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Complex Networks Analysis @ Universita Roma Tre


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lecture done on 03/06/2013 @ Università degli Studi Roma Tre

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Complex Networks Analysis @ Universita Roma Tre

  1. 1. Complex Networks Analysis 3-6-2013 Università degli Studi Roma Tre Matteo Moci @matteomoci
  2. 2. Why?
  3. 3. Complex systems are around us
  4. 4. 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
  5. 5. Graph theory: 1735, Euler Social Network Research: 1930s, Moreno Communication networks/internet: 1960s Ecological Networks: 1979 History
  6. 6. The Seven Bridges of Königsberg
  7. 7. The Seven Bridges of KönigsbergThe Seven Bridges of Königsberg
  8. 8. What's next? "I think the next century will be the century of complexity” S. Hawking
  9. 9. 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)
  10. 10. Graph Modeling
  11. 11. Single-relational, un-directed G (V, E ⊆ (V x V))
  12. 12. Single-relational, un-directed G (V, E ⊆ (V x V)) friend friend friend Alex Bob Carla
  13. 13. Multi-relational, directed G (V, E) E = (E0, E1, …, Em (V x V)) favourited watched follows watched Alex Bob
  14. 14. Points of view
  15. 15. 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
  16. 16. Examples WWW > directed Protein Interactions > undirected, unweighted Collaboration network > undirected or weighted Mobile phone calls > directed, weighted Facebook Friendship links > undirected, unweighted.
  17. 17. Most graph databases support a graph data model, known as property graph A property graph is a directed, multi-relational graph
  18. 18. Graph morphisms
  19. 19. Graph properties and measures Degree distribution P(k) Average path length <d> Clustering coefficient C
  20. 20. Types of Networks Random Power-law Scale-free (preferential attachment) Small-world (small diameter, high clustering)
  21. 21. How does the Web "work"?
  22. 22. 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
  23. 23. 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)
  24. 24. Social Networks A social structure, determined by interactions between individuals, groups, organisations
  25. 25. Social Networks' Properties Homophily Social Influence
  26. 26. The tendency of individuals to associate and bond with similar others "birds of a feather flock together" Homophily
  27. 27. 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* *
  28. 28. Social Influence Why does it work? Reciprocity Commitment and Consistency Social Proof Authority Liking Scarcity
  29. 29. Can we measure and maximise influence? Goal: "Cascades"
  30. 30. 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?
  31. 31.
  32. 32. Influence is related to many aspects! Thesis: Sviluppo di un Framework per il Calcolo dell’Influenza su Twitter Edoardo Venturini @edoventurini
  33. 33. Popularity
  34. 34. Activity
  35. 35. Engagement
  36. 36. Topic Relevance
  37. 37. Influence Maximization Problem NP-Complete Heuristics • Simulated Annealing
  38. 38. Q&A Matteo Moci @matteomoci