| Summary: | 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.
|
|---|
