A Shadowing Problem in the Detection of Overlapping Communities: Lifting the Resolution Limit through a Cascading Procedure
Complete detection is achieved with 6 iterations for Amazon (black squares), 8 iterations for DBLP (orange circles), and 10 iterations for the YouTube (blue triangles). (Top left panel) Normalized mutual information as a function of the number of iterations. (Top center panel) Selected similarity threshold at each iteration (cf. Eq (1)). (Top right panel) Density of the optimal link partition, in the sparser network. (Bottom left panel) Elapsed fraction of the total running time, averaged over 10 independent realizations. (Bottom center panel) Cumulative fraction of assigned edges. (Bottom right panel) Number of detected communities at each iteration. Numerical results are summarized in the Supporting Information (S4 Table).