Scale-free graphs with many edges

Published 12 Dec 2022 in math.PR | (2212.05907v4)

Abstract: We develop tail estimates for the number of edges in a Chung-Lu random graph with regularly varying weight distribution. Our results show that the most likely way to have an unusually large number of edges is through the presence of one or more hubs, i.e.\ vertices with degree of order $n$.

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