Non-Conservative Diffusion and its Application to Social Network Analysis

Is the random walk appropriate for modeling and analyzing social processes? We argue that many interesting social phenomena, including epidemics and information diffusion, cannot be modeled as a random walk, but instead must be modeled as broadcast-based or non-conservative diffusion. To produce meaningful results, social network analysis algorithms have to take into account differences between these diffusion processes. We formulate conservative (random walk-based) and non-conservative (broadcast-based) diffusion mathematically and show how these are related to well-known metrics: PageRank and Alpha-Centrality respectively. This formulation allows us to unify two distinct areas of network analysis — centrality and epidemic models — and leads to insights into the relationship between diffusion and network structure, specifically, the existence of an epidemic threshold in nonconservative diffusion. We demonstrate, by ranking nodes in an online social network used for broadcasting news, that non-conservative Alpha-Centrality leads to a better agreement with empirical ranking schemes than conservative PageRank. In addition, we give a scalable approximate algorithm for computing the Alpha-Centrality in a massive graph. We hope that our investigation will inspire further exploration of the applications of non-conservative diffusion in social network analysis. Keywords-social networks; centrality; diffusion