Large-Scale Network Dynamics: A New Frontier Jie Wang Dept of Computer Science University of Massachusetts Lowell Jie Wang Dept of Computer Science University of Massachusetts Lowell Presented at Dept. of Computer Science, Boston University, Nov. 6, 2009 At Dept. of Computer Science, University of Texas at Dallas, Oct. 30, 2009 At Dept. of Electrical and Computer Engineering, Michigan State Univ., Sept. 24, 2009

2 “The earth to be spann’d, connected by network, The races, neighbors, to marry and be given in marriage, The oceans to be cross’d, the distant brought near, The lands to be welded together” Walt Whitman ( ), Passage to India “The network is the computer” John Gage ( ), Sun Microsystems “The network is the information and the storage” Weibo Gong, UMass Amherst

3 Small-World Phenomenon Two persons are linked if they are coauthors of an article. The Erdős number is the collaboration distance with mathematician Paul Erdős. Six degrees of separation What is your Erdős number? Erdös number person Erdös number people Erdös number people Erdös number people Erdös number people Erdös number people Erdös number people Erdös number people Erdös number people Erdös number people Erdös number people Erdös number people Erdös number people Erdös number people The median Erdös number is 5; the mean is 4.65, and the standard deviation is 1.21

4 The Watts-Strogatz  -Model between order and randomness Small-World Networks - Short mean path; or short characteristic path - Large clustering coefficient

5 What Are Big-World Networks? Acquaintance Networks over Generations From “Mathematics Genealogy Project” Gottfried Leibniz ( ) Jacob Bernoulli ( ) Johann Bernoulli ( ) Leonhard Euler ( ) Joseph Lagrange ( ) Simeon Poisson ( ) Michel Chasles ( ) H. A. Newton ( ) E. H. Moore ( ) Oswald Veblen ( ) Alonzo Church ( ) John B. Rosser ( ) Gerald Sacks (1933 -) 343 academic descendants Stephen HomerJie Wang

6 Scale-Free Phenomenon Power law distribution: f(x) ~ x –α Log-log scale: log f(x) ~ –αlog x Scale-free networks are small-wolrd Small-world may not be scale-free Subnets of scale-free networks may not be scale-free

7 Brain Networks “A mental state M is nothing other than brain state B. The mental state "desire for a cup of coffee" would thus be nothing more than the "firing of certain neurons in certain brain regions.” -- E. G. Boring ( )

8 Are Brain Networks Small-World? Brian networks are highly dynamic Can process 100 trillion instructions per second Some believe brain networks are small-world Mathematical challenge: Work out a mathematical model consistent with brain functionalities There are 100 billion (10 11 ) neurons in the human brain, and 100 trillion (10 14 ) connections (synapses)

9 Connecting the Dots Networks are connected dots “You can't connect the dots looking forward; you can only connect them looking backwards.” Steven Jobs (1955 -)

10 Infectious Disease Spreading How Were Dots Connected? Sept 05 – Sept 12, 2009 Sept 12 – Sept 19, 2009Sept 19 – Sept 26, 2009Sept 26 – Oct 03, 2009Oct 03 – Oct 10, 2009Oct 10 – Oct 17, 2009

11 How Will the Dots Be Connected? Dynamic connections are not deterministic, nor random. But they have patterns and trends. Statistical analysis is like connecting the dots backward, while predicting disease spread is like connecting the dots forward …

12 A Simple Relational Model: The SIR Dynamics Structure-biased k-acquaintance model  Homophily: the tendency to associate with people like yourself  Symmetry: undirected links  Triad closure: the tendency of one’s acquaintances to also be acquainted with each other An 8-acquaitance node under SIR

13 Structure-Biased Spread

14 A Mathematical Model of Spread Prediction

15 Mathematical Epidemiology Most mathematical methods study differential equations based on simplified assumptions of uniform mixing or ad hoc contact processes Example:

16 Percolation and Outbreak Large-scale graphs based on scale-free and small-world models are common platforms to study epidemics Individuals (sites) are connected by social contacts (bonds) Each site is susceptible with probability p and each bond is open with probability q, indicating infectiousness A percolation threshold exists for phase transition of disease spread –When both p and q are high, a cluster of infectious sites connected by open bonds will permeate the entire population, resulting in an outbreak –Otherwise, infectious clusters will be small and isolated

17 Percolation Threshold Demo 65 x 65 grid q = 0.2 q = 0.51q = 0.578

18 Modeling Challenges Population and demographics –urban, suburban, rural, mobility –income, age, gender, education, religion, culture, ethnic background, household size Social contact pattern –household, work, study, shopping, entertainment, travel, medical activities, … –dense and frequent local contacts; sparse and occasional long- distance contacts Infection process –disease characteristics: infectious speed & recovery levels –people's general health level and vaccination history –frequency and duration of contacts B. Liu and J. Wang et al It seems difficult to address these challenges using mathematical methods alone

