Random networks created by biological evolution

Abstract

We investigate a model of evolving random network, introduced by us previously {[}{\it Phys. Rev. Lett.} {\bf 83}, 5587 (1999){]} . The model is a generalization of the Bak-Sneppen model of biological evolution, with the modification that the underlying network can evolve by adding and removing sites. The behavior and the averaged properties of the network depend on the parameter $p$, the probability to establish link to the newly introduced site. For $p=1$ the system is self-organized critical, with two distinct power-law regimes with forward-avalanche exponents $\tau =1.98\pm 0.04$ and ${\tau }^{\prime }=1.65\pm 0.05$. The average size of the network diverge as power-law when $p\to 1$. We study various geometrical properties of the network: probability distribution of sizes and connectivities, size and number of disconnected clusters and the dependence of mean distance between two sites on the cluster size. The connection with models of growing networks with preferential attachment is discussed.

9 pages, 11 figures, submitted to Phys. Rev. E (substantially revised version)

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• Mean-field solution of the small-world network model
• Topological Evolution of Dynamical Networks: Global Criticality from Local Dynamics
• Exact results and scaling properties of small-world networks
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Cited by in corpus (10)

• Statistical mechanics of complex networks
• Evolution of networks
• Measuring preferential attachment for evolving networks
• Growing networks with local rules: preferential attachment, clustering hierarchy and degree correlations
• Infinite-Order Percolation and Giant Fluctuations in a Protein Interaction Network
• Evolving networks through deletion and duplication
• Multifractal properties of growing networks
• Harms and benefits from social imitation
• Coevolutionary dynamics on scale-free networks
• Dynamic scaling and universality in evolution of fluctuating random networks