  We introduce a nonlinear operator to model diffusion on a complex undirected
network under crowded conditions. We show that the asymptotic distribution of
diffusing agents is a nonlinear function of the nodes' degree and saturates to
a constant value for sufficiently large connectivities, at variance with
standard diffusion in the absence of excluded-volume effects. Building on this
observation, we define and solve an inverse problem, aimed at reconstructing
the a priori unknown connectivity distribution. The method gathers all the
necessary information by repeating a limited number of independent measurements
of the asymptotic density at a single node that can be chosen randomly. The
technique is successfully tested against both synthetic and real data, and
shown to estimate with great accuracy also the total number of nodes.
