Comparison of LMM to SMD on real and simulated data
In order to evaluate the relationship between modules detected with SMD versus LMM, we chose modules on the Great Lakes dataset using SMD at R-value thresholds ranging from 0.05 to 0.7 and with LMM at the same R-value thresholds and gamma values ranging from 0.15 to 0.9. We found that with both LMM and SMD, modularity increased with increasing R-value thresholds. However, SMD produced less modular partitions and smaller modules than LMM, even when LMM was applied with very low values for the gamma parameter that controls module size (Figure 3 A,B).
In order to determine whether SMD produced related modules to LMM (e.g. since SMD modules are smaller, whether they represent sub-graphs of the larger LMM modules), we calculated a homogeneity score (described in methods section) between SMD and LMM modules in simulated networks. All networks contained 500 nodes. Modularity was calculated for the LMM partitions, and the homogeneity of SMD and LMM partitions was calculated. From our simulated networks, the homogeneity between SMD and LMM module partitions was between 0.55 and 0.87 (Figure 3 C,D). Notably, we found that for networks simulated with both power law and regular node degree distributions, as modularity of LMM partitions increased, the homogeneity between SMD- and LMM-partitioned modules increased (power law network Pearson R = 0.87, p < 0.001; regular network Pearson R = 0.93, p < 0.001). Thus, when network modularity is high (i.e. there is a high number of edges within the module compared to between modules), SMD partitions tend to be sub-partitions of LMM partitions.