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The generation of random graphs using edge swaps provides a reliable method to draw uniformly random samples of sets of graphs respecting some simple constraints (e.g., degree distributions). However, in general, it is not necessarily possible to access all graphs obeying some given constraints through a classical switching procedure calling on pairs of edges. Therefore, we propose to get around this issue by generalizing this classical approach through the use of higher-order edge switches. This method, which we denote by “k-edge switching,” makes it possible to progressively improve the covered portion of a set of constrained graphs, thereby providing an increasing, asymptotically certain confidence on the statistical representativeness of the obtained sample.

Generating constrained random graphs using multiple edge switches