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It’s a “small world” after all
1. It’s a “small world” after all - Social networks and their modeling Michael Li, Ph.D Incubator2.cn [email_address] CBC2006, Hangzhou, PRC October 29, 2006
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3. What are Social Networks? “ To speak of social life is to speak of the association between people – their associating in work and in play, in love and in war, to trade or to worship, to help or to hinder. It is in the social relations men establish that their interests find expression and their desires become realized.” Peter M. Blau Exchange and Power in Social Life , 1964
4. Society Nodes : individuals Links : social relationship (family/work/friendship/etc.)
7. Paul Erdös collaboration graph Erdös had 507 direct collaborators (Erdös # of 1), many of whom have other collaborators (Erdös #2). Source: Valdis Krebs
10. The Erdös-Rényi model Albert and Barabasi. REVIEWS OF MODERN PHYSICS, 74 2002 48-97 N nodes, every pair of nodes being connected with probability p Modeling Social Networks – 1. Random Nets
11. Watts and Strogatz. Nature (1998) 393 440-442 Starting from a ring lattice with n vertices and k edges per vertex, each edge is rewired at random with probability p. Interpolating between regular and random networks Modeling Social Networks – 2. Small World Nets
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14. Across a large number of substantive settings, Barab á si points out that the distribution of network involvement ( degree ) is highly and characteristically skewed. Modeling Social Networks – 3. Scale Free Nets
15. Many large networks are characterized by a highly skewed distribution of the number of partners (degree)
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17. Nodes : actors Links : cast jointly N = 212,250 (actors) k = 28.78 P(k) ~k^(- ) =2.3 Days of Thunder (1990) Far and Away (1992) Eyes Wide Shut (1999) Movies Net
18. The importance of the connected nodes in the scale-free network: 27% of the nodes are reached by the five most connected nodes, in the scale-free network more than 60% are reached. Comparing Random Vs. Scale-free Networks (both with 130 nodes and 215 links) Modified from Albert et al. Science (2000) 406 378-382 Five nodes with most links First neighbors of red nodes
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20. Examples of real networks with power law degree distributions Modeling Social Networks – 3. Scale Free Nets Network Nodes Links/Edges Attributes World-Wide Web Web pages Hyperlinks Directed Internet Computers and Routers Wires and cables Undirected Actor Collaboration Actors Films Undirected Science Collaboration Authors Papers Undirected Citation Articles Citation Directed Phone-call Telephone Number Phone call Directed Power grid Generators, transformers and substations High voltage transmission lines Directed
21. Albert and Barabasi. REVIEWS OF MODERN PHYSICS, 74 2002 48-97 Many real networks are small-world networks
24. Failure: Removal of a random node. Attack: The selection and removal of a few nodes that play a vital role in maintaining the network’s connectivity. Failure and Attack Albert et al. Science (2000) 406 378-382 a macroscopic snapshot of Internet connectivity by K. C. Claffy Future Directions: Network Topology and Dynamics
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