Motifs in Temporal Networks

TL;DR

This paper introduces a new framework for identifying and counting motifs in temporal networks, providing efficient algorithms and revealing domain-specific motif patterns and time-scale variations.

Contribution

It defines temporal network motifs, develops fast counting algorithms, and demonstrates their effectiveness across various real-world networks.

Findings

Networks from different domains have distinct motif counts.

Networks within the same domain show similar motif patterns.

Motifs occur at different time scales, indicating structural and functional diversity.

Abstract

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. 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 in temporal networks, which contain many timestamped links between the nodes, is not yet 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 temporal edges, design fast algorithms for counting temporal motifs, and prove their runtime complexity. Our fast algorithms achieve up to 56.5x speedup compared to a baseline method. Furthermore, we use our algorithms to count temporal motifs in a variety of networks. Results show that networks from different domains have significantly different motif counts, whereas networks from the same domain tend to have similar motif counts. We also find that different motifs occur at different time scales, which provides further insights into structure and function of temporal networks.