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Are Randomly Grown Graphs Really Random?
 

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.

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? Are Randomly Grown Graphs Really Random? Presentation Transcript

    • 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.
    • Degree Distribution
    • Component Distribution Evolution
    • Component Distribution Evolution
    • Generating Function for Component Distribution
    • Giant Component Phase Transition
    • Arbitrary Static Distribution
    • Comparison with Static Graph
    • 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).