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 for the mean and variance of the ...

In this article, we use newly developed statistical methods to examine the generative processes that give rise to widespread patterns in friendship networks. The methods incorporate both traditional ...

A PHASE relation familiar to students of applied mathematics exists between a simple harmonic oscillation and its derivative. Similar relations exist between exponential functions and their ...