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 ...

This is a preview. Log in through your library . Abstract In a random graph, counts for the number of vertices with given degrees will typically be dependent. We show via a multivariate normal and a ...

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 ...

This is a preview. Log in through your library . Abstract We derive the full phase diagram for a large family of two-parameter exponential random graph models, each containing a first order transition ...

As mathematical abstractions go, graphs are among the simplest. Scatter a bunch of points in a plane. Connect some of them with lines. That’s all a graph is. And yet they are incredibly powerful. They ...