Some Models of Reproducing Graphs: I Pure Reproduction

Richard Southwell, Chris Cannings

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DOI: 10.4236/am.2010.13018                

Abstract

Many real world networks change over time. This may arise due to individuals joining or leaving the network or due to links forming or being broken. These events may arise because of interactions between the vertices which occasion payoffs which subsequently determine the fate of the nodes, due to ageing or crowding, or perhaps due to isolation. Such phenomena result in a dynamical system which may lead to complex behaviours, to self-replication, to chaotic or regular patterns, to emergent phenomena from local interactions. They give insight to the nature of the real-world phenomena which the network, and its dynamics, may approximate. To a large extent the models considered here are motivated by biological and social phenomena, where the vertices may be genes, proteins, genomes or organisms, and the links interactions of various kinds. In this, the first paper of a series, we consider the dynamics of pure reproduction models where networks grow relentlessly in a deterministic way.

Keywords

Reproduction, Graph, Network, Adaptive, Evolution

Conflicts of Interest

The authors declare no conflicts of interest.

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