Coates graph
From HandWiki
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
- Flow graph (mathematics)
- Mason graph
References
- ↑ Thulasiraman, K.; Swamy, M. N. S. (1992). "§6.11 The Coates and Mason graphs". Graphs:Theory and Algorithms. John Wiley & Sons. pp. 163–169. ISBN 0-471-51356-3. https://books.google.com/books?id=4kHN6uSinQoC&q=%22coates+method%22&pg=PA163.
- ↑ Coates, C.L. (1959). "Flow-graph solutions of linear algebraic equations". IRE Trans. Circuit Theory CT-6 (2): 170–187. doi:10.1109/TCT.1959.1086537.
- ↑ Wai-Kai Chen (1976). "The associated Coates graph". Applied Graph Theory. North Holland Publishing Company. p. 142. https://www.google.com/search?tbm=bks&q=%22For+a+square+matrix%22+%22is+an+n-node,+weighted,+labeled,+directed+graph%22.
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