Dynamic Network Modeling from Motif-Activity

Graph structure in dynamic networks changes rapidly. Using temporal information about their connections, models for dynamic networks can be developed and used to understand the process of how their structure changes over time. Additionally, higher-order motifs have been established as building blocks for the structure of networks. In this paper, we first demonstrate empirically in three dynamic network datasets, that motifs with edges: (1) do not transition from one motif type to another (e.g, wedges becoming triangles and vice-versa); (2) motifs re-appear in other time periods and the rate depends on their configuration. We propose the Dynamic Motif-Activity Model (DMA) for sampling synthetic dynamic graphs with parameters learned from an observed network. We evaluate our DMA model, with two dynamic graph generative model baselines, by measuring different graph structure metrics in the generated synthetic graphs and comparing with the graph used as input. Our results show that employing motifs captures the underlying graph structure and modeling their activity recreates the fast changes seen in dynamic networks.