A uniform random graph model for directed acyclic networks and its effect on motif-finding

Abstract

Random graph models are commonly used as a null-hypothesis in the study of real-world networks. It is important that these networks resemble the real network under study, since they are used to deduce the significance of specific properties of the real network. Existing random graph models introduce unwanted features such as multiple edges and directed cycles when randomizing directed acyclic networks. This paper proposes a new random graph model for directed acyclic networks which overcomes these shortcomings. This ordered switching method is shown to sample uniformly from a suitable graph ensemble. After introducing this method, its use in motif-finding experiments is investigated. Even though the new and existing random network models result in networks with different properties, the patterns that are identified as network motifs in the two citation networks examined in this paper do not depend on the choice of null-model. However, when using the commonly used switching model as a null-model, sometimes anti-motifs are found that contain directed cycles, which is not the case when the ordered switching method is used. The ordered switching method is the first random graph model for directed acyclic networks that takes into account the degree sequences, topological ordering and does not introduce multiple edges, and should therefore have many applications in the study of directed acyclic networks.