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We focus at the interface between multiscale computations, bifurcation theoryand social networks. In particular we address how the Equation-Free approach, arecently developed computational framework, can be exploited to systematicallyextract coarse-grained, emergent dynamical information by bridging detailed,agent-based models of social interactions on networks, with macroscopic,systems-level, continuum numerical analysis tools. For our illustrations we usea simple dynamic agent-based model describing the propagation of informationbetween individuals interacting under mimesis in a social network with privateand public information. We describe the rules governing the evolution of theagents emotional state dynamics and discover, through simulation, multiplestable stationary states as a function of the network topology. Using theEquation-Free approach we track the dependence of these stationary solutions onnetwork parameters and quantify their stability in the form of coarse-grainedbifurcation diagrams.

Equation-Free Multiscale Computations in Social Networks: from Agent-based Modelling to Coarse-grained Stability and Bifurcation Analysis