Matrix Interpretation
If an undirected graph G has a matrix A as its adjacency matrix, then the adjacency matrix of the double cover of G is
and the biadjacency matrix of the double cover of G is just A itself. That is, the conversion from a graph to its double cover can be performed simply by reinterpreting A as a biadjacency matrix instead of as an adjacency matrix. More generally, the reinterpretation the adjacency matrices of directed graphs as biadjacency matrices provides a combinatorial equivalence between directed graphs and balanced bipartite graphs.
Read more about this topic: Bipartite Double Cover
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