19 Computational Methods Simulations with contingent parameters –Modeling disease outbreaks in realistic urban social networks (S. Eubank et al. Nature, 2004) –Understanding the spreading patterns of mobile phone viruses (P. Wang et al., Science, 2009) BT susceptible phones within the range of an infected BT phone will all be infected. An MMS virus can infect all susceptible phones whose numbers are in the phonebook of an infected phone

20 Mobile Networks and OSes Location, mobility, and communication pattern dynamics

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22 Online Social Networks (OSNs) Topological dynamics –temporal attribute of node and edge arrivals and departures –explain why the mean degree and characteristic path length tend to be stable over time, while density and scale do not Communication dynamics –friendships vs. activities Mobility dynamics –GPS-enabled smartphones –location-based applications G. Chen, B. Liu, J. Wang et al

23 The Rise of OSNs 1997: SixDegrees allowed users to create profiles, list and surf and friend lists : a number of community tools support profile and friend lists, AsianAvenue, BlackPlanet, MiGente, LiveJournal present : business and professional social network emerged, Ryze, LinkedIn 2003: MySpace attracts teens, bands, among others and grows to largest OSN 2004: Facebook designed for college networking (Harvard), expanded to other colleges, high schools, and other individuals

24 Common OSNs

25 OSNs Go Mobile Location aware –GPS-enabled phones, sharing current location, availability, attaching location to user-generated content Outlook –anticipated $3.3 billion revenue by 2013 Dodgeball, Loopt, Brightkite, Whrrl, Google Latitude, Foursquare

26 PageRank for Measuring Page Popularity Biased Random Walks Just walk at random?

27 Association Rank for Friendship Prediction G. Chen and J. Wang et al

28 Startup in 2005, Denver, CO; opened to public: 2008 User activities –Check in, status update, photo upload –All attached with current location –Updates through SMS, , Web, iPhone … Social graph with mutual connection –See your friends’ or local activity streams

29 Data Trace Brightkite Web APIs 12/9/08-1/9/09: 18,951 active users Back traced to 3/21/08: 1,505,874 updates Profile: age, gender, tags, friends list Social graph: 41,014 nodes and 46,172 links Testing data: next 45 days had 5,098 new links added G. Chen and N. Li

30 Snapshots taken from 12/09/08 to 01/09/09

31 Three Attributes to Measure Community Rank Tags Social Distance Location

32 Probability Measure

33 Tag Graph Metric

34 Social Distance

35 Location Metric

36 Community Rank Value Indicating the likelihood of friendship

37 ROC Curve

38 MySpace Launched in Santa Monica, CA, in 2003 Grew rapidly and attracted Friendster’s users, bands, … Teenagers began joining en masse in 2004 Three distinct populations began to form: – musicians/artists – teenagers – post-college urban social crowd Purchased by News Corporation for $580M in 2005 Arguably the largest online social network site

39 MySpace Profile and Activities Each profile: age, gender, location, last login time, etc; identified by a unique ID –Some profiles claim neutral gender, e.g, bands Profiles can be set to private (default is public) What can users do? –search and add friends to their friend lists –post messages to friend’s blog space Only friends have access to private profile’s friend list and blog space Other functions: IM/Call, Block/Rank User, Add to Group favorite

40 Measurement: SnailCrawler Generate random IDs uniformly between 1 and max (1,500,000,000) Many IDs are not occupied (invalid) Retrieve profile information from MySpace (HTTP) –name, ID, gender, age, location, public/private/custom –other information for public profiles: company, religion, marriage, children, smoke/drink, orientation, zodiac, education, ethnicity, occupation, hometown, body-type, mood, last login, … W. Gauvin, B. Liu, X. Fu, J. Wang et al

41 Data Trace People of 16 years old or younger are protected by law Teenagers and twenties post most blogs False ages at years old Among teenagers 16-19, female publish more than male After 20, no significant differences; often male publish more than female Scanned: 3,090,016 –Blogs: 67,045

42 Blog publish time (on special days) FebSeptDec females publish more than males, and male more than neutral spikes on holidays, e.g., Valentine’s day, Christmas Valentine’s day Christmas

43 Blog publish time (month & week) females publish more than males more blogs posted May to Oct slightly more blogs posted during weekdays SunMon JanDecSun Sat

44 Blog publish time (within a day) big jump at 1 pm people tend to publish from afternoon well into mid-night peak around 10pm, bottom around 5am

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