  This work discusses the homogenization analysis for diffusion processes on
scale-free metric graphs, using weak variational formulations. The oscillations
of the diffusion coefficient along the edges of a metric graph induce internal
singularities in the global system which, together with the high complexity of
large networks constitute significant difficulties in the direct analysis of
the problem. At the same time, these facts also suggest homogenization as a
viable approach for modeling the global behavior of the problem. To that end,
we study the asymptotic behavior of a sequence of boundary problems defined on
a nested collection of metric graphs. This paper presents the weak variational
formulation of the problems, the convergence analysis of the solutions and some
numerical experiments.
