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
Canonical name	IncidenceMatrixWithRespectToAnOrientation
Date of creation	2013-05-16 21:09:13
Last modified on	2013-05-16 21:09:13
Owner	Mathprof (13753)
Last modified by	unlord (1)
Numerical id	7
Author	Mathprof (1)
Entry type	Definition
Classification	msc 05C50
Defines	orientation