Title: Combinatorial Miller-Hagberg Algorithm for Randomization of Dense Networks,
Abstract: We propose a slightly revised Miller-Hagberg (MH) algorithm that efficiently
generates a random network from a given expected degree sequence. The revision
was to replace the approximated edge probability between a pair of nodes with a
combinatorically calculated edge probability that better captures the
likelihood of edge presence especially where edges are dense. The computational
complexity of this combinatorial MH algorithm is still in the same order as the
original one. We evaluated the proposed algorithm through several numerical
experiments. The results demonstrated that the proposed algorithm was
particularly good at accurately representing high-degree nodes in dense,
heterogeneous networks. This algorithm may be a useful alternative of other
more established network randomization methods, given that the data are
increasingly becoming larger and denser in today's network science research.