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Finding Statistically Significant Communities in Networks

Figure 2

Probability distributions of the scores of vertices external to a given subgraph of the graph.

The score is the -th smallest score of the external vertices. In this particular case there are external vertices. In the figure, we plot , , , , (from left to right). As an example, the shaded areas show the cumulative probability for a few values of that would correspond to the values estimated in a practical situation. In this case, the black area, , is the least extensive and so . If , the vertices with scores , , and will be added to .

Figure 2