Connecting boundary and interior - "Gauss's law" for graphs
  The Gauss's law, in an abstract sense, is a theorem that relates quantities on the boundary (flux) to the interior (charge) of a surface. An identity for soap froths were proved with the same boundary-interior relation. In this article, we try to construct a definition of flux for other graphs, such that a similar boundary-interior relation can be satisfied. 
Ching King Chan and Kwok Yip Szeto
cond-mat.stat-mech