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. However, some authors define the incidence matrix to be the transpose of this (including the standard form of the embedding-encoding generalization known as the rigidity matrix), with a column for each vertex and a row for each edge. The physicist Kirchhoff was the first to define the incidence matrix. The incidence matrix of a graph (using the first definition) can be computed in the Wolfram Language using IncidenceMatrix[g]. Precomputed incidence matrices for a many named graphs are given in the Wolfram Language by GraphData[graph, IncidenceMatrix].

adjacency matrix | integer matrix | k-chain | k-circuit | rigidity matrix