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Socialnetworkanalysis (Tin180 Com)


Published on - Trang tin tức văn hóa lành mạnh - Trang tin tức văn hóa lành mạnh

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    • 1. Social Network Analysis
      • Social Network Introduction
      • Statistics and Probability Theory
      • Models of Social Network Generation
      • Networks in Biological System
    • 2. Society Nodes : individuals Links : social relationship (family/work/friendship/etc.) S. Milgram (1967) Social networks: Many individuals with diverse social interactions between them. John Guare Six Degrees of Separation
    • 3. Communication networks The Earth is developing an electronic nervous system, a network with diverse nodes and links are -computers -routers -satellites -phone lines -TV cables -EM waves Communication networks: Many non-identical components with diverse connections between them.
    • 4. New York Times Complex systems Made of many non-identical elements connected by diverse interactions . NETWORK
    • 5. “ Natural” Networks and Universality
      • Consider many kinds of networks:
        • social, technological, business, economic, content,…
      • These networks tend to share certain informal properties:
        • large scale; continual growth
        • distributed, organic growth: vertices “decide” who to link to
        • interaction restricted to links
        • mixture of local and long-distance connections
        • abstract notions of distance: geographical, content, social,…
      • Do natural networks share more quantitative universals?
      • What would these “universals” be?
      • How can we make them precise and measure them?
      • How can we explain their universality?
      • This is the domain of social network theory
      • Sometimes also referred to as link analysis
    • 6. Some Interesting Quantities
      • Connected components :
        • how many, and how large?
      • Network diameter :
        • maximum (worst-case) or average?
        • exclude infinite distances? (disconnected components)
        • the small-world phenomenon
      • Clustering :
        • to what extent that links tend to cluster “locally”?
        • what is the balance between local and long-distance connections?
        • what roles do the two types of links play?
      • Degree distribution :
        • what is the typical degree in the network?
        • what is the overall distribution?
    • 7. A “Canonical” Natural Network has…
      • Few connected components:
        • often only 1 or a small number, indep. of network size
      • Small diameter:
        • often a constant independent of network size (like 6)
        • or perhaps growing only logarithmically with network size or even shrink?
        • typically exclude infinite distances
      • A high degree of clustering:
        • considerably more so than for a random network
        • in tension with small diameter
      • A heavy-tailed degree distribution:
        • a small but reliable number of high-degree vertices
        • often of power law form
    • 8. Probabilistic Models of Networks
      • All of the network generation models we will study are probabilistic or statistical in nature
      • They can generate networks of any size
      • They often have various parameters that can be set:
        • size of network generated
        • average degree of a vertex
        • fraction of long-distance connections
      • The models generate a distribution over networks
      • Statements are always statistical in nature:
        • with high probability , diameter is small
        • on average , degree distribution has heavy tail
      • Thus, we’re going to need some basic statistics and probability theory
    • 9. Zipf’s Law
      • Look at the frequency of English words:
        • “ the” is the most common, followed by “of”, “to”, etc.
        • claim: frequency of the n-th most common ~ 1/n (power law, α = 1)
      • General theme:
        • rank events by their frequency of occurrence
        • resulting distribution often is a power law!
      • Other examples:
        • North America city sizes
        • personal income
        • file sizes
        • genus sizes (number of species)
      • People seem to dither over exact form of these distributions (e.g. value of α ), but not heavy tails
    • 10. Zipf’s Law Linear scales on both axes Logarithmic scales on both axes The same data plotted on linear and logarithmic scales. Both plots show a Zipf distribution with 300 datapoints
    • 11. Social Network Analysis
      • Social Network Introduction
      • Statistics and Probability Theory
      • Models of Social Network Generation
      • Networks in Biological System
      • Summary
    • 12. Some Models of Network Generation
      • Random graphs (Erdös-Rényi models):
        • gives few components and small diameter
        • does not give high clustering and heavy-tailed degree distributions
        • is the mathematically most well-studied and understood model
      • Watts-Strogatz models:
        • give few components, small diameter and high clustering
        • does not give heavy-tailed degree distributions
      • Scale-free Networks:
        • gives few components, small diameter and heavy-tailed distribution
        • does not give high clustering
      • Hierarchical networks:
        • few components, small diameter, high clustering, heavy-tailed
      • Affiliation networks:
        • models group-actor formation
    • 13. The Clustering Coefficient of a Network
      • Let nbr(u) denote the set of neighbors of u in a graph
        • all vertices v such that the edge (u,v) is in the graph
      • The clustering coefficient of u:
        • let k = |nbr(u)| (i.e., number of neighbors of u)
        • choose(k,2): max possible # of edges between vertices in nbr(u)
        • c(u) = ( actual # of edges between vertices in nbr(u))/choose(k,2)
        • 0 <= c(u) <= 1; measure of cliquishness of u’s neighborhood
      • Clustering coefficient of a graph:
        • average of c(u) over all vertices u
      k = 4 choose(k,2) = 6 c(u) = 4/6 = 0.666…
    • 14. Clustering : My friends will likely know each other! Probability to be connected C » p C = # of links between 1,2,…n neighbors n(n-1)/2 Networks are clustered [large C(p)] but have a small characteristic path length [small L(p)]. The Clustering Coefficient of a Network
    • 15. Erdos-Renyi: Clustering Coefficient
      • Generate a network G according to G(N,p)
      • Examine a “typical” vertex u in G
        • choose u at random among all vertices in G
        • what do we expect c(u) to be?
