Centrality informed embedding of networks for temporal feature extraction

Abstract

We propose a two-step methodology for exploring the temporal characteristics of a network. First, we construct a graph time series, where each snapshot is the result of a temporal whole-graph embedding. The embedding is carried out using the degree, Katz and betweenness centralities to characterize first and higher order proximities among vertices. Then a principal component analysis is performed over the collected temporal graph samples, which exhibits eigengraphs, graphs whose temporal weight variations model the sampled graph series. Analysis of the temporal timeline of each of the main eigengraphs reveals moments of importance in terms of structural graph changes. Parameters such as the dimension of the embeddings and the number of temporal samples are explored. Two case studies are presented: a Bitcoin subgraph, where findings are cross-checked by looking at the subgraph behavior itself, and the Enron email network, which allows us to compare our findings with prior studies. In both cases, the proposed methodology successfully identified temporal structural changes in the graph evolution.