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Entropic determination of the phase transition in a coevolving opinion-formation model

We study an opinion formation model by the means of a co-evolving complex network where the vertices represent the individuals, characterised by their evolving opinions, and the edges represent the interactions among them. The network adapts to the spreading of opinions in two ways: not only connected agents interact and eventually change their thinking but an agent may also rewire one of its links to a neighborhood holding the same opinion as his. The dynamics depends on an external parameter Φ, which controls the plasticity of the network. We show how the information entropy associated to the distribution of group sizes, allows to locate the phase transition between full consensus and a society where different opinions coexist. We also determine the minimum size of the most informative sampling. At the transition the distribution of the sizes of groups holding the same opinion is scale free.