Editing Adjacency matrix (section)

===Of a bipartite graph===
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The adjacency matrix {{mvar|A}} of a [[bipartite graph]] whose two parts have {{mvar|r}} and {{mvar|s}} vertices can be written in the form 
: <math>A = \begin{pmatrix} 0_{r,r} & B \\ B^\mathsf{T} & 0_{s,s} \end{pmatrix},</math>
where {{mvar|B}} is an {{math|''r'' × ''s''}} matrix, and {{math|0<sub>''r'',''r''</sub>}} and {{math|0<sub>''s'',''s''</sub>}} represent the {{math|''r'' × ''r''}} and {{math|''s'' × ''s''}} [[zero matrix|zero matrices]]. In this case, the smaller matrix {{mvar|B}} uniquely represents the graph, and the remaining parts of {{mvar|A}} can be discarded as redundant. {{mvar|B}} is sometimes called the ''biadjacency matrix''.

Formally, let {{math|''G'' {{=}} (''U'', ''V'', ''E'')}} be a [[bipartite graph]] with parts {{math|''U'' {{=}} {''u''<sub>1</sub>, ..., ''u''<sub>''r''</sub>}<nowiki/>}}, {{math|''V'' {{=}} {''v''<sub>1</sub>, ..., ''v''<sub>''s''</sub>}<nowiki/>}} and edges {{mvar|E}}. The biadjacency matrix is the {{math|''r'' × ''s''}} 0–1 matrix {{mvar|B}} in which {{math|''b''<sub>''i'',''j''</sub> {{=}} 1}} [[if and only if]] {{math|(''u''<sub>''i''</sub>, ''v''<sub>''j''</sub>) ∈ ''E''}}.

If {{mvar|G}} is a bipartite [[multigraph]] or [[weighted graph]], then the elements {{mvar|b''<sub>i,j</sub>''}} are taken to be the number of edges between the vertices or the weight of the edge {{math|(''u''<sub>''i''</sub>, ''v''<sub>''j''</sub>)}}, respectively.