Coates graph

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""c"(A) associated with an "n" × "n" 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""ji" ≠ 0 then there is a directed edge from node "i" to node "j" with weight "a""ji". In other words, the Coates graph for matrix A is the one whose adjacency matrix is the transpose of A.