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Relationship to matrix bandwidth |
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The '''weighted graph bandwidth problem''' is a generalization wherein the edges are assigned weights ''w<sub>ij</sub>'' and the [[Loss function|cost function]] to be minimized is <math>\max\{\, w_{ij} |f(v_i) - f(v_j)| : v_iv_j \in E \,\}</math>.
In terms of matrices, the (unweighted) graph bandwidth is the minimal [[bandwidth (matrix theory)|bandwidth]] of
The bandwidth may also be defined as one less than the [[maximum clique]] size in a [[proper interval graph|proper interval]] supergraph of the given graph, chosen to minimize its clique size {{harv|Kaplan|Shamir|1996}}.
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