  Let $\ell$ be a prime number. The Iwasawa theory of multigraphs is the
systematic study of growth patterns in the number of spanning trees in abelian
$\ell$-towers of multigraphs. In this context, growth patterns are realized by
certain analogues of Iwasawa invariants, which depend on the prime $\ell$ and
the abelian $\ell$-tower of multigraphs. We formulate and study statistical
questions about the behaviour of the Iwasawa $\mu$ and $\lambda$ invariants.
