# Incidence matrix vs Adjacent Matrix

1. Jun 21, 2010

### John Creighto

What is the difference between an http://en.wikipedia.org/wiki/Incidence_matrix" [Broken]. They sound the same to me but this paper says they are different:
http://eprints.pascal-network.org/archive/00005332/01/barber_newton.pdf [Broken]

edit: My guess is that adjacent matrices refer to non directed graphs so the matrix will be symmetric while an incidence matrix also incidence directed graphs so need not be symmetric.

Last edited by a moderator: May 4, 2017
2. Jun 21, 2010

### John Creighto

The deffinition at mathworld clarified it for me:

The incidence matrix of a graph gives the (0,1)-matrix which has a row for each vertex and column for each edge, and (v,e)=1 iff vertex v is incident upon edge e (Skiena 1990, p. 135). However, some authors define the incidence matrix to be the transpose of this, with a column for each vertex and a row for each edge. The physicist Kirchhoff (1847) was the first to define the incidence matrix. ​
http://mathworld.wolfram.com/IncidenceMatrix.html