Talk:Algebraic connectivity
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Values of the algebraic connectivity in actual networks
[edit]FWIW, here's a table of values for the algebraic connectivity for lots of real networks: http://konect.uni-koblenz.de/statistics/alcon –Jérôme (talk) 08:16, 23 January 2014 (UTC)
- Disclaimer, I'm the author of that page.–Jérôme (talk) 08:16, 23 January 2014 (UTC)
Bounds for algebraic connectivity
[edit]I am slightly confused by the sentence 'Furthermore, the value of the algebraic connectivity is bounded above by the traditional (vertex) connectivity of the graph'. It purports to be from [1] but I can find no such statement on that page. Slight testing in Mathematica reveals it to be false for complete graphs (where vertex connectivity = n - 1, algebraic connectivity = n). Any thoughts? Erik (talk) 08:47, 22 May 2015 (UTC)
References
- ↑ J.L. Gross and J. Yellen. Handbook of Graph Theory, CRC Press, 2004, page 314
Non-negative edges
[edit]The article says "The algebraic connectivity of undirected graphs with nonnegative weights is , with the inequality being strict if and only if G is connected." I believe "nonnegative" should be "positive". If zero-weight edges are allowed, then a connected graph (even a clique) can have a zero connectivity matrix, and hence . LachlanA (talk) LachlanA (talk) 04:47, 8 June 2025 (UTC)
