We study the asymptotics for sparse exponential random graph models where the parameters may depend on the number of vertices of the graph. We obtain exact estimates ...

Before reading this guide, you may find it helpful to read the guide on graphs from Module 7 (M7) and the guide on indices from Module 8 (M8). In Module 7 (M7) Graphs, you learned that simultaneous ...

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 ...