Table 1. Topological data for the ten real networks studied.

size of the networks (N), number of edges (E), mean degree (〈k〉), modularity (Q), relative size of the largest community ($N_{mod}^{max}$), fraction of edges linking distinct communities (E _inter), and the overall efficiency gain of the MBA method (η, see Eq (3) for definition). For the four parameters related with community detection we display the values corresponding to the most efficient case among ten seeds of infomap (I) and ten seeds of Louvain (L). These data is presented for node and edge attacks.

					Node Attack				Edge Attack
Network	N	E	〈k〉	Q	$N_{mod}^{max}$	E inter	η		Q	$N_{mod}^{max}$	E inter	η
Facebook	2888	2981	2.06	0.81	0.262	0.012	4.19	(L)	0.81	0.262	0.012	4.19	(L)
Twitter	23370	32831	2.81	0.82	0.018	0.169	38.44	(I)	0.83	0.018	0.168	38.30	(I)
Google Plus	23628	39194	3.32	0.69	0.070	0.279	22.80	(I)	0.69	0.070	0.279	22.80	(I)
US power grid	4941	6594	2.67	0.94	0.049	0.033	111.02	(L)	0.82	0.007	0.178	72.92	(I)
Euro roads	1174	1417	2.41	0.79	0.016	0.203	108.40	(I)	0.79	0.014	0.198	95.16	(I)
Open flights	2939	15677	10.67	0.65	0.184	0.142	8.30	(L)	0.65	0.182	0.139	8.14	(L)
US airports	1574	17215	21.87	0.35	0.296	0.363	4.16	(L)	0.34	0.267	0.341	4.10	(L)
Yeast Protein	1846	2203	2.39	0.77	0.025	0.223	36.14	(I)	0.77	0.025	0.220	35.14	(I)
H pylori	724	1403	3.88	0.54	0.124	0.364	19.59	(L)	0.49	0.047	0.485	14.35	(I)
C elegans	453	2025	8.94	0.43	0.163	0.423	12.04	(L)	0.43	0.163	0.423	12.04	(L)