Spectral centrality measures in temporal networks

In our previous article we defined temporal quantities used for the description of temporal networks with zero latency and we showed that some centrality measures (e.g. degree, betweenness, closeness) can be extended to the case of temporal networks. In this article we broaden the scope of centrality measures in temporal networks to centrality measures derived from the eigenvectors of network matrices, namely the eigenvector in-centrality, the eigenvector out-centrality, the Katz centrality, the Bonacich alpha and (alpha, beta)-centrality, the HITS algorithm (also known as Hubs and Authorities) introduced by Kleinberg, and the PageRank algorithm defined by Page and Brin. We extended our Python library TQ (Temporal Quantities) to include the algorithms from our research. The library is available online. The procedures will also be added to the user friendly program called Ianus. We tested the proposed algorithms on Franzosi's violence network and on Corman's Reuter terror news network and show the results.