Biadjacency matrix

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 = egin{pmatrix}0 & B \B^T & 0 end{pmatrix}.

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


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