Spectral clustering based on the graph p-Laplacian
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
In how many steps the k peg version of the towers of Hanoi game can be solved?
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
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We study the relation between the diameter, the first positive eigenvalue of the discrete p-Laplacian, and the @?"p-distortion of a finite graph. We prove an inequality relating these three quantities, and apply it to families of Cayley and Schreier graphs. We also show that the @?"p-distortion of Pascal graphs, approximating the Sierpinski gasket, is bounded, which allows one to obtain estimates for the convergence to zero of the spectral gap as an application of the main result.