Table 3.

Network characteristics and controllability results for the real-world networks considered in this paper.

Network type	Name	Nodes	Edges	N r	N u	$\frac{{\mathit{\mu }}_{\mathbf{0}}\mathbf{+}\mathit{d}}{{\mathit{N}}^{\mathit{u}}}$	η
Biology, transcr.	E. coli-transcr.	1623	3620	1692	1466	1.13	1.16
	Yeast-transcr.	664	1064	759	500	1.45	1.52
Biology, signal.	EGFR-signal	329	852	123	67	1.84	1.84
	Toll-signal	680	2204	249	147	1.65	1.69
	Macrophage	678	1582	300	185	1.60	1.62
Biology, metab.	Yeast-metab.	780	4420	174	142	1.21	1.23
	E. coli-metab.	757	6116	116	102	1.02	1.14
Power grid	North Europe	236	320	85	43	1.95	1.98
	USPowerGrid	4941	6591	3887	2166	1.72	1.79
	French Power Grid	1888	2531	1692	945	1.75	1.79
Transport	US Air lines	332	2126	191	111	1.51	1.72
	US Air traffic	1206	13106	511	420	1.15	1.21
Internet	Gnutella	6301	20777	8047	4106	1.94	1.96
	AS-733	3015	10312	1928	1883	1.03	1.03
Food-web	Florida	128	2106	35	30	1.10	1.17
	Michigan	39	221	16	13	1.23	1.23
	Mangdry	97	1491	26	22	1.14	1.18
	Everglades	69	916	26	21	1.14	1.24
Trade	Similar export	866	2532	100	84	1.19	1.19
	Wheat	166	1789	59	35	1.60	1.69
Water dist.	EXNET	1893	4832	167	113	1.47	1.48
	Richmond	865	1870	110	65	1.57	1.69

See SI for data sources. Just as for Erdős–Rényi networks and directed scale-free networks, η is in many cases close to the lower bound (d + μ ₀)/N ^u.