Incidence matrix vs Adjacent Matrix

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    Incidence Matrix
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SUMMARY

The discussion clarifies the differences between incidence matrices and adjacency matrices in graph theory. An adjacency matrix represents undirected graphs and is symmetric, while an incidence matrix can represent directed graphs and is not necessarily symmetric. The incidence matrix is defined as a (0,1)-matrix with rows for vertices and columns for edges, indicating the incidence relationship between them. This definition is supported by sources such as Skiena (1990) and MathWorld.

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

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.
 
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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
 

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