Bipartitioning of directed and mixed random graphs

01/27/2019

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by   Adam Lipowski, et al.

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We show that an intricate relation of cluster properties and optimal bipartitions, which takes place in undirected random graphs, extends to directed and mixed random graphs. In particular, the satisfability threshold coincides with the relative size of the giant OUT component reaching 1/2. Moreover, when counting undirected links as two directed ones, the partition cost, and cluster properties, as well as location of the replica symmetry breaking transition for these random graphs depend primarily on the total number of directed links and not on their specific distribution.