SUSCEPTIBILITY OF RANDOM GRAPHS WITH GIVEN VERTEX DEGREES

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

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