Cyclic Entropy Optimization of Social Networks Using an Evolutionary Algorithm

Abstract

We design and apply a Genetic Algorithm that maximizes the cyclic-entropy of a social network model, hence optimizing its robustness to failures. Our algorithm was applied on three types of social networks: scale-free, small-world and random networks. The three types of networks were generated using Barabasi and Albertpsilas generative model, Watts and Strogatzpsilas model and Erdos-Renyipsilas model, respectively. The maximum optimal entropy achieved among all three types was the one displayed by the small-world network, which was equal to 2.6887, corresponding to an optimal network distribution found when the initial distribution was subject to 11 random edge removals and 19 additions of random edges regardless of the initial distribution. The random-network model came next with optimal entropy equal to 2.5692, followed by the scale-free network which had optimal entropy of 2.5190. We observed by keeping track of the topology of the network and the cyclespsila length distribution within it, that all different types of networks evolve almost to the same network, possibly a random network, after being subject to the cyclic-entropy optimization algorithm.