Laplacian Spectral Properties of Graphs from Random Local Samples

  title={Laplacian Spectral Properties of Graphs from Random Local Samples},
  author={Zhengwei Wu and Victor M. Preciado},
The Laplacian eigenvalues of a network play an important role in the analysis of many structural and dynamical network problems. In this paper, we study the relationship between the eigenvalue spectrum of the normalized Laplacian matrix and the structure of `local' subgraphs of the network. We call a subgraph \emph{local} when it is induced by the set of nodes obtained from a breath-first search (BFS) of radius $r$ around a node. In this paper, we propose techniques to estimate spectral… 

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