Table 1. Number of nodes N, average degree 〈k〉, and the relative size 
of the mimimum controlling set found in 35 different real world networks. The values of 
reported are expressed as percentage of the network size N. The algorithms used to find approximations of minimum controlling sets, mark as controllers also nodes not controlling other nodes, simply because, at a certain iteration of the greedy procedure, they have remained with no out-going links. Therefore, we also report in parenthesis the relative size of the effective minimum controlling set and the percentage of the controlled nodes. The notation x% → y%, indicates that x% of the nodes is able to control the centrality of y% of the network. We report also, for each network, the relative size 
of the controlling set in randomized versions which preserve the original degree sequence. We have considered averages over 100 different randomizations. In the last two columns we report, respectively, the ratio α between the total degree of the nodes in the minimum controlling set and the number of nodes in the network, and the percentage p quantifying how many of the top-100 nodes with the highest degree belong to the minimum controlling set. From top to bottom, the networks are divided into six classes, respectively World-Wide-Web, collaboration/communication, citation, spatial, words and socio–economical networks.
| Network | N | 〈k〉 |
 (G) |
 (Grnd) |
α | p |
|---|---|---|---|---|---|---|
| Web (Berkley and Stanford)29 | 654782 | 22.2 | 8% (3%→95%) | 12% | 1.41 | 17% |
| Web (Google)29 | 875713 | 11.1 | 15% (9%→94%) | 22% | 1.74 | 92% |
| Web (Notre Dame)30 | 325729 | 9.2 | 13% (8%→95%) | 21% | 1.57 | 28% |
| Web (Stanford)29 | 281904 | 16.4 | 8% (3%→95%) | 15% | 1.45 | 21% |
| Jazz musicians31 | 198 | 27.7 | 8% (5%→97%) | 13% | 1.63 | – |
| Movie actors32 | 392340 | 7.2 | 11% (8%→97%) | 22% | 3.63 | 90% |
| Cond-Mat coauthorship33 | 12722 | 6.3 | 23%(18%→93%) | 29% | 1.24 | 23% |
| AstroPh coauthorship33 | 13259 | 18.7 | 16% (10%→94%) | 27% | 1.48 | 8% |
| Networks coauthorship34 | 379 | 4.8 | 20% (15%→94%) | 29% | 1.05 | – |
| URV email35 | 1133 | 9.6 | 23% (16%→91%) | 27% | 2.40 | 20% |
| ENRON email29,36 | 2351 | 118.7 | 7%(4%→97%) | 8% | 1.11 | 5% |
| Email EU-All37 | 265214 | 3.5 | 16% (1%→85%) | 26% | 1.49 | 95% |
| Wiki-talk38 | 2394385 | 4.20 | 2% (1%→99%) | 23% | 2.48 | 5% |
| Hep-Ph citation37 | 34401 | 12.25 | 16% (10%→94%) | 22% | 2.72 | 25% |
| Hep-Th citation37 | 27400 | 12.7 | 17%(8%→91%) | 22% | 2.27 | 15% |
| Patents37 | 3774768 | 8.75 | 50% (16%→60%) | 26% | 2.21 | 17% |
| Internet AS39 | 11174 | 4.2 | 9% (8%→99%) | 22% | 2.25 | 70% |
| US Airports40 | 500 | 11.9 | 14% (12%→97%) | 19% | 4.31 | – |
| US Power Grid41 | 4941 | 5.33 | 33% (29%→95%) | 23% | 2.21 | 9% |
| roadnet CA29 | 1965206 | 5.63 | 31% (30%→96%) | 23% | 1.96 | 1% |
| roadnet PA29 | 1088092 | 5.67 | 33% (30%→967%) | 23% | 1.98 | 1% |
| roadnet TX29 | 1379917 | 5.57 | 33% (30%→97%) | 23% | 1.99 | 1% |
| Electronic circuit (s208 st)42 | 123 | 3.1 | 29% (26%→96%) | 28% | 1.01 | – |
| Electronic circuit (s420 st)42 | 253 | 3.1 | 29% (25%→96%) | 28% | 1.01 | – |
| Electronic circuit (s838 st)42 | 513 | 3.2 | 29% (25%→96%) | 28% | 1.03 | – |
| Wordnet43 | 77595 | 3.44 | 26% (19%→92%) | 26% | 1.63 | 64% |
| USF Words associations44 | 10618 | 13.6 | 22% (8%→56%) | 25% | 5.15 | 22% |
| PGP45 | 10680 | 4.5 | 22% (18%→77%) | 29% | 1.84 | 39% |
| Amazon46 | 410236 | 16.36 | 17% (9%→91%) | 17% | 1.70 | 35% |
| Epinions47 | 75879 | 13.41 | 22% (19%→95%) | 18% | 7.45 | 90% |
| Gnutella37,48 | 62586 | 4.72 | 19%(11%→62%) | 31% | 2.60 | 21% |
| PolBlogs49 | 1224 | 31.2 | 13% (8%→94%) | 18% | 5.23 | 23% |
| PolBooks50 | 105 | 8.4 | 15% (12%→98%) | 22% | 1.48 | – |
| Slashdot29 | 82168 | 23.08 | 25% (21%→58%) | 27% | 1.75 | 3% |
| Wiki-vote38 | 8298 | 25.00 | 16% (15%→99%) | 20% | 11.04 | 56% |