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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. 

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. 

Many papers have addressed the problem of learning the behavior (i.e., the local interaction function at each node) of a networked system through active queries, assuming that the network topology is known. We address the problem of inferring both the network topology and the behavior of such a system through active queries. Our results are for systems where the state of each node is from {0, 1} and the local functions are Boolean. We present inference algorithms under both batch and adaptive query models for dynamical systems with symmetric local functions. These algorithms show that the structure and behavior of such dynamical systems can be learnt using only a polynomial number of queries. Further, we establish a lower bound on the number of queries needed to learn such dynamical systems. We also present experimental results obtained by running our algorithms on synthetic and real-world networks. 

Globalization and climate change facilitate the spread and establishment of invasive species throughout the world via multiple pathways. These spread mechanisms can be effectively represented as diffusion processes on multi-scale, spatial networks. Such network-based modeling and simulation approaches are being increasingly applied in this domain. However, these works tend to be largely domain-specific, lacking any graph theoretic formalisms, and do not take advantage of more recent developments in network science. This work is aimed toward filling some of these gaps. We develop a generic multi-scale spatial network framework that is applicable to a wide range of models developed in the literature on biological invasions. A key question we address is the following: how do individual pathways and their combinations influence the rate and pattern of spread? The analytical complexity arises more from the multi-scale nature and complex functional components of the networks rather than from the sizes of the networks. We present theoretical bounds on the spectral radius and the diameter of multi-scale networks. These two structural graph parameters have established connections to diffusion processes. Specifically, we study how network properties, such as spectral radius and diameter are influenced by model parameters. Further, we analyze a multi-pathway diffusion model from the literature by conducting simulations on synthetic and real-world networks and then use regression tree analysis to identify the important network and diffusion model parameters that influence the dynamics.