Random networks with sublinear preferential attachment: the giant component

Details Random networks with sublinear preferential attachment: the giant component Random networks with sublinear preferential attachment: the giant component

2010-07-06

arxiv.org/abs/1007.0899v1

Mathematics

Probability

47 pages

Scientific paper

We study a dynamical random network model in which at every construction step a new vertex is introduced and attached to every existing vertex independently with a probability proportional to a concave function f of its current degree. We give a criterion for the existence of a giant component, which is both necessary and sufficient, and which becomes explicit when f is linear. Otherwise it allows the derivation of explicit necessary and sufficient conditions, which are often fairly close. We give an explicit criterion to decide when there is a giant component, which is robust under random removal of edges. We also determine asymptotically the size of the giant component and the empirical distribution of component sizes in terms of the survival probability and size distribution of a multitype branching random walk associated with f.

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