Hi All,
I am looking for a method that provides a lower bound for the second smallest eigenvalue (the Fiedler eigenvalue) of a weighted Laplacian of an undirected and connected graph. I have seen several results on unweighted Laplacians, but not on weighted ones. Thank you.
Maybe to check this approach:
https://www.tandfonline.com/doi/abs/10.1080/00207721.2020.1758234?journalCode=tsys20
Have a look at https://www.mathworks.com/help/matlab/math/partition-graph-with-laplacian-matrix.html
https://www.sciencedirect.com/topics/computer-science/laplacian-matrix
You may take a look at the following papers:
1) The Laplacian eigenvalues of graphs: a survey (Section 6).
2) A lower bound for algebraic connectivity based on the connection-graph-stability method.
I am a beginner in this field. Thanks MirSaleh Bahavarnia , Muhammad Ali , and Anton Vrdoljak .
My pleasure Mahdieh S. Sadabadi , I hope those papers would be helpful.
Recently I have read some papers about this issue. An interesting work maybe is :
"Decentralized estimation and control of graph connectivity for mobile
sensor networks", Automatica 2010.
which has provided a DISTRIBUTED approach to estimate the second smallest eigenvalue of a weighted Laplacian matrix. I hope it helps.
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