Community Landscapes: An Integrative Approach to Determine Overlapping Network Module Hierarchy, Identify Key Nodes and Predict Network Dynamics
Panel A: Comparison of the identified modules with the modules of the benchmark graph of Lancichinetti et al. . Modularization has been performed on benchmark graphs with degree and module size distribution exponents γ = 2 and β = 1 using the NodeLand or LinkLand influence function calculation algorithm with the ProportionalHill module membership assignment method with merging highly correlated modules using an arbitrary chosen correlation threshold of 0.9 (see Section VI.1. in the Electronic Supplementary Material S1; red squares with dashed line and red rectangles with solid line for NodeLand and LinkLand, respectively), the InfoMap method (black circles with dotted line, ), the Louvain method (black circles with solid line, ) and the CFinder method with k = 4 cliques (black circles with dashed line, ). The number of nodes of the benchmark graphs was N = 1000, the maximum degree was Kmax = 50, the average degree was K = 15 and the network fuzziness μ of the x-axis of Panel A) was ranging from 0.1 to 0.85, where μ>0.5 means that the modules are no longer defined in the strong sense. Higher normalized mutual information (shown on the y-axis) represents a better recovery of the original modules. The panel shows the averaged results of 50 representations. Panel B: comparison of module assignment of the cAMP-dependent protein kinase family in the yeast protein-protein interaction network. The panel shows the modular assignment of the 3 catalytic and the regulatory subunit of the yeast cAMP-dependent protein kinase together with that of their first neighbors in the high fidelity protein-protein interaction network of Ekman et al. . For the sake of simplicity only intra-subnetwork contacts have been included. The top left, top right, bottom left and bottom right figures show the modular assignment using the NodeLand, InfoMap, Louvain and CFinder methods, respectively, determined as described in the legend of Panel A. Various colors correspond to different modules. Overlapping ModuLand modules of cAMP kinase members and CFinder modules of their casein kinase II neighbor are marked with pie-charts, where the area of color-codes is proportional to the module membership value of the given node in the given module. To simplify the figure, in case of the NodeLand method (top right figure of Panel B) all neighbors of cAMP-dependent protein kinase family members (which should all have similar pie-charts to the 4 central members due to their multiple modules) were assigned to their maximal modules only.