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We adjust the node and edge weightings of graphs using convex optimization to impose bounds on their Laplacian spectra. First, we derive necessary and sufficient conditions that characterize the feasibility of spectral bounds given positive node and edge weightings. Synthesizing these conditions leads naturally to algorithms that exploit convexity to achieve several eigenvalue bounds simultaneously...
We adjust the node and edge weightings of graphs using convex optimization to impose bounds on their Laplacian spectra. We first derive necessary and sufficient conditions that characterize the feasibility of spectral bounds given positive node and edge weightings. Next, we propose algorithms that exploit convexity to achieve these bounds. The design and analysis tools are useful for a variety of...
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