A unifying framework for fast randomization of ecological networks with fixed (node) degrees.

The Curveball algorithm is an efficient and unbiased procedure for randomizing bipartite networks (or their matrix counterpart) while preserving node degrees. Here we introduce two extensions of the procedure, making it capable to randomize also unimode directed and undirected networks. We provide formal mathematical proofs that the two extensions, as the original Curveball, are fast and unbiased (i.e. they sample uniformly from the universe of possible network configurations).