Percolation on sparse random graphs with given degree sequence

Details Percolation on sparse random graphs with given degree sequence Percolation on sparse random graphs with given degree sequence

2007-03-09

arxiv.org/abs/math/0703269v1

Mathematics

Combinatorics

20 pages

Scientific paper

We study the two most common types of percolation process on a sparse random graph with a given degree sequence. Namely, we examine first a bond percolation process where the edges of the graph are retained with probability p and afterwards we focus on site percolation where the vertices are retained with probability p. We establish critical values for p above which a giant component emerges in both cases. Moreover, we show that in fact these coincide. As a special case, our results apply to power law random graphs. We obtain rigorous proofs for formulas derived by several physicists for such graphs.

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