Self-organization of weighted networks for optimal synchronizability

Louis Kempton; Guido Herrmann; Mario di Bernardo

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arXiv · 1505.07279

Self-organization of weighted networks for optimal synchronizability

Louis Kempton·Guido Herrmann·Mario di Bernardo

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Abstract

We show that a network can self-organize its structure in a completely distributed manner in order to optimize its synchronizability whilst satisfying the local constraints: non-negativity of edge weights, and maximum weighted degree of nodes. A novel multilayer approach is presented which uses a distributed strategy to estimate two spectral functions of the graph Laplacian, the algebraic connectivity $\lambda_2$ and the eigenratio $r = \lambda_n / \lambda_2$ . These local estimates are then used to evolve the edge weights so as to maximize $\lambda_2$, or minimize $r$ and, hence, achieve an optimal structure.

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Louis Kempton, Guido Herrmann, Mario di Bernardo. 2015-05-27. Self-organization of weighted networks for optimal synchronizability. https://arxiv.org/abs/1505.07279

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