Biadjacency matrix

In mathematics and computer science, the biadjacency matrix of a finite bipartite graph G with n black vertices and m white vertices is an n × m matrix where the entry a_ij is the number of edges joining black vertex i and white vertex j. In the special case of a finite, undirected, simple bipartite graph, the biadjacency matrix is a (0,1)-matrix.

The adjacency matrix A of a bipartite graph with biadjacency matrix B is given by

$A={\begin{pmatrix}0&B\\B^{T}&0\end{pmatrix}}.$

The relationship between a bipartite graph and its biadjacency matrix is studied in spectral graph theory.