The Annals of Applied Probability, Vol. 16, No. 1 (Feb., 2006), pp. 295-309 (15 pages) We consider the discrete Laplace operator $\Delta ^{(N)}$ on Erdős-Rényi random graphs with N vertices and edge ...

Graph limit theory provides a rigorous framework for analysing sequences of large graphs by representing them as continuous objects known as graphons – symmetric measurable functions on the unit ...

When the mathematicians Jeff Kahn and Gil Kalai first posed their “expectation threshold” conjecture in 2006, they didn’t believe it themselves. Their claim — a broad assertion about mathematical ...

We consider a stochastic SIR (susceptible → infective → recovered) epidemic defined on a configuration model random graph, in which infective individuals can infect only their neighbours in the graph ...

Text: : "Graph Theory" by J. Adrian Bondy and U.S.R. Murty; Graduate Texts in Mathematics 244, Springer 2008. ISBN 978-1-84628-969-9, 2nd printing, 978-1-84628-970-5 (ebook). Notes will be supplied ...