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2007 Percolation on Sparse Random Graphs with Given Degree Sequence
N. Fountoulakis
Internet Math. 4(4): 329-356 (2007).


We study the two most common types of percolation processes 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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N. Fountoulakis. "Percolation on Sparse Random Graphs with Given Degree Sequence." Internet Math. 4 (4) 329 - 356, 2007.


Published: 2007
First available in Project Euclid: 27 May 2009

zbMATH: 1206.68234
MathSciNet: MR2522948

Rights: Copyright © 2007 A K Peters, Ltd.

Vol.4 • No. 4 • 2007
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