Social Networks & Complex Networks Presenter: Xiao － Yang Liu Date: Paul Erdős Stanley Milgram

Celebrities (1/4) Albert-László Barabási Professor at the Northeastern University; Director of the Center for Complex Network Research; Hometown: Csíkszereda, Harghita County, Hungary; Most cited publications Mean-field theory for scale-free random networks Physica A 272, (1999). Emergence of scaling in random networks Science 286, (1999). Diameter of the World Wide Web Nature 401, (1999). The large-scale organization of metabolic networks Nature 407, (2000). Error and attack tolerance in complex networks Nature 406, 378 (2000). Topology of evolving networks: Local events and universality Physical Review Letters 85, 5234 (2000). Lethality and centrality in protein networks Nature 411, (2001). Hierarchical organization of modularity in metabolic networks Science 297, (2002). Statistical mechanics of complex networks Review of Modern Physics 74, (2002). Network Biology: Understanding the cells's functional organization Nature Reviews Genetics 5, (2004). 《 Linked: The new science of networks 》 Perseus Books Group; 1st edition (May 14, 2002)

Celebrities (2/4) Duncan Watts Principal Research Scientist at the Yahoo! Research ; Director of the Human Social Dynamics group; Adjunct senior research fellow at Columbia University Ph.D. in Theoretical and Applied Mechanics from Cornell University. Most cited publications Collective dynamics of 'small-world' networks Nature, 1998 Scaling and percolation in the small-world network model Physical Review E, 1999 Random graphs with arbitrary degree distributions and their applications Physical Review E, 2001 Identity and search in social networks Science, 2002 Experimental study of inequality and unpredictability in an artificial cultural market Science, 2006 A 21st Century ScienceNature, 2007 Social Search in "Small-World" ExperimentsWorld Wide Web (WWW), 2009 《 Six Degrees: The Science of a Connected Age 》 W. W. Norton & Company; 1st edition (February 2003)

Celebrities (3/4) Steven Strogatz Professor at the Cornell University; Director of the Center for Applied Mathematics; BA at Princeton, PhD. at Harvard, Taught in the Department of Mathematics at MIT, Joined the Cornell faculty in Most cited publications Collective dynamics of 'small-world' networks. Nature 393: (1998). Exploring complex networks. Nature 410: (2001). Modeling the dynamics of language death. Nature 424: 900 (2003). Crowd synchrony on the Millennium Bridge.Nature 438: (2005). 《 The Calculus of Friendship: What a Teacher and a Student Learned about Life while Corresponding about Math 》 Perseus Books Group; 1st edition (May 14, 2002) “The best teachers are not always the ones who teach us the most in class, or the ones we choose initially or consciously to be our mentors. Sometimes, they are simply the ones who love the thing we love, or who guide us by example. ”

Celebrities (4/4) Mark Newman Professor at the University of Michigan; Department of Physics and Center for the Study of Complex Systems Most cited publications The structure of scientific collaboration networks PNAS, USA 98, (2001). Random graphs with arbitrary degree distributions and their applications M. E. J. Newman, S. H. Strogatz, and D. J. Watts, Phys. Rev. E 64, (2001). Assortative mixing in networksPhys. Rev. Lett. 89, (2002). The structure and function of complex networksSIAM Review 45, (2003). Diffusion-based method for producing density equalizing maps PNAS, USA 101 (20), (2004). Modularity and community structure in networks PNAS, USA 103, (2006). Hierarchical structure and the prediction of missing links in networks Nature 453, 98–101 (2008). 《 Networks: An Introduction 》 Oxford University Press, USA; 1 edition (May 20, 2010)

Co-author Graph

Agenda Social Networks Property Characterization Does it help? Social Networks on the way

Social Networks(1/2) Internet, Predator-prey interactions Forum, Co-authorship, Sexual contact, Social network sites (SNS)

Social Networks (2/2) What is social networks ? A social network is a set of people or groups of people with some pattern of contacts or interactions between them. ( 狭义的定义 ) A certain kind of networks with the following properties: (1) Small-World （ Diameter ： 弱 “ 六度空间 ” ） (2) Scale-free (Degree distribution: power-law ) (3) Densification: #{Edges} grows faster then #{nodes}; (4) Transitivity or clustering (5) Community structure (6) Network navigation (7) Network resilience ……

