predicting percolation thresholds in...
TRANSCRIPT
Supplemental Material “Predicting percolation thresholds in networks”
Filippo RadicchiCenter for Complex Networks and Systems Research,
School of Informatics and Computing, Indiana University, Bloomington, USA∗
10−3 10−2 10−1 100
pc
10−3
10−2
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100
p c
a
10−3 10−2 10−1 100
pc
10−3
10−2
10−1
100
p c
b
10−3 10−2 10−1 100
pc
10−3
10−2
10−1
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p c
c
10−610−510−410−310−210−1 100
connectance
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abso
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f10−610−510−410−310−210−1 100
connectance
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10−5 10−4 10−3 10−2 10−1 100
absolute error
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ion e
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FIG. 1: a) Comparison between the prediction values pc and pc, b) pc and pc, and c) pc and pc for all 109 realnetworks considered in our analysis. d) Relative errors of the predictions with respect to the best estimates pc asfunctions of the connectance of the network. e) Cumulative distribution of the absolute error committed in usinga prediction value instead of the best estimate of the percolation threshold. f) Abosolute errors as functions ofthe graph connectance.
∗Electronic address: [email protected].
10−1 100
relative error
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pc
pc
10−3 10−2 10−1 100
best estimate
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IPR×N
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10−5 10−4 10−3 10−2 10−1 100
absolute error
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c
FIG. 2: Inverse participation ratio (IPR) multiplied by the network size (N) of the principal eigenvectors of theadjacency (red squares) and the non-backtracking matrices (black circles) as functions of the value of the bestestimate of the percolation threshold pc (panel a), the relative error (panel b), and the absolute error (panel c).Each point refers to numerical results obtained on one of the 109 real networks considered in our analysis.
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network N E pc qc pc pc pc Fig. Refs. Url
Social 3 32 80 0.2500 0.3125 0.2025 0.1675 0.2109 3 [37] url
Karate club 34 78 0.2436 0.3824 0.1477 0.1487 0.1889 4 [56] url
Protein 2 53 123 0.3902 0.6038 0.2278 0.1722 0.2139 5 [37] url
Dolphins 62 159 0.2390 0.3871 0.1723 0.1390 0.1668 6 [32] url
Social 1 67 142 0.3099 0.4030 0.2351 0.1789 0.2294 7 [37] url
Les Miserables 77 254 0.1339 0.3377 0.0905 0.0833 0.0930 8 [23] url
Protein 1 95 213 0.6056 0.8000 0.2533 0.1865 0.2354 9 [37] url
E. Coli, transcription 97 212 0.5189 0.6495 0.2270 0.1531 0.1874 10 [33] url
Political books 105 441 0.1927 0.3429 0.0915 0.0838 0.0941 11 [1] url
David Copperfield 112 425 0.1035 0.1786 0.0783 0.0760 0.0867 12 [41] url
College football 115 613 0.1338 0.2087 0.1027 0.0928 0.1024 13 [14] url
S 208 122 189 0.4656 0.5492 0.3614 0.2435 0.3640 14 [37] url
High school, 2011 126 1, 709 0.0380 0.0873 0.0315 0.0294 0.0304 15 [13] url
Bay Dry 128 2, 106 0.0304 0.0469 0.0253 0.0249 0.0257 16 [24, 52] url
Bay Wet 128 2, 075 0.0308 0.0469 0.0256 0.0252 0.0260 17 [24] url
Radoslaw Email 167 3, 250 0.0203 0.0419 0.0158 0.0165 0.0168 18 [24, 36] url
High school, 2012 180 2, 220 0.0437 0.0944 0.0350 0.0332 0.0345 19 [13] url
Little Rock Lake 183 2, 434 0.0300 0.0874 0.0239 0.0242 0.0250 20 [24, 34] url
Jazz 198 2, 742 0.0314 0.0859 0.0266 0.0250 0.0258 21 [15] url
S 420 252 399 0.4511 0.5357 0.3437 0.2294 0.3462 22 [37] url
C. Elegans, neural 297 2, 148 0.0540 0.1044 0.0399 0.0410 0.0439 23 [54] url
Network Science 379 914 0.3982 0.6359 0.1424 0.0964 0.1148 24 [41] url
Dublin 410 2, 765 0.0778 0.1951 0.0564 0.0428 0.0450 25 [19, 24] url
US Air Trasportation 500 2, 980 0.0268 0.1080 0.0189 0.0208 0.0215 26 [11] url
S 838 512 819 0.4493 0.5449 0.3301 0.1996 0.3401 27 [37] url
Yeast, transcription 662 1, 062 0.2458 0.3414 0.0799 0.1002 0.1538 28 [38] url
URV email 1, 133 5, 451 0.0646 0.1068 0.0565 0.0482 0.0519 29 [17] url
Political blogs 1, 222 16, 714 0.0168 0.0442 0.0125 0.0135 0.0138 30 [1] url
Air traffic 1, 226 2, 408 0.1815 0.2871 0.1573 0.1086 0.1336 31 [24] url
Yeast, protein 1, 458 1, 948 0.2988 0.3752 0.1632 0.1327 0.1980 32 [20] url
Petster, hamster 1, 788 12, 476 0.0273 0.0587 0.0224 0.0217 0.0226 33 [24] url
UC Irvine 1, 893 13, 835 0.0248 0.0449 0.0183 0.0208 0.0216 34 [24, 44] url
Yeast, protein 2, 224 6, 609 0.0794 0.1245 0.0639 0.0525 0.0577 35 [9] url
Japanese 2, 698 7, 995 0.0318 0.1160 0.0093 0.0233 0.0262 36 [37] url
Open flights 2, 905 15, 645 0.0199 0.0792 0.0182 0.0159 0.0163 37 [24, 43] url
GR-QC, 1993-2003 4, 158 13, 422 0.1345 0.2244 0.0589 0.0219 0.0225 38 [29] url
Tennis 4, 338 81, 865 0.0073 0.0274 0.0063 0.0062 0.0062 39 [47] none
US Power grid 4, 941 6, 594 0.6583 0.7353 0.3483 0.1336 0.1606 40 [54] url
HT09 5, 352 18, 481 0.0283 0.1700 0.0050 0.0211 0.0244 41 [19] url
Hep-Th, 1995-1999 5, 835 13, 815 0.1081 0.1973 0.1231 0.0554 0.0588 42 [40] url
TABLE I: Analysis of real networks. From left to right, we report: name of the network, number of nodes in thegiant component, number of edges in the giant component, best estimate of the bond percolation threshold, bestestimate of the site percolation threshold, prediction values p, pc and pc, figure showing the numerical results ofthe simulations of the bond percolation process, references of the paper(s) where the network was analyzed, andurl where network data have been dowloaded.
