Use this tag for questions in graph theory. Here a graph is a collection of vertices and connecting edges. Use (graphing-functions) instead if your question is about graphing or plotting functions.

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a closed formula to enumerate the self avoiding walks of a graph

Let $G$ be a directed graph with $N$ nodes and weighted adjacency matrix $W $ defined by $$ W_{ij} = \left\{ \begin{array}{cl} w_{ij} & \text{ if } \ i \ \text{ is connected to } j \\ 0 & ...