Biadjacency matrix

In mathematics and computer science, the biadjacency matrix for 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 relationship between a bipartite graph and its biadjacency matrix is studied in spectral graph theory.

Property

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

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