Incidence matrix vs Adjacent Matrix

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    Incidence Matrix
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The discussion clarifies the differences between incidence matrices and adjacency matrices in graph theory. Incidence matrices represent the relationship between vertices and edges, indicating which vertices are connected to which edges, and can be asymmetric for directed graphs. In contrast, adjacency matrices are typically used for undirected graphs and are symmetric. The definition of incidence matrices can vary, with some sources presenting them as transposed versions. Understanding these distinctions is crucial for accurately analyzing graph structures.
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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