Unbounded quantum graphs with unbounded boundary conditions
  We consider metric graphs with a uniform lower bound on the edge lengths but no further restrictions. We discuss how to describe every local self-adjoint Laplace operator on such graphs by boundary conditions in the vertices given by projections and self-adjoint operators. We then characterize the lower bounded self-adjoint Laplacians and determine their associated quadratic form in terms of the operator families encoding the boundary conditions. 
Daniel Lenz, Carsten Schubert and Ivan Veseli\'c
math-ph math.MP