      • Answer: exactly p!
      • In G(N,m), expect c(u) to be 2m/N(N-1)
      • Both cases: c(u) entirely determined by overall density
      • Baseline for comparison with “more clustered” models
        • Erdos-Renyi has no bias towards clustered or local edges
    • 16. Scale-free Networks
      • The number of nodes (N) is not fixed
        • Networks continuously expand by additional new nodes
          • WWW: addition of new nodes
          • Citation: publication of new papers
      • The attachment is not uniform
        • A node is linked with higher probability to a node that already has a large number of links
          • WWW: new documents link to well known sites (CNN, Yahoo, Google)
          • Citation: Well cited papers are more likely to be cited again
    • 17. Scale-Free Networks
      • Start with (say) two vertices connected by an edge
      • For i = 3 to N:
        • for each 1 <= j < i, d(j) = degree of vertex j so far
        • let Z = S d(j) (sum of all degrees so far)
        • add new vertex i with k edges back to {1, …, i-1}:
          • i is connected back to j with probability d(j)/Z
      • Vertices j with high degree are likely to get more links!
      • “ Rich get richer”
      • Natural model for many processes:
        • hyperlinks on the web
        • new business and social contacts
        • transportation networks
      • Generates a power law distribution of degrees
        • exponent depends on value of k
    • 18.
      • Preferential attachment explains
        • heavy-tailed degree distributions
        • small diameter (~log(N), via “hubs”)
      • Will not generate high clustering coefficient
        • no bias towards local connectivity, but towards hubs
      Scale-Free Networks
    • 19. Social Network Analysis
      • Social Network Introduction
      • Statistics and Probability Theory
      • Models of Social Network Generation
      • Networks in Biological System
      • Mining on Social Network
      • Summary
    • 20. Bio-Map protein-gene interactions protein-protein interactions PROTEOME GENOME Citrate Cycle METABOLISM Bio-chemical reactions
    • 21. Citrate Cycle METABOLISM Bio-chemical reactions Metabolic Network
    • 22. Boehring-Mennheim
    • 23. Metab-movie Nodes : chemicals (substrates) Links : bio-chemical reactions Metabolic Network
    • 24. Meta-P(k) Organisms from all three domains of life are scale-free networks! H. Jeong, B. Tombor, R. Albert, Z.N. Oltvai, and A.L. Barabasi, Nature, 407 651 (2000) Archaea Bacteria Eukaryotes Metabolic Network
    • 25. Bio-Map protein-gene interactions protein-protein interactions PROTEOME GENOME Citrate Cycle METABOLISM Bio-chemical reactions
    • 26. Protein Network protein-protein interactions PROTEOME
    • 27. Prot Interaction map Nodes : proteins Links : physical interactions (binding) P. Uetz, et al. Nature 403 , 623-7 (2000). Yeast Protein Network
    • 28. Prot P(k) H. Jeong, S.P. Mason, A.-L. Barabasi, Z.N. Oltvai, Nature 411, 41-42 (2001) Topology of the Protein Network
    • 29. P53 … “ One way to understand the p53 network is to compare it to the Internet. The cell, like the Internet, appears to be a ‘ scale-free network ’.” p53 Network Nature 408 307 (2000)
    • 30. P53 P(k) p53 Network (mammals)