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BUILT-IN MATHEMATICA SYMBOL
IncidenceMatrix
IncidenceMatrix[g]
gives the vertex-edge incidence matrix of the graph g.
Details
- IncidenceMatrix returns a SparseArray object, which can be converted to an ordinary matrix using Normal.
- For an undirected graph, an entry
of the incidence matrix is given by: -
0 vertex 
is not incident to edge 
1 vertex 
is incident to edge 
2 vertex 
is incident to edge 
and a self-loop - For a directed graph, an entry
of the incidence matrix is given by: -
0 vertex 
is not incident to edge 
1 vertex 
is incident to edge 
and 
is the head of 
-1 vertex 
is incident to edge 
and 
is the tail of 
2 vertex 
is incident to edge 
and a self-loop - The vertices
are assumed to be in the order given by VertexList[g] and the edges 
are assumed to be in the order given by EdgeList[g]. - The incidence matrix for a graph will have an
×
matrix, where 
is the number of vertices and 
is the number of edges, counting multiplicity.
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