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We propose a new paradigm to design a network-based self-adaptive epidemicmodel that relies on the interplay between the network and its line graph. Weimplement this proposal on a Susceptible-Infected-Susceptible model in whichboth nodes and edges are considered susceptible and their respectiveprobabilities of being infected result in a real-time re-modulation of theweights of both the graph and its line graph. The new model can be consideredas an appropriate perturbation of the standard Susceptible-Infected-Susceptiblemodel, and the coupling between the graph and its line graph is interpreted asa reinforcement factor that fosters diffusion or adoption through a continuousadjustment of the parameters involved. We study the existence and stabilityconditions of the endemic and disease-free states for general networktopologies. Moreover, we introduce, through the asymptotic values in theendemic steady states, a new type of eigenvector centrality where the score ofa node depends on both the neighboring nodes and the edges connected to it. Wealso investigate the properties of this new model on some specific syntheticgraphs, such as cycle, regular, and star graphs. Finally, we perform a seriesof numerical simulations and provide its effectiveness in capturing someempirical evidence on behavioral adoption mechanisms.

A Novel Self-Adaptive SIS Model Based on the Mutual Interaction between a Graph and its Line Graph