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Connected Components in Random Graphs with Given Expected Degree Sequences
Authors:Fan Chung  Linyuan Lu
Institution:(2) University of California, San Diego, USA;
Abstract:We consider a family of random graphs with a given expected degree sequence. Each edge is chosen independently with probability proportional to the product of the expected degrees of its endpoints. We examine the distribution of the sizes/volumes of the connected components which turns out depending primarily on the average degree d and the second-order average degree d~. Here d~ denotes the weighted average of squares of the expected degrees. For example, we prove that the giant component exists if the expected average degree d is at least 1, and there is no giant component if the expected second-order average degree d~ is at most 1. Examples are given to illustrate that both bounds are best possible.
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