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Community Landscapes: An Integrative Approach to Determine Overlapping Network Module Hierarchy, Identify Key Nodes and Predict Network Dynamics

Figure 4

Overlapping modules of a school-friendship network.

We have determined the modular structure of Community-44 of the Add Health survey [27] using the LinkLand influence function calculation method together with the ProportionalHill module membership assignment method. During the post-processing of the module assignment, we merged the modules with ProportionalHill module membership assignment-based correlation higher than 0.9 (see Section VI. in the Electronic Supplementary Material S1, we received similar results without this merging process; data not shown). Panel A: modules of Community-44. The school friendship network was laid out using the Kamada-Kawai algorithm. Nodes represent the individual students, and were colored according to the color of the friendship module they assigned the most. We show the modular structure of the first hierarchical level having 18 modules. The inset of Panel A shows color-codes of the modules with an area proportional to the size of the respective module. Panel B: the number of network modules in case of boys (blue, solid bars) and girls (red-black hatched bars) with mixed racial contents at the lowest hierarchical level (level 0). The extent of mixed racial content was monitored using the “effective number of races” (Section V.6.b. in the Electronic Supplementary Material S1) with a bin-size of 0.5. Panel C: overlaps of boys and girls in friendship circles. The number of boys (blue, solid bars) and girls (red-black hatched bars) having different overlaps in friendship circles were determined in the first hierarchical level with a bin-size of 1. Overlap was measured as the “effective number” (Section V.6.b. in the Electronic Supplementary Material S1) of modules of the given student.

Figure 4