Transcript of "Are Randomly Grown Graphs Really Random?"
Abhranil Das Spring 2012
Real vs. Random• Many real networks grow.• These have highly skewed degree distributions: often a power law.• Random graphs usually have Poisson distribution
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.
Degree EvolutionEquations are approximate only in the short term.
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).