Comparative topological signatures of growing collaboration networks

Abstract

We study topological signatures in growing collaboration networks using standard and persistent homology. Persistent homology has thus far been primarily used for topological data analysis using a point cloud representation. In contrast, we apply persistent homology on temporal networks, and use it as a tool to compare and contrast between different growing networks. Specifically, we consider two collaboration networks: the paper collaboration network DBLP, and the actor collaboration network IMDB. We compare the evolution of their network properties, and of the homology (Betti numbers) with time. We also compare their topological signatures using persistent homology. We introduce a distance metric for comparing the topological signatures, and using it, visualize the similarity between individual segments through multidimensional scaling. We observe that, while the DBLP network has substantially evolved over time, the nature of collaboration in the IMDB network has relatively remained unchanged over the period 1950–2008. Our work shows that homology-based signatures can be effective in discriminating between real-world networks.