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Introductory Graph and Metric Notions

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Part of the Lecture Notes in Mathematics book series (LNMECOLE,volume 2100)

Abstract

In this section we start by reviewing some geometric properties of graphs. Those will be related to the behavior of random processes on the graphs in later sections.

Keywords

  • Cayley Graph
  • Transitive Graph
  • Intermediate Growth
  • Galton Watson Process
  • Cheeger Constant

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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Fig. 1.1
Fig. 1.2
Fig. 1.3
Fig. 1.4
Fig. 1.5
Fig. 1.6

Notes

  1. 1.

    For every choice of v ∈ V and r > 0.

  2. 2.

    A graph that can be embedded in the plane.

  3. 3.

    The number of vertices at distance ≤ n from some fixed vertex growth polynomially.

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Benjamini, I. (2013). Introductory Graph and Metric Notions. In: Coarse Geometry and Randomness. Lecture Notes in Mathematics(), vol 2100. Springer, Cham. https://doi.org/10.1007/978-3-319-02576-6_1

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