Are Randomly Grown Graphs Really Random?

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A paper that discusses whether randomly grown graphs, as opposed to static random graphs, are truly random.

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Are Randomly Grown Graphs Really Random?

  1. 1. Abhranil Das Spring 2012
  2. 2. Real vs. Random• Many real networks grow.• These have highly skewed degree distributions: often a power law.• Random graphs usually have Poisson distribution
  3. 3. The Model• Start from a single vertex without edges.• At each step a vertex is added.• With probability δ, two vertices are joined with an undirected edge.• At time t: t vertices and δt (avg.) edges.• Different from preferential attachment model.
  4. 4. Degree EvolutionEquations are approximate only in the short term.
  5. 5. Degree Distribution
  6. 6. Component Distribution Evolution
  7. 7. Component Distribution Evolution
  8. 8. Generating Function for Component Distribution
  9. 9. Giant Component Phase Transition
  10. 10. Arbitrary Static Distribution
  11. 11. Comparison with Static Graph
  12. 12. ReferencesAre randomly grown graphs really random?Callaway et al, arXiv:cond-mat/0104546v2, 14 June 2001M. Molloy and B. Reed, Random Structures andAlgorithms 6, 161 (1995).M. Molloy and B. Reed, Combinatorics,Probability and Computing 7, 295 (1998).

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