Random walker's view of networks whose growth it shapes
Robert J H Ross1, Charlotte Strandkvist1, Walter Fontana1
1Department of Systems Biology, Harvard Medical School, 200 Longwood Avenue, Boston, Massachusetts 02115, USA.
Abstract:
We study a simple model in which the growth of a network is determined by the location of one or more random walkers. Depending on walker motility rate, the model generates a spectrum of structures situated between well-known limiting cases. We demonstrate that the average degree observed by a walker is a function of its motility rate. Modulating the extent to which the location of node attachment is determined by the walker as opposed to random selection is akin to scaling the speed of the walker and generates new limiting behavior. The model raises questions about energetic and computational resource requirements in a physical instantiation.
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