Non-conservative diffusion and its application to social network analysis.

The article examines the appropriateness of random walk models for social processes and argues that many social phenomena, such as epidemics and information diffusion, are better represented by non-conservative diffusion processes, where the quantity spreading can grow rather than remain constant. It mathematically formulates conservative diffusion (random walk-based) and non-conservative diffusion (broadcast-based), linking them to the centrality metrics PageRank and Alpha-Centrality, respectively, and highlights the existence of an epidemic threshold in non-conservative diffusion. Empirical analysis of the Digg social news network demonstrates that Alpha-Centrality, a non-conservative metric, more accurately identifies influential users in broadcast-driven information diffusion than PageRank. Additionally, the article presents a scalable approximate algorithm for computing Alpha-Centrality in large graphs, emphasizing the importance of matching centrality metrics to the underlying diffusion dynamics in social network analysis.