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network N E pc qc pc pc pc Fig. Refs. Url
Reactome 5, 973 145, 778 0.0114 0.0591 0.0070 0.0048 0.0048 43 [21, 24] url
Jung 6, 120 50, 290 0.0093 0.1239 0.0010 0.0070 0.0078 44 [24, 50] url
Gnutella, Aug. 8, 2002 6, 299 20, 776 0.0455 0.1121 0.0600 0.0352 0.0377 45 [29, 49] url
JDK 6, 434 53, 658 0.0091 0.1173 0.0010 0.0070 0.0077 46 [24] url
AS Oregon 6, 474 12, 572 0.0356 0.1767 0.0061 0.0216 0.0285 47 [28] url
English 7, 377 44, 205 0.0114 0.1590 0.0031 0.0091 0.0096 48 [37] url
Gnutella, Aug. 9, 2002 8, 104 26, 008 0.0451 0.1099 0.0632 0.0351 0.0376 49 [29, 49] url
French 8, 308 23, 832 0.0236 0.1284 0.0046 0.0165 0.0191 50 [37] url
Hep-Th, 1993-2003 8, 638 24, 806 0.0755 0.1363 0.0834 0.0322 0.0333 51 [29] url
Gnutella, Aug. 6, 2002 8, 717 31, 525 0.0648 0.1005 0.0746 0.0447 0.0489 52 [29, 49] url
Gnutella, Aug. 5, 2002 8, 842 31, 837 0.0565 0.1017 0.0725 0.0425 0.0463 53 [29, 49] url
PGP 10, 680 24, 316 0.0642 0.1935 0.0559 0.0236 0.0244 54 [5] url
Gnutella, August 4 2002 10, 876 39, 994 0.0762 0.0942 0.0771 0.0585 0.0655 55 [29, 49] url
Hep-Ph, 1993-2003 11, 204 117, 619 0.0048 0.0565 0.0077 0.0041 0.0041 56 [29] url
Spanish 11, 558 43, 050 0.0127 0.2093 0.0022 0.0098 0.0107 57 [37] url
DBLP, citations 12, 495 49, 563 0.0325 0.0652 0.0234 0.0234 0.0263 58 [24, 31] url
Spanish 12, 643 55, 019 0.0119 0.2347 0.0012 0.0090 0.0100 59 [24] url
Cond-Mat, 1995-1999 13, 861 44, 619 0.0637 0.1649 0.0798 0.0400 0.0432 60 [40] url
Astrophysics 14, 845 119, 652 0.0182 0.0551 0.0225 0.0135 0.0138 61 [40] url
Google 15, 763 148, 585 0.0078 0.0636 0.0011 0.0057 0.0064 62 [45] url
AstroPhys, 1993-2003 17, 903 196, 972 0.0132 0.0323 0.0155 0.0106 0.0108 63 [29] url
Cond-Mat, 1993-2003 21, 363 91, 286 0.0367 0.0836 0.0466 0.0264 0.0279 64 [29] url
Gnutella, Aug. 25, 2002 22, 663 54, 693 0.1150 0.1265 0.1026 0.0916 0.1066 65 [29, 49] url
Internet 22, 963 48, 436 0.0193 0.1940 0.0038 0.0140 0.0155 66 none url
Thesaurus 23, 132 297, 094 0.0112 0.0174 0.0098 0.0100 0.0102 67 [22, 24] url
Cora 23, 166 89, 157 0.0454 0.1184 0.0441 0.0317 0.0342 68 [24, 51] url
Linux, mailing list 24, 567 158, 164 0.0052 0.2261 0.0029 0.0045 0.0045 69 [24] url
AS Caida 26, 475 53, 381 0.0210 0.1640 0.0036 0.0144 0.0168 70 [28] url
Gnutella, Aug. 24, 2002 26, 498 65, 359 0.1060 0.1174 0.0906 0.0511 0.0927 71 [29, 49] url
Hep-Th, citations 27, 400 352, 021 0.0110 0.0245 0.0095 0.0090 0.0094 72 [24, 29] url
Cond-Mat, 1995-2003 27, 519 116, 181 0.0342 0.0814 0.0470 0.0248 0.0261 73 [40] url
Digg 29, 652 84, 781 0.0413 0.0577 0.0369 0.0324 0.0362 74 [12, 24] url
Linux, soft. 30, 817 213, 208 0.0076 0.0457 0.0012 0.0059 0.0065 75 [24] url
Enron 33, 696 180, 811 0.0100 0.4460 0.0071 0.0084 0.0087 76 [30] url
Hep-Ph, citations 34, 401 420, 784 0.0158 0.0332 0.0160 0.0131 0.0135 77 [24, 29] url
Cond-Mat, 1995-2005 36, 458 171, 735 0.0256 0.0585 0.0372 0.0195 0.0203 78 [40] url
Gnutella, Aug. 30, 2002 36, 646 88, 303 0.0968 0.1122 0.0956 0.0773 0.0878 79 [29, 49] url
Slashdot 51, 083 116, 573 0.0262 0.0435 0.0124 0.0170 0.0222 80 [16, 24] url
Gnutella, Aug. 31, 2002 62, 561 147, 878 0.0956 0.1082 0.0943 0.0759 0.0871 81 [29, 49] url
Facebook 63, 392 816, 886 0.0086 0.0192 0.0115 0.0075 0.0076 82 [53] url
TABLE II: Continuation of table I.
