Adjacency Matrix of A Bipartite Graph
The adjacency matrix A of a bipartite graph whose parts have r and s vertices has the form
where B is an r × s matrix and O is an all-zero matrix. Clearly, the matrix B uniquely represents the bipartite graphs. It is sometimes called the biadjacency matrix. Formally, let G = (U, V, E) be a bipartite graph with parts and . The biadjacency matrix is the r x s 0-1 matrix B in which iff .
If G is a bipartite multigraph or weighted graph then the elements are taken to be the number of edges between the vertices or the weight of the edge respectively.
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