Edmonds matrix

In graph theory, the Edmonds matrix $A$ of a bipartite graph $G(U,V,E)$ with sets of vertices $U=\{u_{1},u_{2},\dots ,u_{n}\}$ and $V=\{v_{1},v_{2},\dots ,v_{n}\}$ is defined by

$A_{ij}=\left\{{\begin{array}{ll}x_{ij}&(u_{i},v_{j})\in E\\0&(u_{i},v_{j})\notin E.\end{array}}\right.$