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**1 - 2**of**2**### ECEASST Modelling Adaptive Networks: The Case of the Petrified Voters

"... Abstract: Adaptive networks are characterised by mutual dependencies between nodes ’ local state changes and evolving topology. Stochastic graph transformation systems are ideally suited to model such networks, but in order to analyse their prop-erties we require more scalable methods. We present a ..."

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Abstract: Adaptive networks are characterised by mutual dependencies between nodes ’ local state changes and evolving topology. Stochastic graph transformation systems are ideally suited to model such networks, but in order to analyse their prop-erties we require more scalable methods. We present a case study of a simple but representative example of adaptive networks. In this social network of opinionated voters a node connected to another of different opinion will either convert (changing state) or disconnect and establish a new connection with a node of the same opinion (changing topology). To analyse quantitative properties of the model, such as the long-term average ra-tio of edges connecting nodes of different opinions or the overall rate of change of opinions or connections, we use a refinement technique developed for the Kappa graph rewriting approach to derive a stochastic Petri net, replacing graphs as states by markings representing the frequency of occurrences of certain patterns. In gen-eral the number of patterns (and therefore places) is unbounded, but approximations can be used to replace complex patterns by combinations of simpler ones.