Coverage centralities for temporal networks

TL;DR

This paper introduces two parameter-free, robust centrality measures for temporal vertices in networks, efficiently computed to reveal key bottleneck times critical for information spread in real-world temporal networks.

Contribution

It defines novel centrality measures for temporal vertices, demonstrating their heterogeneity and identifying bottleneck times crucial for network dynamics.

Findings

Highly central vertices cluster around specific bottleneck times

Distributions of centrality values are heterogeneous

Most information flow passes through few key temporal vertices

Abstract

Structure of real networked systems, such as social relationship, can be modeled as temporal networks in which each edge appears only at the prescribed time. Understanding the structure of temporal networks requires quantifying the importance of a temporal vertex, which is a pair of vertex index and time. In this paper, we define two centrality measures of a temporal vertex based on the fastest temporal paths which use the temporal vertex. The definition is free from parameters and robust against the change in time scale on which we focus. In addition, we can efficiently compute these centrality values for all temporal vertices. Using the two centrality measures, we reveal that distributions of these centrality values of real-world temporal networks are heterogeneous. For various datasets, we also demonstrate that a majority of the highly central temporal vertices are located within a narrow time window around a particular time. In other words, there is a bottleneck time at which most information sent in the temporal network passes through a small number of temporal vertices, which suggests an important role of these temporal vertices in spreading phenomena.