A matter of time - intrinsic or extrinsic - for diffusion in evolving complex networks

Abstract

Diffusion phenomena occur in many kinds of real-world complex networks, e.g., biological, information or social networks. Because of this diversity, several types of diffusion models have been proposed in the literature: epidemiological models, threshold models, innovation adoption models, among others. Many studies aim at investigating diffusion as an evolving phenomenon but mostly occurring on static networks, and much remains to be done to understand diffusion on evolving networks. In order to study the impact of graph dynamics on diffusion, we propose in this paper an innovative approach based on a notion of intrinsic time, where the time unit corresponds to the appearance of a new link in the graph. This original notion of time allows us to isolate somehow the diffusion phenomenon from the evolution of the network. The objective is to compare the diffusion features observed with this intrinsic time concept from those obtained with traditional (extrinsic) time, based on seconds. The comparison of these time concepts is easily understandable yet completely new in the study of diffusion phenomena. We experiment our approach on synthetic graphs, as well as on a dataset extracted from the Github sofware sharing platform.