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From populations to networks: Relating diversity indices and frustration in signed graphs
Angela Fontan1, Marco Ratta2, Claudio Altafini3
1Division of Decision and Control Systems, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm SE-100 44, Sweden.
Abstract:
Diversity indices of quadratic type, such as fractionalization and Simpson index, are measures of heterogeneity in a population. Even though they are univariate, they have an intrinsic bivariate interpretation as encounters among the elements of the population. In the paper, it is shown that this leads naturally to associate populations to weakly balanced signed networks. In particular, the frustration of such signed networks is shown to be related to fractionalization by a closed-form expression. This expression allows to simplify drastically the calculation of frustration for weakly balanced signed graphs.
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