A centrality measure for quantifying spread on weighted, directed networks

While many centrality measures for complex networks have been proposed, relatively few have been developed specifically for weighted, directed (WD) networks. Here we propose a centrality measure (Viral Centrality) for spread (of information, pathogens, etc.) through WD networks based on the independent cascade model (ICM). While calculating the most accurate results for the ICM generally requires Monte Carlo simulations, we show that Viral Centrality provides excellent approximation to ICM results for networks in which the weighted strength of cycles is not too large. We show this can be quantified with the leading eigenvalue of the weighted adjacency matrix, and we show that Viral Centrality outperforms other common centrality measures in both simulated and empirical WD networks. A Python implementation of the Viral Centrality algorithm has been made available at the Stanford Network Analysis Project repository.