Random Graph Models

Abstract

The network of interbank counterparty relationships, or skeleton, is the random graph that acts as the medium through which financial contagion is propagated. The basic properties are developed for several promising families of random graph constructions including configuration graphs and inhomogeneous random graphs. A new extension, called the assortative configuration model, is proposed. The main results of this chapter are theorems describing the large graph asymptotics of this new assortative configuration model, including a proof of the locally tree-like property. Finally, measures of network structure are surveyed.

Ye cannot live for yourselves; a thousand fibres connect you with your fellow-men, and along those fibres, as along sympathetic threads, run your actions as causes, and return to you as effects (Rev. Henry Melvill, Golden Lectures, (London, 1855), p. 454).