Property Characterization(1/7) The famous experiment by Stanley Milgram Steps: 1. Add your name to the poster at the bottom of the sheet; 2. Detach one postcard. Fill it out and return it to Harvard university; 3. If you know the target person on a personal basis, mail this folder directory to him/her. 4. If you do not know the target person on a personal basis, do not try to contact him directly. Instead, mail this folder to a personal acquaintance who is more likely than you to know the target person. Results: 1. Small-world Milgram, S., The small world problem ， Psychology Today (1967) 2. Effective navigation in the “small world” J. Kleinberg, Navigation in a small world, Nature, August, 2000 N1N2N3Nn

Property Characterization(2/7) Small-world (or Six degree of separation) Despite their often large size, in most networks there is a relatively short path between any two nodes. E.g. Actors of Hollywood : 3; Chemicals in a cell ： 3; (Internet: 3.31 ; WWW: / about 19 ) (Paul Erdős) Small-world isn’t a indication of a particular organizing principle.

Property Characterization(3/7) Small-world Relational Graph: Mechanism: (Reducing path length by adding a small number of short-cuts.) Physical links (long distance with low rate; high-low bar?); Logical links; Spatial Graph: Regular  Small-world  Random Initial Deployment  Mobility?  (Random mobile networks) Usages: 1. The maximum hops that a packet may travel before expiration, in the internet, P2P networks, opportunistic mobile networks, etc.; 2. The spreading of information/opinion is quite fast than expectation. And also the spreading of disease or virus; 3. (?) Using the shortest path for packet forwarding: low delay, energy efficient, higher capacity, etc; 1. Collective dynamics of 'small-world' networks Nature, Diameter of the World Wide Web Nature 401, (1999) 3. Diameter of opportunistic mobile networks CoNEXT 2007 (Best Paper) 4. Densification arising from sampling fixed graphs (SIGMETRICS 2008) 4. Tight lower bunds for greedy routing in uniform small world rings. (STOC 2009) 5. Affiliation networks. (Small-world, scale-free, densification STOC 2009) 6. On the searchability of small-world networks with arbitrary underlying structure. (STOC 2010)

Property Characterization(4/7) Degree distribution (Power law) A famous experiment taken on the Internet; Contributions: 1. Organization principle of the internet; 2. Finding order in chaos (Not purely random); 3. Random graph expired in the biggest real world network. (Next page.) 1. On power-law relationships of the internet topology SIGCOMM Emergence of scaling in random networks Science 286, (1999). Inter_Router SIGCOMM 99 Actor Collaboration Science 99

Property Characterization(5/7) Degree distribution Random Graphs: Binomial Distribution For large N, it can be replaced by Poisson Distribution Social Networks (Power law) Power law everywhere !! Scale-free: scale invariant! Modeled by preferential attachment ( Densification) (Emergence of scaling in random networks Science 286, (1999).) Inter_Router SIGCOMM 99 Actor Collaboration Science 99

Property Characterization(6/7) Giant component Random graph has this property already. Percolation Theory (P=0.5) Phase Transition (3) Densification: (4) Transitivity or clustering (5) Community structure (7) Network resilience

Property Characterization(7/7) Network Resilience Bigger, more skewed, more nodes with big degree. (Edge removal and node removal)

Social Networks (4/4) Does it help?

Does it help ? (1/5) People-related Social networks An Analysis of Social Network-Based Sybil Defenses. (SIGCOMM 2010) Sybil Attack ―Attack by forging identities in P2P networks. ―Named after the subject of the book Sybil, a case study of a woman with multiple personality disorder. Social Network ―Individuals: called “nodes” ―Interdependency: friendship, financial exchange, etc.

Does it help ? (2/5) Communication networks Network Diversity and Economic Development (Science, May, 2010)

Does it help ? (3/5) Life-related networks The Fragility of interdependency (Nature, April 2010) The fragility of travelling networks, electric power grid network, telecommunications, water- supply systems!

Does it help ? (4/5) Providing insights for life “Link communities reveal multiscale complexity in networks.” Nature, 2010.

Does it help ? (5/5) Disease / virus / opinion Spreading A high-resolution human contact network for infectious disease transmission (PNAS November 2010) Understanding the spreading patterns of mobile phone viruses. (Science 2009)

Thank you!