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Local Limits of Graphs

  • Itai Benjamini
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2100)

Abstract

In this section we will only consider connected simple graphs (i.e. without loops or multiple edges). We start by recalling few definitions from previous sections. If G = (V, E) is such a graph, and x, yV, the graph distance between x and y in G is defined to be the length of a shortest path in G between x and y, and is denoted by d G (x, y). A rooted graph (G, ρ) is a graph G together with a distinguished vertex ρ of G.

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Itai Benjamini
    • 1
  1. 1.Department of MathematicsThe Weizmann Institute of ScienceRehovotIsrael

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