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Dirichlet Eigenvalues, Local Random Walks, and Analyzing Clusters in Graphs

  • Pavel KolevEmail author
  • He Sun
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8889)

Abstract

A cluster \(S\) in a massive graph \(G\) is characterised by the property that its corresponding vertices are better connected with each other, in comparison with the other vertices of the graph. Modeling, finding and analyzing clusters in massive graphs is an important topic in various disciplines. In this work we study local random walks that always stay in a cluster \(S\). Moreover, we initiate the study of the local mixing time and the almost stable distribution, by analyzing Dirichlet eigenvalues in graphs. We prove that the Dirichlet eigenvalues of any connected subset \(S\) can be used to bound the \(\epsilon \)-uniform mixing time, which improves the previous best-known result. We further present two applications of our results. The first is a polynomial-time algorithm for finding clusters with an improved approximation guarantee, while the second is the significance ordering of vertices in a cluster.

Keywords

Random Walk Connected Graph Local Algorithm Isoperimetric Inequality Stable Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Max Planck Institute für InformaticsSaarbrückenGermany

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