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Graphs from Zero-One Matrices

A zero-one matrix has entries that are either zero or one. Such matrices are often used to encode a relation between two sets of objects; a one at means the object is related to the object and a zero means they are not. For an undirected graph, a one at means that vertex is joined to vertex .

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For undirected graphs it is sufficient to consider lower-triangular matrices, though the matrix is usually taken to be symmetric.
Self-loops would be indicated by ones on the main diagonal, but such entries are not allowed here.
Directed edges and multiple edges are not considered here. Directed edges correspond to matrices that are not symmetric.
Multiple edges would be indicated by positive integer entries.
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