Susceptibility of random graphs with given vertex degrees

Svante Janson
2010 Journal of Combinatorics  
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.
more » ... amples are given where the critical exponents differ on the subcritical and supercritical sides.
doi:10.4310/joc.2010.v1.n4.a2 fatcat:66el7plaerhs7pnlfmlwenm7em