Advances in Applied Probability, Vol. 50, No. 1 (2018), pp. 272-301 (30 pages) We consider a family of directed exponential random graph models parametrized by edges and outward stars. Much of the ...

Random graph null models have found widespread application in diverse research communities analyzing network datasets, including social, information, and economic networks, as well as food webs, ...

This lecture course is devoted to the study of random geometrical objects and structures. Among the most prominent models are random polytopes, random tessellations, particle processes and random ...

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 ...

Quantum graphs—networks composed of vertices connected by edges on which quantum wave dynamics are defined—have emerged as a versatile model for exploring the interplay between geometry, topology, and ...

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 ...

Expanders graphs are sparse but well-connected. These seemingly contrasting properties have led to many applications in theoretical computer science, from complexity ...

According to mathematical legend, Peter Sarnak and Noga Alon made a bet about optimal graphs in the late 1980s. They’ve now both been proved wrong. It started with a bet. In the late 1980s, at a ...