Complex Networks Analysis @ Universita Roma Tre
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This document discusses complex networks and their analysis. It provides a brief history of network analysis starting in the 18th century with Euler's work on the Seven Bridges of Königsberg problem. It then covers key topics like different types of networks, graph modeling approaches, measures to analyze networks, and applications of network analysis to domains like the web, social networks, and disease spreading. The document emphasizes that understanding network structure and interactions is important for studying complex systems and influences within networks.
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Complex Networks Analysis @ Universita Roma Tre
- 1. Complex Networks Analysis 3-6-2013 Università degli Studi Roma Tre Matteo Moci @matteomoci moci@cybion.it
- 2. Why?
- 7. Complex systems No blueprint No “master-mind” Self-organization Evolution Adaptation Behind each complex system there is a network, that defines the interactions between the components
- 8. Graph theory: 1735, Euler Social Network Research: 1930s, Moreno Communication networks/internet: 1960s Ecological Networks: 1979 History
- 9. The Seven Bridges of Königsberg
- 10. The Seven Bridges of KönigsbergThe Seven Bridges of Königsberg
- 11. What's next? "I think the next century will be the century of complexity” S. Hawking
- 12. Network or Graph? Network often refers to real systems • www, • social network • metabolic network. Language: (Network, node, link) Graph: mathematical representation of a network • web graph, • social graph (a Facebook term) Language: (Graph, vertex, edge)
- 14. Single-relational, un-directed G (V, E ⊆ (V x V))
- 15. Single-relational, un-directed G (V, E ⊆ (V x V)) friend friend friend Alex Bob Carla
- 16. Multi-relational, directed G (V, E) E = (E0, E1, …, Em (V x V)) favourited watched follows watched Alex Bob
- 18. Different problems, different models The choice of the proper network representation determines our ability to use network theory successfully. In some cases there is a unique, unambiguous representation. In other cases, the representation is by no means unique The way we assign the links between a group of individuals will determine the nature of the question we can study
- 19. Examples WWW > directed Protein Interactions > undirected, unweighted Collaboration network > undirected or weighted Mobile phone calls > directed, weighted Facebook Friendship links > undirected, unweighted.
- 20. Most graph databases support a graph data model, known as property graph A property graph is a directed, multi-relational graph
- 22. Graph properties and measures Degree distribution P(k) Average path length <d> Clustering coefficient C
- 23. Types of Networks Random Power-law Scale-free (preferential attachment) Small-world (small diameter, high clustering)
- 24. How does the Web "work"?
- 25. How does the Web "work"? • Content analysis (text mining) • Link analysis (e.g. PageRank) PageRank is an algorithm that assigns a numerical weighting to each element of a set of documents
- 27. Importance of a Node • Degree centrality (# of links) • Betweenness centrality (# of shortest-paths) • Closeness centrality (mean distance to neighbours) • PageRank (P that a random walker visits that node)
- 28. Social Networks A social structure, determined by interactions between individuals, groups, organisations http://www.flickr.com/photos/hanspoldoja/5001818922/
- 29. Social Networks' Properties Homophily Social Influence
- 30. The tendency of individuals to associate and bond with similar others "birds of a feather flock together" Homophily http://www.flickr.com/photos/57574984@N00/81938785/
- 31. Social Influence One's emotions, opinions, or behaviors are affected by others Social networks transmit states and behaviors such as obesity, smoking, drinking and happiness* * http://www.bmj.com/content/337/bmj.a2338
- 32. Social Influence Why does it work? Reciprocity Commitment and Consistency Social Proof Authority Liking Scarcity http://en.wikipedia.org/wiki/Special:BookSources/0321011473
- 33. Can we measure and maximise influence? Goal: "Cascades" http://www.youtube.com/watch?v=GA8z7f7a2Pk
- 34. Disease spreading • Where to place monitoring stations to detect epidemics? Blogs • Which are the influential blogs? • Which blogs create big cascades? Viral marketing • Who are the influencers? • Where should I advertise?
- 36. Influence is related to many aspects! Thesis: Sviluppo di un Framework per il Calcolo dell’Influenza su Twitter Edoardo Venturini @edoventurini
- 37. Popularity
- 39. Engagement
- 40. Topic Relevance
- 41. Influence Maximization Problem NP-Complete Heuristics • Simulated Annealing