Enumerating simple paths from connected induced subgraphs
  We present an exact formula for the ordinary generating series of the simple paths between any two vertices of a graph. Our formula involves the adjacency matrix of the connected induced subgraphs and remains valid on weighted and directed graphs. As a particular case, we obtain a relation linking the Hamiltonian paths and cycles of a graph to its dominating connected sets. 
Pierre-Louis Giscard, Paul Rochet (LMJL)
math.CO