Motifs in Temporal Networks

Networks are a fundamental tool for modeling complex systems in a variety of domains including social and communication networks as well as biology and neuroscience. The counts of small subgraph patterns in networks, called network motifs, are crucial to understanding the structure and function of these systems. However, the role of network motifs for temporal networks, which contain many timestamped links between nodes, is not well understood. Here we develop a notion of a temporal network motif as an elementary unit of temporal networks and provide a general methodology for counting such motifs. We define temporal network motifs as induced subgraphs on sequences of edges, design several fast algorithms for counting temporal network motifs, and prove their runtime complexity. We also show that our fast algorithms achieve 1.3x to 56.5x speedups compared to a baseline method. We use our algorithms to count temporal network motifs in a variety of real-world datasets. Results show that networks from different domains have significantly different motif frequencies, whereas networks from the same domain tend to have similar motif frequencies. We also find that measuring motif counts at various time scales reveals different behavior.