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network N E pc qc pc pc pc Fig. Refs. Url
Epinions 75, 877 405, 739 0.0062 0.0148 0.0055 0.0054 0.0055 83 [24, 48] url
Slashdot zoo 79, 116 467, 731 0.0088 0.0162 0.0069 0.0077 0.0078 84 [24, 26] url
Flickr 105, 722 2, 316, 668 0.0142 0.0662 0.0029 0.0016 0.0016 85 [24, 35] url
Wikipedia, edits 113, 123 2, 025, 910 0.0029 0.0085 0.0015 0.0025 0.0026 86 [7, 24] url
Petster, cats 148, 826 5, 447, 464 0.0010 0.0303 0.0001 0.0008 0.0009 87 [24] url
Gowalla 196, 591 950, 327 0.0073 0.0310 0.0033 0.0059 0.0063 88 [10, 24] url
Libimseti 220, 970 17, 233, 144 0.0011 0.0028 0.0006 0.0011 0.0011 89 [8, 24, 25] url
EU email 224, 832 339, 925 0.0119 0.5975 0.0018 0.0098 0.0103 90 [24, 29] url
Web Stanford 255, 265 1, 941, 926 0.0598 0.1932 0.0005 0.0022 0.0024 91 [30] url
Amazon, Mar. 2, 2003 262, 111 899, 792 0.0940 0.1539 0.0987 0.0425 0.0562 92 [27] url
DBLP, collaborations 317, 080 1, 049, 866 0.0337 0.0658 0.0482 0.0086 0.0087 93 [24, 31] url
Web Notre Dame 325, 729 1, 090, 108 0.0847 0.2037 0.0036 0.0054 0.0057 94 [2] url
MathSciNet 332, 689 820, 644 0.0478 0.0805 0.0648 0.0277 0.0298 95 [46] url
CiteSeer 365, 154 1, 721, 981 0.0250 0.0473 0.0211 0.0172 0.0190 96 [6, 24] url
Zhishi 372, 840 2, 318, 025 0.0301 0.0738 0.0000 0.0010 0.0011 97 [24, 42] url
Actor coll. net. 374, 511 15, 014, 839 0.0013 0.0047 0.0024 0.0012 0.0012 98 [4, 24] url
Amazon, Mar. 12, 2003 400, 727 2, 349, 869 0.0401 0.0761 0.0341 0.0178 0.0285 99 [27] url
Amazon, Jun. 6, 2003 403, 364 2, 443, 311 0.0364 0.0759 0.0338 0.0175 0.0248 100 [27] url
Amazon, May 5, 2003 410, 236 2, 439, 437 0.0360 0.0759 0.0334 0.0172 0.0248 101 [27] url
Petster, dogs 426, 485 8, 543, 321 0.0015 0.0380 0.0005 0.0013 0.0014 102 [24] url
Road network PA 1, 087, 562 1, 541, 514 0.6923 0.7571 0.4547 0.2263 0.3216 103 [30] url
YouTube friend. net. 1, 134, 890 2, 987, 624 0.0063 0.0171 0.0020 0.0048 0.0054 104 [24, 55] url
Road network TX 1, 351, 137 1, 879, 201 0.7362 0.7875 0.4661 0.2038 0.2809 105 [30] url
AS Skitter 1, 694, 616 11, 094, 209 0.0018 0.0130 0.0007 0.0015 0.0015 106 [28] url
Road network CA 1, 957, 027 2, 760, 388 0.6933 0.7582 0.4609 0.2156 0.3011 107 [30] url
Wikipedia, pages 2, 070, 367 42, 336, 614 0.0014 0.0046 0.0003 0.0012 0.0013 108 [46] url
US Patents 3, 764, 117 16, 511, 740 0.0290 0.0515 0.0492 0.0088 0.0091 109 [18, 24] url
DBpedia 3, 915, 921 12, 577, 253 0.0170 0.0380 0.0001 0.0014 0.0022 110 [3, 24] url
LiveJournal 5, 189, 809 48, 688, 097 0.0028 0.0116 0.0065 0.0019 0.0019 111 [24, 39] url
TABLE III: Continuation of tables I and II.
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0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
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susc
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FIG. 3: Social 3, N = 32, E = 80, pc = 0.2500, qc = 0.3125, pc = 0.2025, pc = 0.1675, pc = 0.2109
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
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0.0 0.50.0
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ngth a
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FIG. 4: Karate club, N = 34, E = 78, pc = 0.2436, qc = 0.3824, pc = 0.1477, pc = 0.1487, pc = 0.1889
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0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
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FIG. 5: Protein 2, N = 53, E = 123, pc = 0.3902, qc = 0.6038, pc = 0.2278, pc = 0.1722, pc = 0.2139
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
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FIG. 6: Dolphins, N = 62, E = 159, pc = 0.2390, qc = 0.3871, pc = 0.1723, pc = 0.1390, pc = 0.1668
0.0 0.2 0.4 0.6 0.8 1.0
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FIG. 7: Social 1, N = 67, E = 142, pc = 0.3099, qc = 0.4030, pc = 0.2351, pc = 0.1789, pc = 0.2294
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0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
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FIG. 8: Les Miserables, N = 77, E = 254, pc = 0.1339, qc = 0.3377, pc = 0.0905, pc = 0.0833, pc = 0.0930
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
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ngth a
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FIG. 9: Protein 1, N = 95, E = 213, pc = 0.6056, qc = 0.8000, pc = 0.2533, pc = 0.1865, pc = 0.2354
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0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
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0.0 0.5 1.00.00
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ility
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FIG. 10: E. Coli, transcription, N = 97, E = 212, pc = 0.5189, qc = 0.6495, pc = 0.2270, pc = 0.1531,pc = 0.1874
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
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1.0
0.0 0.2 0.4 0.60.0
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perc
olat
ion
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ngth a
0.0 0.2 0.4 0.60.00
0.02
0.04
susc
eptib
ility
b
FIG. 11: Political books, N = 105, E = 441, pc = 0.1927, qc = 0.3429, pc = 0.0915, pc = 0.0838, pc = 0.0941
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0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
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0.0 0.2 0.40.0
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rcol
atio
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reng
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0.0 0.2 0.40.00
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eptib
ility
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FIG. 12: David Copperfield, N = 112, E = 425, pc = 0.1035, qc = 0.1786, pc = 0.0783, pc = 0.0760,pc = 0.0867
10
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
