade begins

  3:46 p.m. A Mifth 345 kV line, the Tidd-‐Canton Central line, trips ofMline.

  4:05:57 p.m. The Sammis-‐Star 345 kV line trips due to undervoltage and overcurrent interpreted as a short circuit. Later analysis suggests that the blackout could have been averted prior to this failure by cutting 1.5 GW of load in the Cleveland–Akron area.

  4:06–4:08 p.m. Sustained power surge north toward Cleveland overloads 3 138 kV lines.

  4:09:02 p.m. Voltage sags deeply as Ohio draws 2 GW of power from Michigan, creating simultaneous undervoltage and overcurrent conditions as power attempts to Mlow in such a way as to rebalance the system's voltage.

  4:10:34 p.m. Many transmission lines trip out, Mirst in Michigan and then in Ohio, blocking the eastward Mlow of power around the south shore of Lake Erie. Suddenly bereft of demand, generating stations go ofMline, creating a huge power deMicit. In seconds, power surges in from the east, overloading east-‐coast power plants whose generators go ofMline as a protective measure, and the blackout is on.

  4:10:37 p.m. The eastern and western Michigan power grids disconnect from each other. Two 345 kV lines in Michigan trip. A line that runs from Grand Ledge to Ann Arbor known as the Oneida-‐Majestic interconnection trips. A short time later, a line running from Bay City south to Flint in Consumers Energy's system known as the Hampton-‐Thetford line also trips.

  4:10:38 p.m. Cleveland separates from the Pennsylvania grid.


Blackout of 2003: Timeline -- Crescendo

  4:10:39 p.m. 3.7 GW power Mlows from the east along the north shore of Lake Erie, through Ontario to southern Michigan and northern Ohio, a Mlow more than ten times greater than the condition 30 seconds earlier, causing a voltage drop across the system. 4:10:40 p.m. Flow Mlips to 2 GW eastward from Michigan through Ontario (a net reversal of 5.7 GW of power), then reverses back westward again within a half second.

  4:10:40 p.m. Flow Mlips to 2 GW eastward from Michigan through Ontario (a net reversal of 5.7 GW of power), then reverses back westward again within a half second.

  4:10:43 p.m. International connections between the United States and Canada begin failing.   4:10:45 p.m. Northwestern Ontario separates from the east when the Wawa-‐Marathon 230 kV

line north of Lake Superior disconnects. The Mirst Ontario power plants go ofMline in response to the unstable voltage and current demand on the system.

  4:10:46 p.m. New York separates from the New England grid.   4:10:50 p.m. Ontario separates from the western New York grid.   4:11:57 p.m. The Keith-‐Waterman, Bunce Creek-‐Scott 230 kV lines and the St. Clair-‐Lambton #1

230 kV line and #2 345 kV line between Michigan and Ontario fail.   4:12:03 p.m. Windsor, Ontario and surrounding areas drop off the grid.   4:12:58 p.m. Northern New Jersey separates its power-‐grids from New York and the Philadelphia

area, causing a cascade of failing secondary generator plants along the Jersey coast and throughout the inland west.

  4:13 p.m. End of cascading failure. 256 power plants are off-‐line, 85% of which went ofMline after the grid separations occurred, most due to the action of automatic protective controls.


Milgram’s Small World Experiment   Travers & Milgram 1969: classic early social

network study   destination: a Boston stockbroker; lived in Sharon, MA

  sources: Nebraska stockowners;   forward letter to a Mirst-‐name acquaintance “closer” to target

  Information provided:   name, address, occupation, Mirm, college, wife’s name and hometown

  navigational value?   Basic Mindings:

  64 of 296 chains reached the target   20% of senders reached target.   average chain length = 6.5: “Six degrees of separation”   average length of completed chains: 5.2

  interaction of chain length and navigational difMiculties

  main approach routes: home (6.1) and work (4.6)

  Boston sources (4.4) faster than Nebraska (5.5)   no advantage for Nebraska stockowners

NE

MA


Recent small world experiment

Setup   Email experiment Dodds,

Muhamad, Watts, Science 301, (2003)

  18 targets, 13 different countries 60,000+ participants

  a professor at an Ivy League university,

  an archival inspector in Estonia,   a technology consultant in India,   a policeman in Australia,   a veterinarian in the Norwegian

army.

Basic Analysis   Approximate 37% participation rate

approximately .   Probability of a chain of length 10

getting through:   .3710 ~ 5 x 10-‐5   so only one out of 20,000 chains would

make it   actual # of completed chains: 384

(1.6% of all chains).   Average path length: 4, median: 7   Small changes in attrition rates lead to

large changes in completion rates   e.g., a 15% decrease in attrition rate

would lead to a 800% increase in completion rate


Estimating ‘recovered’ chain lengths for uncompleted chains

  <L> = 4.05 for all completed chains   L* = Estimated `true' median chain length   Intra-‐country chains: L* = 5   Inter-‐country chains: L* = 7   All chains: L* = 7   Milgram: L * ~ 8-‐9 hops


Attrition rate stays approx. constant throughout

  rL – probability of not passing on the message at distance L from the source

average 95 % confidence interval


Estimated ‘recovered’ chain lengths

  observed chain lengths

  ‘recovered’ histogram of path lengths

  inter-‐country intra-‐country


Small world experiment at Columbia

 Successful chains disproportionately used   weak ties (Granovetter)   professional ties (34% vs. 13%)   ties originating at work/college   target's work (65% vs. 40%)

 . . . and disproportionately avoided   hubs (8% vs. 1%) (+ no evidence of funnels)   family/friendship ties (60% vs. 83%)

 Strategy: Geography -‐> Work


How many hops actually separate any two individuals in the world?

  Participants are not perfect in routing messages   They use only local information   “The accuracy of small world chains in social networks”

Peter D. Killworth, Chris McCarty , H. Russell Bernard& Mark House:   Analyze 10920 shortest path connections between 105 members of an interviewing bureau,

  together with the equivalent conceptual, or ‘small world’ routes, which use individuals’ selections of intermediaries.

  This permits the Mirst study of the impact of accuracy within small world chains.

  The mean small world path length (3.23) is 40% longer than the mean of the actual shortest paths (2.30)

  Model suggests that people make a less than optimal small world choice more than half the time.


Tentative Schedule

  Week 1 – Module 1. December 1-‐2 (Wednesday, & Thursday)   Wednesday(1st December): Introduction to Network Science   Thursday(2nd December): SDS and Diffusion on Networks,   Friday (Extra Class if interest): EpiCure – modeling environment for studying

malware propagation in wireless networks.   Week 2 – Module 2 December 7-‐9 (Monday, Tuesday, Thursday)

  Monday (6th December): Control and InMluence maximization   Tuesday (7th December): Branching process result, proof of Fastdiffuse. Introduction to

various diffusion style modeling environments   Wednesday (Extra class if interest): Population and Network Synthesis. Introduction

to graph analysis   Thursday (9th December): SIMDEMICS and related modeling environments.

  Week 3 – Module 3 and Module 4 (December 13-‐16)   Monday (13th December): Markets, Games, Mechanism Design and SIGMA: a modeling

environment to study commodity markets on networks,   Tuesday (14th December): Shortest Paths, Formal language constrained paths, Greedy

routing, routing in small world networks, Introduction to TRANSIMS.   Thursday (15th December): Concluding remarks, Brief discussion of uncovered topics,

Open Problems, Directions for Future Work.