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measure to determine whether or not a graph is a Small-world Network .

First, let us define a graph in terms of a set of n Vertices V=v_1,v_2,\dots,v_n and a set of Edges E, where e_{ij} denotes an edge between vertices v_i and v_j. Below we assume v_i, v_j and v_k are members of ''V''.

We define the Neighbourhood ''N'' for a vertex v_i as its immediately connected neighbours as follows:

: N_i = \{v_j\} : e_{ij} \in E.