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1.0
0.0 0.2 0.40.0
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rcol
atio
nst
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0.0 0.2 0.40.00
0.02
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eptib
ility
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FIG. 13: College football, N = 115, E = 613, pc = 0.1338, qc = 0.2087, pc = 0.1027, pc = 0.0928, pc = 0.1024
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
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1.0
0.0 0.5 1.00.0
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perc
olat
ion
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ngth a
0.0 0.5 1.00.00
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0.02
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susc
eptib
ility
b
FIG. 14: S 208, N = 122, E = 189, pc = 0.4656, qc = 0.5492, pc = 0.3614, pc = 0.2435, pc = 0.3640
11
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
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1.0
0.00 0.05 0.10 0.150.0
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1.0pe
rcol
atio
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reng
th a
0.00 0.05 0.10 0.150.00
0.01
0.02
susc
eptib
ility
b
FIG. 15: High school, 2011, N = 126, E = 1, 709, pc = 0.0380, qc = 0.0873, pc = 0.0315, pc = 0.0294,pc = 0.0304
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
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1.0
0.00 0.05 0.100.0
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perc
olat
ion
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ngth a
0.00 0.05 0.100.00
0.01
0.02
susc
eptib
ility
b
FIG. 16: Bay Dry, N = 128, E = 2, 106, pc = 0.0304, qc = 0.0469, pc = 0.0253, pc = 0.0249, pc = 0.0257
12
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
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0.00 0.05 0.100.0
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1.0pe
rcol
atio
nst
reng
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0.00 0.05 0.100.00
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eptib
ility
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FIG. 17: Bay Wet, N = 128, E = 2, 075, pc = 0.0308, qc = 0.0469, pc = 0.0256, pc = 0.0252, pc = 0.0260
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
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0.8
1.0
0.00 0.050.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.050.00
0.01
0.02su
scep
tibili
tyb
FIG. 18: Radoslaw Email, N = 167, E = 3, 250, pc = 0.0203, qc = 0.0419, pc = 0.0158, pc = 0.0165, pc = 0.0168
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
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1.0
0.00 0.05 0.10 0.150.0
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1.0
perc
olat
ion
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ngth a
0.00 0.05 0.10 0.150.00
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0.03
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eptib
ility
b
FIG. 19: High school, 2012, N = 180, E = 2, 220, pc = 0.0437, qc = 0.0944, pc = 0.0350, pc = 0.0332,pc = 0.0345
13
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.05 0.100.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.00 0.05 0.100.00
0.01
0.02
susc
eptib
ility
b
FIG. 20: Little Rock Lake, N = 183, E = 2, 434, pc = 0.0300, qc = 0.0874, pc = 0.0239, pc = 0.0242,pc = 0.0250
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.05 0.100.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.05 0.100.00
0.01
0.02
susc
eptib
ility
b
FIG. 21: Jazz, N = 198, E = 2, 742, pc = 0.0314, qc = 0.0859, pc = 0.0266, pc = 0.0250, pc = 0.0258
14
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.5 1.00.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.0 0.5 1.00.00
0.01
0.02
0.03
susc
eptib
ility
b
FIG. 22: S 420, N = 252, E = 399, pc = 0.4511, qc = 0.5357, pc = 0.3437, pc = 0.2294, pc = 0.3462
15
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.1 0.20.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.0 0.1 0.20.00
0.01
0.02
susc
eptib
ility
b
FIG. 23: C. Elegans, neural, N = 297, E = 2, 148, pc = 0.0540, qc = 0.1044, pc = 0.0399, pc = 0.0410,pc = 0.0439
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.5 1.00.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.0 0.5 1.00.00
0.02
0.04
susc
eptib
ility
b
FIG. 24: Network Science, N = 379, E = 914, pc = 0.3982, qc = 0.6359, pc = 0.1424, pc = 0.0964, pc = 0.1148
16
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.1 0.2 0.30.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.0 0.1 0.2 0.30.00
0.01
0.02
susc
eptib
ility
b
FIG. 25: Dublin, N = 410, E = 2, 765, pc = 0.0778, qc = 0.1951, pc = 0.0564, pc = 0.0428, pc = 0.0450
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.05 0.100.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.05 0.100.000
0.005
susc
eptib
ility
b
FIG. 26: US Air Trasportation, N = 500, E = 2, 980, pc = 0.0268, qc = 0.1080, pc = 0.0189, pc = 0.0208,pc = 0.0215
17
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.5 1.00.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.0 0.5 1.00.00
0.01
0.02
0.03
susc
eptib
ility
b
FIG. 27: S 838, N = 512, E = 819, pc = 0.4493, qc = 0.5449, pc = 0.3301, pc = 0.1996, pc = 0.3401
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.50.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.0 0.50.00
0.01
0.02
susc
eptib
ility
b
FIG. 28: Yeast, transcription, N = 662, E = 1, 062, pc = 0.2458, qc = 0.3414, pc = 0.0799, pc = 0.1002,pc = 0.1538
18
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.1 0.20.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.0 0.1 0.20.000
0.005
0.010
susc
eptib
ility
b
FIG. 29: URV email, N = 1, 133, E = 5, 451, pc = 0.0646, qc = 0.1068, pc = 0.0565, pc = 0.0482, pc = 0.0519
