Biadjacency matrices

Bipartite graphs can be represented using another type of matrix. Bipartite graphs have two types of vertices, which I'll call row-vertices and column-vertices, for reasons that will become obvious. All edges connect one row-vertex to one column-vertex, so it's not necessary to use a full adjacency matrix connecting all possible vertex pairs. Instead, we represent the edge from the ith row-vertex to the jth column-vertex by setting the element of the matrix at row i and column j. This type of matrix is called a biadjacency matrix, and is typically denoted as B. Because the number of row vertices and column vertices can be different, the biadjacency matrix does not need to be square. The bipartite graph can be projected into a graph containing only row-nodes (or only column-nodes) by using simple matrix operations.

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