554 citations · 1.7k across the 51 of their papers we have counts for
4 papers · 1 filter
Metrics for sparse graphs
B. Bollobas, O. Riordan
Recently, Bollobás, Janson and Riordan introduced a very general family of random graph models, producing inhomogeneous random graphs with edges. Roughly speaking, there is…
Rigorous confidence intervals for critical probabilities
Oliver Riordan, Mark Walters
We use the method of Balister, Bollobas and Walters to give rigorous 99.9999% confidence intervals for the critical probabilities for site and bond percolation on the 11 Archimedea…
Line-of-sight percolation
Bela Bollobas, Svante Janson, Oliver Riordan
Given , let be the graph with vertex set in which two vertices are joined if they agree in one coordinate and differ by at most in the other. (Thus $Z…
Percolation on dense graph sequences
Béla Bollobás, Christian Borgs, Jennifer Chayes +1
In this paper we determine the percolation threshold for an arbitrary sequence of dense graphs . Let be the largest eigenvalue of the adjacency matrix of , and le…