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.02 0.04 0.060.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.02 0.04 0.060.000
0.005
0.010
susc
eptib
ility
b
FIG. 30: Political blogs, N = 1, 222, E = 16, 714, pc = 0.0168, qc = 0.0442, pc = 0.0125, pc = 0.0135,pc = 0.0138
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.60.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.0 0.2 0.4 0.60.000
0.005
0.010
susc
eptib
ility
b
FIG. 31: Air traffic, N = 1, 226, E = 2, 408, pc = 0.1815, qc = 0.2871, pc = 0.1573, pc = 0.1086, pc = 0.1336
19
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.5 1.00.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.0 0.5 1.00.000
0.005
0.010
0.015
susc
eptib
ility
b
FIG. 32: Yeast, protein, N = 1, 458, E = 1, 948, pc = 0.2988, qc = 0.3752, pc = 0.1632, pc = 0.1327,pc = 0.1980
20
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.05 0.100.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.00 0.05 0.100.000
0.005
susc
eptib
ility
b
FIG. 33: Petster, hamster, N = 1, 788, E = 12, 476, pc = 0.0273, qc = 0.0587, pc = 0.0224, pc = 0.0217,pc = 0.0226
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.050.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.050.000
0.005
susc
eptib
ility
b
FIG. 34: UC Irvine, N = 1, 893, E = 13, 835, pc = 0.0248, qc = 0.0449, pc = 0.0183, pc = 0.0208, pc = 0.0216
21
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.1 0.2 0.30.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.0 0.1 0.2 0.30.000
0.005
susc
eptib
ility
b
FIG. 35: Yeast, protein, N = 2, 224, E = 6, 609, pc = 0.0794, qc = 0.1245, pc = 0.0639, pc = 0.0525,pc = 0.0577
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.05 0.100.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.05 0.100.000
0.002
0.004
susc
eptib
ility
b
FIG. 36: Japanese, N = 2, 698, E = 7, 995, pc = 0.0318, qc = 0.1160, pc = 0.0093, pc = 0.0233, pc = 0.0262
22
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.02 0.04 0.060.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.00 0.02 0.04 0.060.000
0.002
0.004
susc
eptib
ility
b
FIG. 37: Open flights, N = 2, 905, E = 15, 645, pc = 0.0199, qc = 0.0792, pc = 0.0182, pc = 0.0159,pc = 0.0163
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.40.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.0 0.2 0.40.000
0.002
0.004
susc
eptib
ility
b
FIG. 38: GR-QC, 1993-2003, N = 4, 158, E = 13, 422, pc = 0.1345, qc = 0.2244, pc = 0.0589, pc = 0.0219,pc = 0.0225
23
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.01 0.020.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.00 0.01 0.020.000
0.002
0.004
0.006
susc
eptib
ility
b
FIG. 39: Tennis, N = 4, 338, E = 81, 865, pc = 0.0073, qc = 0.0274, pc = 0.0063, pc = 0.0062, pc = 0.0062
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.5 1.00.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.0 0.5 1.00.00
0.02
0.04
susc
eptib
ility
b
FIG. 40: US Power grid, N = 4, 941, E = 6, 594, pc = 0.6583, qc = 0.7353, pc = 0.3483, pc = 0.1336,pc = 0.1606
24
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.05 0.100.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.00 0.05 0.100.000
0.002
0.004
susc
eptib
ility
b
FIG. 41: HT09, N = 5, 352, E = 18, 481, pc = 0.0283, qc = 0.1700, pc = 0.0050, pc = 0.0211, pc = 0.0244
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.40.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.0 0.2 0.40.000
0.002
0.004
susc
eptib
ility
b
FIG. 42: Hep-Th, 1995-1999, N = 5, 835, E = 13, 815, pc = 0.1081, qc = 0.1973, pc = 0.1231, pc = 0.0554,pc = 0.0588
25
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.02 0.040.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.00 0.02 0.040.000
0.002
0.004
susc
eptib
ility
b
FIG. 43: Reactome, N = 5, 973, E = 145, 778, pc = 0.0114, qc = 0.0591, pc = 0.0070, pc = 0.0048, pc = 0.0048
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.01 0.02 0.030.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.01 0.02 0.030.000
0.001
0.002
0.003su
scep
tibili
tyb
FIG. 44: Jung, N = 6, 120, E = 50, 290, pc = 0.0093, qc = 0.1239, pc = 0.0010, pc = 0.0070, pc = 0.0078
26
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.05 0.10 0.150.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.00 0.05 0.10 0.150.000
0.001
0.002
0.003
susc
eptib
ility
b
FIG. 45: Gnutella, Aug. 8, 2002, N = 6, 299, E = 20, 776, pc = 0.0455, qc = 0.1121, pc = 0.0600,pc = 0.0352, pc = 0.0377
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.01 0.02 0.030.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.01 0.02 0.030.000
0.001
0.002
0.003
susc
eptib
ility
b
FIG. 46: JDK, N = 6, 434, E = 53, 658, pc = 0.0091, qc = 0.1173, pc = 0.0010, pc = 0.0070, pc = 0.0077
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.05 0.100.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.05 0.100.000
0.001
0.002
susc
eptib
ility
b
FIG. 47: AS Oregon, N = 6, 474, E = 12, 572, pc = 0.0356, qc = 0.1767, pc = 0.0061, pc = 0.0216, pc = 0.0285
27
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.02 0.040.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.00 0.02 0.040.000
0.001
0.002
0.003
susc
eptib
ility
b
FIG. 48: English, N = 7, 377, E = 44, 205, pc = 0.0114, qc = 0.1590, pc = 0.0031, pc = 0.0091, pc = 0.0096
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.05 0.10 0.150.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.05 0.10 0.150.000
0.001
0.002
susc
eptib
ility
b
FIG. 49: Gnutella, Aug. 9, 2002, N = 8, 104, E = 26, 008, pc = 0.0451, qc = 0.1099, pc = 0.0632,pc = 0.0351, pc = 0.0376
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.050.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.050.000
0.001
0.002
0.003
susc
eptib
ility
b
FIG. 50: French, N = 8, 308, E = 23, 832, pc = 0.0236, qc = 0.1284, pc = 0.0046, pc = 0.0165, pc = 0.0191
28
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.1 0.2 0.30.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.0 0.1 0.2 0.30.000
