Graph Metrics for Temporal Networks

TL;DR

This paper reviews how traditional network metrics are adapted for temporal networks, emphasizing the importance of time ordering in defining connectivity, centrality, and community structures in dynamic graphs.

Contribution

It provides a comprehensive overview of extending static network metrics to temporal networks, including definitions of walks, paths, and centrality measures considering temporal dynamics.

Findings

Definitions of walks, paths, and connectedness for temporal graphs

Methods to characterize link persistence and temporal small-world behavior

Extensions of centrality measures and community detection to temporal networks

Abstract

Temporal networks, i.e., networks in which the interactions among a set of elementary units change over time, can be modelled in terms of time-varying graphs, which are time-ordered sequences of graphs over a set of nodes. In such graphs, the concepts of node adjacency and reachability crucially depend on the exact temporal ordering of the links. Consequently, all the concepts and metrics proposed and used for the characterisation of static complex networks have to be redefined or appropriately extended to time-varying graphs, in order to take into account the effects of time ordering on causality. In this chapter we discuss how to represent temporal networks and we review the definitions of walks, paths, connectedness and connected components valid for graphs in which the links fluctuate over time. We then focus on temporal node-node distance, and we discuss how to characterise link persistence and the temporal small-world behaviour in this class of networks. Finally, we discuss the extension of classic centrality measures, including closeness, betweenness and spectral centrality, to the case of time-varying graphs, and we review the work on temporal motifs analysis and the definition of modularity for temporal graphs.