Susceptibility of random graphs with given vertex degrees

Details Susceptibility of random graphs with given vertex degrees Susceptibility of random graphs with given vertex degrees

2009-11-13

arxiv.org/abs/0911.2636v1

Mathematics

Combinatorics

25 pages

Scientific paper

We study the susceptibility, i.e., the mean cluster size, in random graphs with given vertex degrees. We show, under weak assumptions, that the susceptibility converges to the expected cluster size in the corresponding branching process. In the supercritical case, a corresponding result holds for the modified susceptibility ignoring the giant component and the expected size of a finite cluster in the branching process; this is proved using a duality theorem. The critical behaviour is studied. Examples are given where the critical exponents differ on the subcritical and supercritical sides.

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