  Given the adjacency matrix of an undirected graph, we define a coupling of
the spectral measures at the vertices, whose moments count the rooted closed
paths in the graph. The resulting joint spectral measure verifies numerous
interesting properties that allow to recover minors of analytical functions of
the adjacency matrix from its generalized moments. We prove an extension of
Obata's Central Limit Theorem in growing star-graphs to the multivariate case
and discuss some combinatorial properties using Viennot's heaps of pieces point
of view.
