In mathematics, the Coates graph or Coates flow graph, named after C.L. Coates, is a graph associated with the Coates' method for the solution of a system of linear equations.
The Coates graph G<sub>c</sub>(A) associated with an n àn matrix A is an n-node, weighted, labeled, directed graph. The nodes, labeled 1 through n, are each associated with the corresponding row/column of A. If entry a<sub>ji</sub> â 0 then there is a directed edge from node i to node j with weight a<sub>ji</sub>. In other words, the Coates graph for matrix A is the one whose adjacency matrix is the transpose of A.