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. Author manuscript; available in PMC: 2017 Oct 16.
Published in final edited form as: Algorithms. 2017 Aug 19;10(3):93. doi: 10.3390/a10030093

Figure 1.

Figure 1

(A) Modularity Q(γ) given by Equation (1) versus resolution parameter γ for 50, 000 runs (10% of results displayed here) of the Louvain algorithm [42,47] at different γ on the unweighted NCAA Division I-A (2000) college football network [37,38]. Grey triangles indicate the number of communities that include ≥ 5 nodes in each run, while the green step function shows the number in the optimal partition in each domain; (B) Graphical depiction of CHAMP algorithm (see Section 2). Each line indicates Qσ(γ) given by Equation (2) for a particular partition σ. Both panels show the convex hull of these lines as the dashed green piecewise-linear curve, with the transition values represented by downward triangles.