Table 1.

Relationship between mean average controllability and modularity Q for various graph types

128 nodes	WRG	RL	WS	MD2	MD4	MD8	RG	BA
Gaussian
ρ	−0.0297	−0.1632	−0.2148	−0.1689	−0.2057	−0.0476	−0.4568	−0.0509
p	0.7691	0.1046	0.0321	0.0930	0.0403	0.6374	0.0000	0.6144
Streamline counts
ρ	−0.0376	−0.0539	0.1424	−0.3642	−0.1469	−0.1107	−0.0962	−0.7538
p	0.7097	0.5939	0.1575	0.0002	0.1444	0.2724	0.3404	0.0000

Spearman ρ-values and corresponding p-values for the correlations between mean average controllability and modularity Q. The two weighting schemes used are Gaussian weights and streamline counts, while the eight graph models are the weighted random graph (WRG), the ring lattice (RL), the Watts-Strogatz small-world (WS), the modular graphs (MD2, MD4, MD8), the random geometric (RG), and the Barabasi-Albert preferential attachment (BA) models. The p-values stated to be zero are below 10⁻⁵