Percolation on sparse random graphs with given degree sequence

Fountoulakis, Nikolaos

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Percolation on sparse random graphs with given degree sequence

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Fountoulakis, Nikolaos
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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arXiv:math_0703269.pdf
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Fountoulakis, N. (2007). Percolation on sparse random graphs with given degree sequence. Retrieved from http://arxiv.org/abs/math/0703269.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0028-35C0-8

Abstract

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.