Coates graph

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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.[1][2]

The Coates graph Gc(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 aji ≠ 0 then there is a directed edge from node i to node j with weight aji.[3] In other words, the Coates graph for matrix A is the one whose adjacency matrix is the transpose of A.

See also[edit]


  1. ^ Graphs:Theory and Algorithms, by K. Thulasiraman, M. N. S. Swamy (1992) ISBN 0-471-51356-3, pp. 163-169
  2. ^ C.L. Coates, "Flow-graph solutions of linear algebraic equations," IRE Trans. Circuit Theory, vol. CT-6, pp. 170-187, 1959
  3. ^ Chen, Wai-Kai. Applied Graph Theory. North Holland Publishing Company, 1976.