  We treat the stationary nonlinear Schroodinger equation on two-dimensional
branched domains, so-called fat graphs. The shrinking limit when the domain
becomes one-dimensional metric graph is studied by using analytical estimate of
the convergence of fat graph boundary conditions into those for metric graph.
Detailed analysis of such convergence on the basis of numerical solution of
stationary nonlinear Schrodinger equation on a fat graph is provided.
Possibility for reproducing different metric graph boundary conditions studied
in earlier works is shown. Practical applications of the proposed model for
such problems as Bose-Einstein condensation in networks, branched optical
media, DNA, conducting polymers and wave dynamics in branched capillary
networks are discussed.
