Importance of individual events in temporal networks

TL;DR

This paper introduces an importance measure for individual events in temporal networks, highlighting that a small fraction of highly important events sustain network connectivity mainly due to bursty activity patterns.

Contribution

It generalizes the concept of event importance, providing a new way to quantify the significance of interactions in temporal networks.

Findings

A small fraction of events are crucial for network connectivity.

Importance of events correlates with bursty activity patterns.

Heterogeneous degree distributions are less influential than burstiness.

Abstract

Records of time-stamped social interactions between pairs of individuals (e.g., face-to-face conversations, e-mail exchanges, and phone calls) constitute a so-called temporal network. A remarkable difference between temporal networks and conventional static networks is that time-stamped events rather than links are the unit elements generating the collective behavior of nodes. We propose an importance measure for single interaction events. By generalizing the concept of the advance of event proposed by [Kossinets G, Kleinberg J, and Watts D J (2008) Proceeding of the 14th ACM SIGKDD International conference on knowledge discovery and data mining, p 435], we propose that an event is central when it carries new information about others to the two nodes involved in the event. We find that the proposed measure properly quantifies the importance of events in connecting nodes along time-ordered paths. Because of strong heterogeneity in the importance of events present in real data, a small fraction of highly important events is necessary and sufficient to sustain the connectivity of temporal networks. Nevertheless, in contrast to the behavior of scale-free networks against link removal, this property mainly results from bursty activity patterns and not heterogeneous degree distributions.