Local Limits of Graphs
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, y ∈ V, 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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