Journal of Statistical Physics, Vol. 118, Nos. 3/4, February 2005. p. 721-734.
DOI: 10.1007/s10955-004-8826-0
We derive percolation results in the continuum plane that lead to what appear? 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 functioning connections per node.