0.002
0.004
susc
eptib
ility
b
FIG. 51: Hep-Th, 1993-2003, N = 8, 638, E = 24, 806, pc = 0.0755, qc = 0.1363, pc = 0.0834, pc = 0.0322,pc = 0.0333
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.1 0.20.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.0 0.1 0.20.000
0.002
0.004
susc
eptib
ility
b
FIG. 52: Gnutella, Aug. 6, 2002, N = 8, 717, E = 31, 525, pc = 0.0648, qc = 0.1005, pc = 0.0746,pc = 0.0447, pc = 0.0489
29
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.1 0.20.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.0 0.1 0.20.000
0.001
0.002
0.003
susc
eptib
ility
b
FIG. 53: Gnutella, Aug. 5, 2002, N = 8, 842, E = 31, 837, pc = 0.0565, qc = 0.1017, pc = 0.0725,pc = 0.0425, pc = 0.0463
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.1 0.20.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.0 0.1 0.20.0000
0.0005
0.0010
susc
eptib
ility
b
FIG. 54: PGP, N = 10, 680, E = 24, 316, pc = 0.0642, qc = 0.1935, pc = 0.0559, pc = 0.0236, pc = 0.0244
30
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.1 0.2 0.30.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.0 0.1 0.2 0.30.000
0.002
0.004
0.006
susc
eptib
ility
b
FIG. 55: Gnutella, August 4 2002, N = 10, 876, E = 39, 994, pc = 0.0762, qc = 0.0942, pc = 0.0771,pc = 0.0585, pc = 0.0655
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.000 0.005 0.010 0.0150.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.000 0.005 0.010 0.0150.0000
0.0005
0.0010
0.0015
susc
eptib
ility
b
FIG. 56: Hep-Ph, 1993-2003, N = 11, 204, E = 117, 619, pc = 0.0048, qc = 0.0565, pc = 0.0077, pc = 0.0041,pc = 0.0041
31
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.02 0.040.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.00 0.02 0.040.000
0.001
0.002
susc
eptib
ility
b
FIG. 57: Spanish, N = 11, 558, E = 43, 050, pc = 0.0127, qc = 0.2093, pc = 0.0022, pc = 0.0098, pc = 0.0107
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.05 0.100.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.05 0.100.000
0.001
0.002
0.003su
scep
tibili
tyb
FIG. 58: DBLP, citations, N = 12, 495, E = 49, 563, pc = 0.0325, qc = 0.0652, pc = 0.0234, pc = 0.0234,pc = 0.0263
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.02 0.040.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.02 0.040.000
0.001
0.002
susc
eptib
ility
b
FIG. 59: Spanish, N = 12, 643, E = 55, 019, pc = 0.0119, qc = 0.2347, pc = 0.0012, pc = 0.0090, pc = 0.0100
32
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.1 0.20.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.0 0.1 0.20.000
0.001
0.002
susc
eptib
ility
b
FIG. 60: Cond-Mat, 1995-1999, N = 13, 861, E = 44, 619, pc = 0.0637, qc = 0.1649, pc = 0.0798, pc = 0.0400,pc = 0.0432
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.02 0.04 0.060.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.02 0.04 0.060.000
0.001
0.002
susc
eptib
ility
b
FIG. 61: Astrophysics, N = 14, 845, E = 119, 652, pc = 0.0182, qc = 0.0551, pc = 0.0225, pc = 0.0135,pc = 0.0138
33
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.01 0.02 0.030.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.00 0.01 0.02 0.030.000
0.001
0.002
susc
eptib
ility
b
FIG. 62: Google, N = 15, 763, E = 148, 585, pc = 0.0078, qc = 0.0636, pc = 0.0011, pc = 0.0057, pc = 0.0064
34
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.02 0.040.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.00 0.02 0.040.000
0.001
0.002
0.003
susc
eptib
ility
b
FIG. 63: AstroPhys, 1993-2003, N = 17, 903, E = 196, 972, pc = 0.0132, qc = 0.0323, pc = 0.0155, pc = 0.0106,pc = 0.0108
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.05 0.100.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.05 0.100.000
0.001
0.002
susc
eptib
ility
b
FIG. 64: Cond-Mat, 1993-2003, N = 21, 363, E = 91, 286, pc = 0.0367, qc = 0.0836, pc = 0.0466, pc = 0.0264,pc = 0.0279
35
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.40.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.0 0.2 0.40.000
0.005
susc
eptib
ility
b
FIG. 65: Gnutella, Aug. 25, 2002, N = 22, 663, E = 54, 693, pc = 0.1150, qc = 0.1265, pc = 0.1026,pc = 0.0916, pc = 0.1066
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.02 0.04 0.060.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.02 0.04 0.060.0000
0.0005
0.0010
0.0015
susc
eptib
ility
b
FIG. 66: Internet, N = 22, 963, E = 48, 436, pc = 0.0193, qc = 0.1940, pc = 0.0038, pc = 0.0140, pc = 0.0155
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.02 0.040.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.02 0.040.000
0.002
0.004
susc
eptib
ility
b
FIG. 67: Thesaurus, N = 23, 132, E = 297, 094, pc = 0.0112, qc = 0.0174, pc = 0.0098, pc = 0.0100, pc = 0.0102
36
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.05 0.10 0.150.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.00 0.05 0.10 0.150.000
0.001
0.002
susc
eptib
ility
b
FIG. 68: Cora, N = 23, 166, E = 89, 157, pc = 0.0454, qc = 0.1184, pc = 0.0441, pc = 0.0317, pc = 0.0342
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.01 0.020.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.01 0.020.0000
0.0005
0.0010
0.0015
susc
eptib
ility
b
FIG. 69: Linux, mailing list, N = 24, 567, E = 158, 164, pc = 0.0052, qc = 0.2261, pc = 0.0029, pc = 0.0045,pc = 0.0045
37
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.050.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.00 0.050.0000
0.0005
0.0010
0.0015
susc
eptib
ility
b
FIG. 70: AS Caida, N = 26, 475, E = 53, 381, pc = 0.0210, qc = 0.1640, pc = 0.0036, pc = 0.0144, pc = 0.0168
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.40.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.0 0.2 0.40.000
0.002
0.004
susc
eptib
ility
b
FIG. 71: Gnutella, Aug. 24, 2002, N = 26, 498, E = 65, 359, pc = 0.1060, qc = 0.1174, pc = 0.0906,pc = 0.0511, pc = 0.0927
38
