We investigate the rank of the adjacency matrix of large diluted random graphs: for a sequence of graphs (G n ) n≥0 converging locally to a Galton—Watson tree T (GWT), we provide an explicit formula ...

Journal of Applied Probability, Vol. 47, No. 3 (SEPTEMBER 2010), pp. 826-840 (15 pages) A random intersection graph G(n, m, p) is defined on a set 𝓥 of n vertices. There is an auxiliary set 𝓦 ...

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 ...

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 ...

Venture capital firms use a variety of accumulated resources to inform their investment activities, but do the rely solely on their own resources or do they employ other firms' resources to complement ...

In geography it is important to be able to read and understand data that is presented in a range of different ways. We often use graphs to present data in a clear and accessible way. There are many ...