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Researchers have modeled contagion processes on social networks for wide ranging applications, including spreading of epidemics, financial defaults, actions such as joining social media sites, and rumors. So, too, researchers have developed a host of intervention methods to control harmful contagions on networks; among these approaches are node and edge removal, separating network communities, altering contagion properties, and introducing a second competing contagion. In this work, minimum dominating sets are used to identify blocking nodes—nodes that do not contract a contagion and therefore also do not assist in transmitting it. A novel, generalized method that utilizes integer linear programming to determine exact minimum dominating sets (which is an NP-hard problem) has been developed for a subgraph of any social network for any combination of covering distance and coverage requirement. Three social networks are used to understand and evaluate (i) the method itself and (ii) the efficacy of the blocking nodes that the method produces to stop contagion spread. 

Discrete dynamical systems are commonly used to model the spread of contagions on real-world networks. Under the PAC framework, existing research has studied the problem of learning the behavior of a system, assuming that the underlying network is known. In this work, we focus on a more challenging setting: to learn both the behavior and the underlying topology of a black-box system. We show that, in general, this learning problem is computationally intractable. On the positive side, we present efficient learning methods under the PAC model when the underlying graph of the dynamical system belongs to certain classes. Further, we examine a relaxed setting where the topology of an unknown system is partially observed. For this case, we develop an efficient PAC learner to infer the system and establish the sample complexity. Lastly, we present a formal analysis of the expressive power of the hypothesis class of dynamical systems where both the topology and behavior are unknown, using the well-known Natarajan dimension formalism. Our results provide a theoretical foundation for learning both the topology and behavior of discrete dynamical systems. 

Evolutionary anti-coordination games on networks capture real-world strategic situations such as traffic routing and market competition. Two key problems concerning evolutionary games are the existence of a pure Nash equilibrium (NE) and the convergence time. In this work, we study these two problems for anti-coordination games under sequential and synchronous update schemes. For each update scheme, we examine two decision modes based on whether an agent considers its own previous action (self essential) or not (self non-essential) in choosing its next action. Using a relationship between games and dynamical systems, we show that for both update schemes, finding an NE can be done efficiently under the self non-essential mode but is computationally intractable under the self essential mode. We then identify special cases for which an NE can be obtained efficiently. For convergence time, we show that the dynamics converges in a polynomial number of steps under the synchronous scheme; for the sequential scheme, the convergence time is polynomial only under the self non-essential mode. Through experiments, we empirically examine the convergence time and the equilibria for both synthetic and real-world networks. 

There are myriad real-life examples of contagion processes on human social networks, e.g., spread of viruses, information, and social unrest. Also, there are many methods to control or block contagion spread. In this work, we introduce a novel method of blocking contagions that uses nodes from dominating sets (DSs). To our knowledge, this is the first use of DS nodes to block contagions. Finding minimum dominating sets of graphs is an NP-Complete problem, so we generalize a well-known heuristic, enabling us to customize its execution. Our method produces a prioritized list of dominating nodes, which is, in turn, a prioritized list of blocking nodes. Thus, for a given network, we compute this list of blocking nodes and we use it to block contagions for all blocking node budgets, contagion seed sets, and parameter values of the contagion model. We report on computational experiments of the blocking efficacy of our approach using two mined networks. We also demonstrate the effectiveness of our approach by comparing blocking results with those from the high degree heuristic, which is a common standard in blocking studies. 

Motivated by a wide range of applications, research on agent-based models of contagion propagation over networks has attracted a lot of attention in the literature. Many of the available software systems for simulating such agent-based models require users to download software, build the executable, and set up execution environments. Further, running the resulting executable may require access to high performance computing clusters. Our work describes an open access software system (NetSimS) that works under the “Modeling and Simulation as a Service” (MSaaS) paradigm. It enables users to run simulations by selecting models and parameter values, initial conditions, and networks through a web interface. The system supports a variety of models and networks with millions of nodes and edges. In addition to the simulator, the system includes components that enable users to choose initial conditions for simulations in a variety of ways, to analyze the data generated through simulations, and to produce plots from the data. We describe the components of NetSimS and carry out a performance evaluation of the system. We also discuss two case studies carried out on large networks using the system. NetSimS is a major component within net.science, a cyberinfrastructure for network science. 

Abstract 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 new infections subject to a budget constraint on the total number of available vaccinations for the contagions. While this problem has been considered in the literature for a single contagion, our work considers the simultaneous propagation of two contagions. This optimization problem is NP-hard. We present two main solution approaches for the problem, namely an integer linear programming (ILP) formulation to obtain optimal solutions and a heuristic based on a generalization of the set cover problem. We carry out a comprehensive experimental evaluation of our solution approaches using many real-world networks. The experimental results show that our heuristic algorithm produces solutions that are close to the optimal solution and runs several orders of magnitude faster than the ILP-based approach for obtaining optimal solutions. We also carry out sensitivity studies of our heuristic algorithm.