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.02 0.040.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.00 0.02 0.040.000
0.001
0.002
0.003
susc
eptib
ility
b
FIG. 72: Hep-Th, citations, N = 27, 400, E = 352, 021, pc = 0.0110, qc = 0.0245, pc = 0.0095, pc = 0.0090,pc = 0.0094
39
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.05 0.100.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.00 0.05 0.100.0000
0.0005
0.0010
0.0015
susc
eptib
ility
b
FIG. 73: Cond-Mat, 1995-2003, N = 27, 519, E = 116, 181, pc = 0.0342, qc = 0.0814, pc = 0.0470, pc = 0.0248,pc = 0.0261
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.05 0.10 0.150.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.05 0.10 0.150.000
0.001
0.002
susc
eptib
ility
b
FIG. 74: Digg, N = 29, 652, E = 84, 781, pc = 0.0413, qc = 0.0577, pc = 0.0369, pc = 0.0324, pc = 0.0362
40
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.01 0.02 0.030.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.00 0.01 0.02 0.030.0000
0.0005
0.0010
0.0015
susc
eptib
ility
b
FIG. 75: Linux, soft., N = 30, 817, E = 213, 208, pc = 0.0076, qc = 0.0457, pc = 0.0012, pc = 0.0059,pc = 0.0065
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.01 0.02 0.03 0.040.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.01 0.02 0.03 0.040.0000
0.0005
0.0010
0.0015
susc
eptib
ility
b
FIG. 76: Enron, N = 33, 696, E = 180, 811, pc = 0.0100, qc = 0.4460, pc = 0.0071, pc = 0.0084, pc = 0.0087
41
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.02 0.04 0.060.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.00 0.02 0.04 0.060.000
0.001
0.002
0.003
susc
eptib
ility
b
FIG. 77: Hep-Ph, citations, N = 34, 401, E = 420, 784, pc = 0.0158, qc = 0.0332, pc = 0.0160, pc = 0.0131,pc = 0.0135
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.05 0.100.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.05 0.100.0000
0.0005
0.0010
0.0015
susc
eptib
ility
b
FIG. 78: Cond-Mat, 1995-2005, N = 36, 458, E = 171, 735, pc = 0.0256, qc = 0.0585, pc = 0.0372, pc = 0.0195,pc = 0.0203
42
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.1 0.2 0.30.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.0 0.1 0.2 0.30.000
0.002
0.004
susc
eptib
ility
b
FIG. 79: Gnutella, Aug. 30, 2002, N = 36, 646, E = 88, 303, pc = 0.0968, qc = 0.1122, pc = 0.0956,pc = 0.0773, pc = 0.0878
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.05 0.100.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.05 0.100.0000
0.0005
0.0010
susc
eptib
ility
b
FIG. 80: Slashdot, N = 51, 083, E = 116, 573, pc = 0.0262, qc = 0.0435, pc = 0.0124, pc = 0.0170, pc = 0.0222
43
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.1 0.2 0.30.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.0 0.1 0.2 0.30.000
0.002
0.004
susc
eptib
ility
b
FIG. 81: Gnutella, Aug. 31, 2002, N = 62, 561, E = 147, 878, pc = 0.0956, qc = 0.1082, pc = 0.0943,pc = 0.0759, pc = 0.0871
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.01 0.02 0.030.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.01 0.02 0.030.0000
0.0005
0.0010
0.0015
susc
eptib
ility
b
FIG. 82: Facebook, N = 63, 392, E = 816, 886, pc = 0.0086, qc = 0.0192, pc = 0.0115, pc = 0.0075, pc = 0.0076
44
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.01 0.020.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.00 0.01 0.020.0000
0.0005
susc
eptib
ility
b
FIG. 83: Epinions, N = 75, 877, E = 405, 739, pc = 0.0062, qc = 0.0148, pc = 0.0055, pc = 0.0054, pc = 0.0055
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.01 0.02 0.030.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.01 0.02 0.030.0000
0.0005
0.0010
susc
eptib
ility
b
FIG. 84: Slashdot zoo, N = 79, 116, E = 467, 731, pc = 0.0088, qc = 0.0162, pc = 0.0069, pc = 0.0077,pc = 0.0078
45
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.02 0.040.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.00 0.02 0.040.000
0.002
0.004
susc
eptib
ility
b
FIG. 85: Flickr, N = 105, 722, E = 2, 316, 668, pc = 0.0142, qc = 0.0662, pc = 0.0029, pc = 0.0016, pc = 0.0016
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.000 0.005 0.0100.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.000 0.005 0.0100.0000
0.0005
0.0010
susc
eptib
ility
b
FIG. 86: Wikipedia, edits, N = 113, 123, E = 2, 025, 910, pc = 0.0029, qc = 0.0085, pc = 0.0015, pc = 0.0025,pc = 0.0026
46
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.000 0.001 0.002 0.0030.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.000 0.001 0.002 0.0030.0000
0.0005
0.0010
susc
eptib
ility
b
FIG. 87: Petster, cats, N = 148, 826, E = 5, 447, 464, pc = 0.0010, qc = 0.0303, pc = 0.0001, pc = 0.0008,pc = 0.0009
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.01 0.020.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.01 0.020.0000
0.0002
0.0004
susc
eptib
ility
b
FIG. 88: Gowalla, N = 196, 591, E = 950, 327, pc = 0.0073, qc = 0.0310, pc = 0.0033, pc = 0.0059, pc = 0.0063
47
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.000 0.002 0.0040.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.000 0.002 0.0040.0000
0.0005
0.0010
0.0015
susc
eptib
ility
b
FIG. 89: Libimseti, N = 220, 970, E = 17, 233, 144, pc = 0.0011, qc = 0.0028, pc = 0.0006, pc = 0.0011,pc = 0.0011
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.02 0.040.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.02 0.040.0000
0.0002
0.0004
susc
eptib
ility
b
FIG. 90: EU email, N = 224, 832, E = 339, 925, pc = 0.0119, qc = 0.5975, pc = 0.0018, pc = 0.0098, pc = 0.0103
48
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.1 0.20.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.0 0.1 0.20.000
0.001
0.002
susc
eptib
ility
b
FIG. 91: Web Stanford, N = 255, 265, E = 1, 941, 926, pc = 0.0598, qc = 0.1932, pc = 0.0005, pc = 0.0022,pc = 0.0024
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.1 0.2 0.30.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.0 0.1 0.2 0.30.0000
