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.