Full Connectivity: Corners, edges and faces
arXiv:1201.3123 · doi:10.1007/s10955-012-0493-y
Abstract
We develop a cluster expansion for the probability of full connectivity of high density random networks in confined geometries. In contrast to percolation phenomena at lower densities, boundary effects, which have previously been largely neglected, are not only relevant but dominant. We derive general analytical formulas that show a persistence of universality in a different form to percolation theory, and provide numerical confirmation. We also demonstrate the simplicity of our approach in three simple but instructive examples and discuss the practical benefits of its application to different models.
28 pages, 8 figures
References in corpus (5)
- Uncovering the overlapping community structure of complex networks in nature and society
- Quantifying social group evolution
- Understanding the spreading patterns of mobile phone viruses
- The critical effect of dependency groups on the function of networks
- Continuum percolation of wireless ad hoc communication networks
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