0.0005
0.0010
susc
eptib
ility
b
FIG. 92: Amazon, Mar. 2, 2003, N = 262, 111, E = 899, 792, pc = 0.0940, qc = 0.1539, pc = 0.0987,pc = 0.0425, pc = 0.0562
49
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.05 0.100.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.00 0.05 0.100.0000
0.0002
0.0004
susc
eptib
ility
b
FIG. 93: DBLP, collaborations, N = 317, 080, E = 1, 049, 866, pc = 0.0337, qc = 0.0658, pc = 0.0482,pc = 0.0086, pc = 0.0087
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.1 0.2 0.30.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.0 0.1 0.2 0.30.000
0.001
0.002
0.003
susc
eptib
ility
b
FIG. 94: Web Notre Dame, N = 325, 729, E = 1, 090, 108, pc = 0.0847, qc = 0.2037, pc = 0.0036, pc = 0.0054,pc = 0.0057
50
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.05 0.10 0.150.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.00 0.05 0.10 0.150.0000
0.0002
0.0004
susc
eptib
ility
b
FIG. 95: MathSciNet, N = 332, 689, E = 820, 644, pc = 0.0478, qc = 0.0805, pc = 0.0648, pc = 0.0277,pc = 0.0298
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.05 0.100.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.05 0.100.0000
0.0002
0.0004
0.0006
susc
eptib
ility
b
FIG. 96: CiteSeer, N = 365, 154, E = 1, 721, 981, pc = 0.0250, qc = 0.0473, pc = 0.0211, pc = 0.0172,pc = 0.0190
51
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.05 0.100.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.00 0.05 0.100.0000
0.0002
0.0004
susc
eptib
ility
b
FIG. 97: Zhishi, N = 372, 840, E = 2, 318, 025, pc = 0.0301, qc = 0.0738, pc = 0.0000, pc = 0.0010, pc = 0.0011
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.000 0.002 0.0040.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.000 0.002 0.0040.0000
0.0001
0.0002
0.0003
susc
eptib
ility
b
FIG. 98: Actor coll. net., N = 374, 511, E = 15, 014, 839, pc = 0.0013, qc = 0.0047, pc = 0.0024,pc = 0.0012, pc = 0.0012
52
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.05 0.10 0.150.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.00 0.05 0.10 0.150.0000
0.0005
susc
eptib
ility
b
FIG. 99: Amazon, Mar. 12, 2003, N = 400, 727, E = 2, 349, 869, pc = 0.0401, qc = 0.0761, pc = 0.0341,pc = 0.0178, pc = 0.0285
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.05 0.100.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.05 0.100.0000
0.0002
0.0004
0.0006
susc
eptib
ility
b
FIG. 100: Amazon, Jun. 6, 2003, N = 403, 364, E = 2, 443, 311, pc = 0.0364, qc = 0.0759, pc = 0.0338,pc = 0.0175, pc = 0.0248
53
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.05 0.100.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.00 0.05 0.100.0000
0.0002
0.0004
0.0006
susc
eptib
ility
b
FIG. 101: Amazon, May 5, 2003, N = 410, 236, E = 2, 439, 437, pc = 0.0360, qc = 0.0759, pc = 0.0334,pc = 0.0172, pc = 0.0248
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.000 0.002 0.0040.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.000 0.002 0.0040.0000
0.0002
0.0004
0.0006
susc
eptib
ility
b
FIG. 102: Petster, dogs, N = 426, 485, E = 8, 543, 321, pc = 0.0015, qc = 0.0380, pc = 0.0005, pc = 0.0013,pc = 0.0014
54
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.5 1.00.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.0 0.5 1.00.00
0.01
0.02
0.03
susc
eptib
ility
b
FIG. 103: Road network PA, N = 1, 087, 562, E = 1, 541, 514, pc = 0.6923, qc = 0.7571, pc = 0.4547, pc =0.2263, pc = 0.3216
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.01 0.020.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.01 0.020.00000
0.00005
0.00010
0.00015
susc
eptib
ility
b
FIG. 104: YouTube friend. net., N = 1, 134, 890, E = 2, 987, 624, pc = 0.0063, qc = 0.0171, pc = 0.0020,pc = 0.0048, pc = 0.0054
55
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.5 1.00.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.0 0.5 1.00.00
0.01
0.02
susc
eptib
ility
b
FIG. 105: Road network TX, N = 1, 351, 137, E = 1, 879, 201, pc = 0.7362, qc = 0.7875, pc = 0.4661, pc =0.2038, pc = 0.2809
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.000 0.002 0.004 0.0060.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.000 0.002 0.004 0.0060.00000
0.00005
susc
eptib
ility
b
FIG. 106: AS Skitter, N = 1, 694, 616, E = 11, 094, 209, pc = 0.0018, qc = 0.0130, pc = 0.0007, pc = 0.0015,pc = 0.0015
56
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.5 1.00.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.0 0.5 1.00.00
0.01
0.02
0.03
susc
eptib
ility
b
FIG. 107: Road network CA, N = 1, 957, 027, E = 2, 760, 388, pc = 0.6933, qc = 0.7582, pc = 0.4609, pc =0.2156, pc = 0.3011
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.000 0.002 0.0040.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.000 0.002 0.0040.0000
0.0001
0.0002
0.0003
susc
eptib
ility
b
FIG. 108: Wikipedia, pages, N = 2, 070, 367, E = 42, 336, 614, pc = 0.0014, qc = 0.0046, pc = 0.0003,pc = 0.0012, pc = 0.0013
57
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.05 0.100.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.00 0.05 0.100.0000
0.0001
0.0002
susc
eptib
ility
b
FIG. 109: US Patents, N = 3, 764, 117, E = 16, 511, 740, pc = 0.0290, qc = 0.0515, pc = 0.0492, pc = 0.0088,pc = 0.0091
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.02 0.04 0.060.0
0.5
1.0
perc
olat
ion
stre
ngth a
0.00 0.02 0.04 0.060.0000
0.0001
0.0002
susc
eptib
ility
b
FIG. 110: DBpedia, N = 3, 915, 921, E = 12, 577, 253, pc = 0.0170, qc = 0.0380, pc = 0.0001, pc = 0.0014,pc = 0.0022
58
0.0 0.2 0.4 0.6 0.8 1.0
occupation probability
0.0
0.2
0.4
0.6
0.8
1.0
0.000 0.005 0.0100.0
0.5
1.0pe
rcol
atio
nst
reng
th a
0.000 0.005 0.0100.00000
0.00002
0.00004
susc
eptib
ility
b
FIG. 111: LiveJournal, N = 5, 189, 809, E = 48, 688, 097, pc = 0.0028, qc = 0.0116, pc = 0.0065, pc = 0.0019,pc = 0.0019
59
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