Evolving networks: eras and turning points

Within the large body of research in complex network analysis, an important topic is the temporal evolution of networks. Existing approaches aim at analyzing the evolution on the global and the local scale, extracting properties of either the entire network or local patterns. In this paper, we focus on detecting clusters of temporal snapshots of a network, to be interpreted as eras of evolution. To this aim, we introduce a novel hierarchical clustering methodology, based on a dissimilarity measure (derived from the Jaccard coefficient) between two temporal snapshots of the network, able to detect the turning points at the beginning of the eras. We devise a framework to discover and browse the eras, either in top-down or a bottom-up fashion, supporting the exploration of the evolution at any level of temporal resolution. We show how our approach applies to real networks and null models, by detecting eras in an evolving co-authorship graph extracted from a bibliographic dataset, a collaboration graph extracted from a cinema database, and a network extracted from a database of terrorist attacks; we illustrate how the discovered temporal clustering highlights the crucial moments when the networks witnessed profound changes in their structure. Our approach is finally boosted by introducing a meaningful labeling of the obtained clusters, such as the characterizing topics of each discovered era, thus adding a semantic dimension to our analysis.