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Python and networks -- Class notes -- 2016-04-26

1.  Scale-Free model

  • Definition
  • Analytical (continuous) derivation of degree exponent, see 1999 Physica A paper by Barabasi group
    1. Node degree grows as square root of time
    2. Degree distribution is power law with exponent 3

2.  Girvan-Newman clustering

  • "Greedy" (gradient) method of modularity optimization
    • Removing edges in the descending order of their initial edge betweenness centralities
    • Stop at highest modularity, Q
  • Optimization with simulated annealing
    • Many similar high Q values, finding best takes very long
    • Results from greedy method are usually quite close to best