Abstract
We derive percolation results in the continuum plane that lead to what appears to be a general tendency of many stochastic network models. Namely, when the selection mechanism according to which nodes are connected to each other, is sufficiently spread out, then a lower density of nodes, or on average fewer connections per node, are sufficient to obtain an unbounded connected component. We look at two different transformations that spread-out connections and decrease the critical percolation density while preserving the average node degree. Our results indicate that real networks can exploit the presence of spread-out and unreliable connections to achieve connectivity more easily, provided they can maintain the average number of functioningconnections per node.
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Franceschetti, M., Booth, L., Cook, M. et al. Continuum Percolation with Unreliable and Spread-Out Connections. J Stat Phys 118, 721–734 (2005). https://doi.org/10.1007/s10955-004-8826-0
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DOI: https://doi.org/10.1007/s10955-004-8826-0