fastball: a fast algorithm to randomly sample bipartite graphs with fixed degree sequences

Abstract

Abstract Many applications require randomly sampling bipartite graphs with fixed degrees or randomly sampling incidence matrices with fixed row and column sums. Although several sampling algorithms exist, the ‘curveball’ algorithm is the most efficient with an asymptotic time complexity of $O(n~log~n)$ and has been proven to sample uniformly at random. In this article, we introduce the ‘fastball’ algorithm, which adopts a similar approach but has an asymptotic time complexity of $O(n)$. We show that a C$\texttt{++}$ implementation of fastball randomly samples large bipartite graphs with fixed degrees faster than curveball, and illustrate the value of this faster algorithm in the context of the fixed degree sequence model for backbone extraction.