• Corpus ID: 18329687

Random walks on graphs

  title={Random walks on graphs},
  • Sodin
  • Published 2004
  • Mathematics
Most of the material in this handout is taken from: Daniel Spielman, Spectral and Algebraic Graph Theory. Manuscript, 2019. Let A be the adjacency matrix of a graph G. We use α1 ≥ · · · ≥ αn to denote the eigenvalues of A (note that they are ordered in the opposite direction with respect to the eigenvalues λ1 ≤ · · · ≤ λn of the Laplacian matrix L). If G is d-regular, then L = I − 1 dA and therefore λi = 1− αi d . Since λi ∈ [0, 2] for any G (even not regular), we have that αi ∈ [−d, d] for any… 

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