# incidence matrix with respect to an orientation

Let $G$ be a finite graph with $n$ vertices, $\{v_{1},\ldots,v_{n}\}$ and $m$ edges, $\{e_{1},\ldots,e_{m}\}$. For each edge $e=(v_{i},v_{j})$ of $G$ choose one vertex to be the positive end and the other to be the negative end. In this way, we assign an orientation to $G$. The of $G$ with respect an orientation is an $n\times m$ matrix $D=(d_{ij})$ where

 $d_{ij}=\left\{\begin{array}[]{ll}+1&\textrm{if v_{i} is the positive end of % e_{j}}\\ -1&\textrm{if v_{i} is the negative end of e_{j}}\\ 0&\textrm{otherwise}.\end{array}\right.$
Title incidence matrix with respect to an orientation IncidenceMatrixWithRespectToAnOrientation 2013-05-16 21:09:13 2013-05-16 21:09:13 Mathprof (13753) unlord (1) 7 Mathprof (1) Definition msc 05C50 orientation