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 for spread (of information, pathogens, etc.) through WD networks based on the independent cascade model (ICM). While deriving exact results for the ICM requires Monte Carlo simulations, we show that our centrality measure (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.Comment: 3 figure

A Congressional Twitter network dataset quantifying pairwise probability of influence

We present a social network dataset based on interactions between members of the 117th United States Congress between Feb. 9, 2022, and June 9, 2022. The dataset takes the form of a directed, weighted network in which the edge weights are empirically obtained “probabilities of influence” between all pairs of Congresspeople. Twitter's application programming interface (API) V2 was used to determine the number of times each member of Congress retweeted, quote tweeted, replied to, or mentioned other Congressional members, and the probability of influence was found by normalizing the summed influence by the number of tweets issued by each Congressperson. This network may be of particular interest to the study of information diffusion within social networks