A Unified Model of Influence in Social Networks?

It is difficult to obtain accurate prediction results of cascades over online social networks, therefore a variety of diffusion models have been proposed in the literature to simulate diffusion processes instead. We argue that such models require extensive simulation results to produce good estimates of future spreads, while at the same time requiring training over observed data to learn the parameters that they incorporate into the various influence mechanisms that drive diffusion. In this work, we take a complimentary approach. We present a generalized, analytical model of influence in social networks that captures social influence at various levels of granularity, ranging from pairwise influence, to local neighborhood, to the general population, and external events, therefore capturing the complex dynamics of human behavior. Commonly used diffusion models in social networks can be reduced to special cases of our model, by carefully defining their parameters. Our goal is to provide a closed-form expression for the probability of infection for every node in an arbitrary, directed network at any time t. However prior work in the literature has shown that exact computation of infection probabilities is #P-hard. We make an independence assumption about the infection events of a node’s incoming neighbors, which results our formula being an approximation. We quantitatively evaluate the approximation quality of our analytical solution as compared to numerous popular diffusion models on a real-world dataset and a series of synthetic graphs. Keywords-analytical framework; computational models; diffusion models; dynamics; evolutionary models; influence