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Finding Statistically Significant Communities in Networks

Figure 1

A schematic representation of a subgraph , whose significance is to be assessed.

The subgraph is embedded within a random graph generated by the configuration model. The degrees of all vertices of the network are fixed, in the figure we have highlighted the degrees of (), of the vertex at the center of the analysis () and of the rest of the graph (). These quantities are expressed as sums of contributions which are internal to their own set of vertices (as ) or related to subgraph (in or out). This notation is used in the distribution of Eq. 1.

Figure 1