Temporal motifs in time-dependent networks

TL;DR

This paper introduces the concept of temporal motifs to analyze the mesoscale structure of time-dependent networks, capturing both topological and temporal patterns of events.

Contribution

It presents a novel framework for classifying and efficiently identifying temporal motifs in networks with non-overlapping events, including algorithms and statistical analysis.

Findings

Efficient algorithm for identifying temporal motifs

Application to a large mobile call network

Insights into causality and null models in temporal motifs

Abstract

Temporal networks are commonly used to represent systems where connections between elements are active only for restricted periods of time, such as networks of telecommunication, neural signal processing, biochemical reactions and human social interactions. We introduce the framework of temporal motifs to study the mesoscale topological-temporal structure of temporal networks in which the events of nodes do not overlap in time. Temporal motifs are classes of similar event sequences, where the similarity refers not only to topology but also to the temporal order of the events. We provide a mapping from event sequences to colored directed graphs that enables an efficient algorithm for identifying temporal motifs. We discuss some aspects of temporal motifs, including causality and null models, and present basic statistics of temporal motifs in a large mobile call network.