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Growing Well-connected Graphs
Abstract
The algebraic connectivity of a graph is the second smallest eigenvalue of the graph Laplacian, and is a measure of how well-connected the graph is. We study the problem of adding edges (from a set of candidate edges) to a graph so as to maximize its algebraic connectivity. This is a difficult combinatorial optimization, so we seek a heuristic for approximately solving the problem. The standard convex relaxation of the problem can be expressed as a semidefinite program (SDP); for modest sized problems, this yields a cheaply computable upper bound on the optimal value, as well as a heuristic for choosing the edges to be added. We describe a new greedy heuristic for the problem. The heuristic is based on the Fiedler vector, and therefore can be applied to very large graphs
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Boyd, S., & Vandenberghe, L. (2004) · doi:10.1017/cbo9780511804441 · Cited by 56,601
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Metadata
- Authors
- Ghosh, A., & Boyd, S.
- Venue
- Proceedings of the 45th IEEE Conference on Decision and Control
- Publisher
- IEEE
- Published
- 2006
- Pages
- 6605-6611
- ISSN
- 0191-2216 (ISSN-L)
- OpenAlex
- W2116673134
- Cited by
- 341
- References
- 1
- FWCI
- 22.87
- Type
- conference paper
- Language
- en
- Open access
- closed
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