2015/07/01 by June Zhang, José M. F. Moura, Zhang, June +1
Computer Science · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Computer and information sciences #FOS: Physical sciences #Opinion Dynamics and Social Influence #Physics and Society (physics.soc-ph) #Social and Information Networks (cs.SI) #Stochastic processes and statistical mechanics #cs.SI #physics.soc-ph
paper · pdf · doi:10.48550/arxiv.1507.00396
arxiv created 2015/07/01 · openalex publication_date 2015/07/01 · arxiv updated 2015/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Propagation of contagion in networks depends on the graph topology. This paper is concerned with studying the time-asymptotic behavior of the extended contact processes on static, undirected, finite-size networks. This is a contact process with nonzero exogenous infection rate (also known as the ε-SIS, ε susceptible-infected-susceptible, model [1]). The only known analytical characterization of the equilibrium distribution of this process is for complete networks. For large networks with arbitrary topology, it is infeasible to numerically solve for the equilibrium distribution since it requires solving the eigenvalue-eigenvector problem of a matrix that is exponential in N , the size of the network. We show that, for a certain range of the network process parameters, the equilibrium distribution of the extended contact process on arbitrary, finite-size networks is well approximated by the equilibrium distribution of the scaled SIS process, which we derived in closed-form in prior work. We confirm this result with numerical simulations comparing the equilibrium distribution of the extended contact process with that of a scaled SIS process. We use this approximation to decide, in polynomial-time, which agents and network substructures are more susceptible to infection by the extended contact process.