E. Roberts

A. Coolen

The analysis of real networks which contain many short loops requires novel methods, because they break the assumptions of tree-like models.

Networks observed in the real world often have many short loops. This violates the tree-like assumption
that underpins the majority of random graph models and most of the methods used for their analysis. In this
paper we sketch possible research routes to be explored in order to make progress on networks with many short
loops, involving old and new random graph models and ideas for novel mathematical methods. We do not present
conclusive solutions of problems, but aim to encourage and stimulate new activity and in what we believe to be
an important but under-exposed area of research. We discuss in more detail the Strauss model, which can be seen
as the ‘harmonic oscillator’ of ‘loopy’ random graphs, and a recent exactly solvable immunological model that
involves random graphs with extensively many cliques and short loops.

Random graph ensembles with many short loops