Counting Multilayer Temporal Motifs in Complex Networks

Abstract

This paper proposes a novel approach to count temporal motifs in multilayer complex networks. Network motifs, i.e., small characteristic patterns of a handful of nodes and edges, have repeatedly been shown to be instrumental in understanding real-world complex systems. However, exhaustively enumerating these motifs is computationally infeasible for larger networks. Therefore, the focus of this work is on algorithms that efficiently count network motifs. This facilitates the discovery of motifs in networks with millions of nodes and edges, enabling the following three contributions of this paper. First, we propose an extension of an existing counting algorithm to also efficiently count multilayer temporal motifs. In addition to dealing with the timestamp at which a link (re-)occurs, the algorithm also efficiently counts interaction patterns across different network layers. Second, we demonstrate how partial timing, a common phenomenon in real-world settings where only part of the layers are timed, can be incorporated. Third, we assess the performance of the proposed temporal multilayer counting algorithm on a number of real-world network datasets. Experiments reveal interesting insights in the heterogen eous interplay between network layers in, for example, online expert communities, showing how particular temporal motifs are characteristic for certain layers of interaction.