Switching edges to randomize networks: What goes wrong and how to fix it

The switching model is a well-known random network model that randomizes a network while keeping its degree sequence fixed. The idea behind the switching model is simple: a network is randomized by repeatedly rewiring pairs of edges. In this paper we demonstrate that despite its simple description, and in part due to it, much can go wrong when implementing the switching model. Specifically, we show that the model needs to be implemented carefully, to avoid biased sampling. We propose a precise definition of the switching model which guides its implementation. Furthermore, we argue that we should refer to the switching model with respect to a specific network class, and in fact define a family of switching models. This formalizes previous use of the switching model to randomize networks from numerous network classes. We show that the properties of these models depend on the network class, and in particular that their stationary distributions differ. Hence it is important to take into account which class of networks is being randomized. We derive conditions, and where possible adjust the models, such that sampling is unbiased for the switching model with respect to eight common network classes. These unbiased null-models are important, since common network analysis techniques such as motif finding and community detection rely on them