Eikonal Blog


Applied graph theory (“Social Networks Analysis”)


Graph theory:

  • nodes and edges
  • degree = number of edges for a given node
  • isolated nodes
  • connected nodes
  • hub = well connected node
  • Scale-free networks = average number of nodes stays constant
  • preferential attachment:
    • the fraction of nodes with k edges: p(k) \sim k^{-\gamma}
    • a long tail distribution
  • Degree of distribution

SNAs on YouTube

Six degrees of separation, Small Worlds, Kevin Bacon metric, Erdos metric, etc


Authors and Sites


  • “Power laws, Pareto distributions and Zipf’s law” by M.E.J. Newman (arXiv) – http://arxiv.org/abs/cond-mat/0412004
    • When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf’s law or the Pareto distribution. Power laws appear widely in physics, biology, earth and planetary sciences, economics and finance, computer science, demography and the social sciences. For instance, the distributions of the sizes of cities, earthquakes, solar flares, moon craters, wars and people’s personal fortunes all appear to follow power laws. The origin of power-law behaviour has been a topic of debate in the scientific community for more than a century. Here we review some of the empirical evidence for the existence of power-law forms and the theories proposed to explain them.
    • more papers by M.E.J. Newman at arXiv – arxiv.org/find/cond-mat/1/au:+Newman_M/0/1/0/all/0/1



  • “Gossip or “Viruses in the Body Politic” by Rod Graham (2010.08.07) – http://grahamsoc.wordpress.com/2010/08/07/gossip-or-viruses-in-the-body-politic/
  • “The effect of gossip on social networks” by Allison K. Shaw, Milena Tsvetkova and Roozbeh Daneshvar (Complexity; 2010.08.17; DOI: 10.1002/cplx.20334) – http://onlinelibrary.wiley.com/doi/10.1002/cplx.20334/abstract
      Abstract: In this article, we develop a simple model for the effect of gossip spread on social network structure. We define gossip as information passed between two individuals A and B about a third individual C which affects the strengths of all three relationships: it strengthens A-B and weakens both B-C and A-C. We find, in both an analytic derivation and model simulations, that if gossip does not spread beyond simple triads, it destroys them but if gossip propagates through large dense clusters, it strengthens them. Additionally, our simulations show that the effect of gossip on network metrics (clustering coefficient, average-path-length, and sum-of-strengths) varies with network structure and average-node-degree.

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