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We consider the simultaneous propagation of two contagions over a social network. We assume a threshold model for the propagation of the two contagions and use the formal framework of discrete dynamical systems. In particular, we study an optimization problem where the goal is to minimize the total number of infected nodes subject to a budget constraint on the total number of nodes that can be vaccinated. While this problem has been considered in the literature for a single contagion, our work considers the simultaneous propagation of two contagions. Since the optimization problem is NP-hard, we develop a heuristic based on a generalization of the set cover problem. Using experiments on three real-world networks, we compare the performance of the heuristic with some baseline methods. 

We investigate questions related to the time evolution of discrete graph dynamical systems where each node has a state from {0,1}. The configuration of a system at any time instant is a Boolean vector that specifies the state of each node at that instant. We say that two configurations are similar if the Hamming distance between them is small. Also, a predecessor of a configuration B is a configuration A such that B can be reached in one step from A. We study problems related to the similarity of predecessor configurations from which two similar configurations can be reached in one time step. We address these problems both analytically and experimentally. Our analytical results point out that the level of similarity between predecessors of two similar configurations depends on the local functions of the dynamical system. Our experimental results, which consider random graphs as well as small world networks, rely on the fact that the problem of finding predecessors can be reduced to the Boolean Satisfiability problem (SAT). 

Protest is a collective action problem and can be modeled as a coordination game in which people take an action with the potential to achieve shared mutual benefits. In game-theoretic contexts, successful coordination requires that people know each others’ willingness to participate, and that this information is common knowledge among a sufficient number of people. We develop an agent-based model of collective action that was the first to combine social structure and individual incentives. Another novel aspect of the model is that a social network increases in density (i.e., new graph edges are formed) over time. The model studies the formation of common knowledge through local interactions and the characterizing social network structures. We use four real-world, data-mined social networks (Facebook, Wikipedia, email, and peer-to-peer networks) and one scale-free network, and conduct computational experiments to study contagion dynamics under different conditions.