Eigenvector-Based Centrality Measures for Temporal Networks

Numerous centrality measures have been developed to quantify the importances of nodes in time-independent networks, and many of them can be expressed as the leading eigenvector of some matrix. With the increasing availability of network data that changes in time, it is important to extend such eigenvector-based centrality measures to time-dependent networks. In this paper, we introduce a principled generalization of network centrality measures that is valid for any eigenvector-based centrality. We consider a temporal network with $N$ nodes as a sequence of $T$ layers that describe the network during different time windows, and we couple centrality matrices for the layers into a supracentrality matrix of size $NT\times NT$ whose dominant eigenvector gives the centrality of each node $i$ at each time $t$. We refer to this eigenvector and its components as a joint centrality, as it reflects the importances of both the node $i$ and the time layer $t$. We also introduce the concepts of marginal and conditional...