# 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.[1][2]

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}.[3] In other words, the Coates graph for matrix **A** is the one whose adjacency matrix is the transpose of **A**.

## See also

## References

- K. Thulasiraman, M. N. S. Swamy (1992). "§6.11 The Coates and Mason graphs".
*Graphs:Theory and Algorithms*. pp. 163–169. ISBN 0-471-51356-3. - C.L. Coates (1959). "Flow-graph solutions of linear algebraic equations".
*IRE Trans. Circuit Theory*.**CT-6**: 170–187. doi:10.1109/TCT.1959.1086537. -
Definition from Wai-Kai Chen (1976). "The associated Coates graph".
*Applied Graph Theory*. North Holland Publishing Company. p. 142.

This article is issued from
Wikipedia.
The text is licensed under Creative
Commons - Attribution - Sharealike.
Additional terms may apply for the media files.