KONECT
KONECT > Statistics > Power law exponent

## Power law exponent

The power law exponent is a number that characterizes the degrees of the nodes in the network. In many circumstances, networks are modeled to follow a degree distribution power law, i.e., the number of nodes with degree $$n$$ is taken to be proportional to the power $$n^{-\gamma}$$, for a constant $$\gamma$$ larger than one [1]. This constant $$\gamma$$ is called the power law exponent. Given a network, its degree distribution can be used to estimate a value $$\gamma$$. There are multiple ways of estimating $$\gamma$$, and thus a network does not have a single definite value of it. In KONECT, we estimate $$\gamma$$ using the robust method given in [2] \begin{align} \gamma &= 1 + n \left( \sum_{u\in V} \ln \frac {d(u)} {d_{\min}} \right) ^{-1}, \end{align} in which $$d_{\min}$$ is the minimal degree.

 [1] M. E. J. Newman. Power laws, Pareto distributions and Zipf's law. Contemporary Phys., 46(5):323–351, 2006. [2] Albert-LÃ¡szlÃ³ BarabÃ¡si and RÃ©ka Albert. Emergence of scaling in random networks. Science, 286(5439):509–512, 1999.

 Code Name Category F. W. M. $$n$$ $$m$$ $$\gamma$$ with $$d_{min}$$ $$\gamma$$ DN DNC emails co-recipients ⬤ OnlineContact 2,029 136,602 1.4510 (dmin = 1) 1.5832 Â±  0.0194 FG Flickr ⬤ Affiliation 895,589 8,545,307 1.4510 (dmin = 1) 1.5832 Â±  0.0008 Dut Delicious ut ⬤ Folksonomy 6,178,261 301,186,579 1.4710 (dmin = 2) 2.1012 Â±  0.0005 HA Haggle ⬤ HumanContact 274 28,244 1.5010 (dmin = 1) 1.6729 Â±  0.0406 CO Wikipedia conflict ⬤ OnlineContact 118,100 2,917,785 1.5010 (dmin = 2) 1.5346 Â±  0.0016 Fr Filmtipset ⬤ Rating 225,153 19,554,219 1.5310 (dmin = 22) 1.2865 Â±  0.0008 Fc Filmtipset ⬤ Interaction 104,890 1,266,753 1.5810 (dmin = 4) 1.5780 Â±  0.0021 EX Wikipedia (en) ⬤ Text 279,519 7,846,807 1.5910 (dmin = 4) 2.6120 Â±  0.0031 GE DBpedia genre ⬤ Feature 525,651 463,497 1.6210 (dmin = 12) 3.2360 Â±  0.0043 WU WebUni Magdeburg ⬤ Text 212,552 3,869,707 1.6410 (dmin = 2) 2.2230 Â±  0.0027 Tpt Wikipedia talk, Portuguese ⬤ Communication 541,355 2,424,962 1.6610 (dmin = 32) 2.2611 Â±  0.0017 W2 WikiSigned ⬤ OnlineContact 138,592 740,397 1.6810 (dmin = 1) 2.0085 Â±  0.0027 MZ Zebra ⬤ Animal 27 111 1.6910 (dmin = 2) 1.8412 Â±  0.1619 ES Epinions ⬤ Social 75,879 508,837 1.6910 (dmin = 1) 2.0258 Â±  0.0037 Vut vi.sualize.us u-t ⬤ Folksonomy 116,279 2,298,816 1.7010 (dmin = 2) 2.4397 Â±  0.0046 FL Flickr ⬤ Social 2,302,925 33,140,017 1.7110 (dmin = 7) 2.0174 Â±  0.0007 TH arXiv hep-th ⬤ Coauthorship 22,908 2,673,133 1.7210 (dmin = 58) 1.2339 Â±  0.0015 MF Human protein (Figeys) ⬤ Metabolic 2,239 6,452 1.7210 (dmin = 1) 2.0927 Â±  0.0231 PH arXiv hep-ph ⬤ Coauthorship 28,093 4,596,803 1.7310 (dmin = 59) 1.2199 Â±  0.0013 FI Flickr ⬤ Misc 105,938 2,316,948 1.7310 (dmin = 7) 1.4072 Â±  0.0013 LF Flickr links ⬤ Social 1,715,255 15,551,250 1.7310 (dmin = 8) 2.0397 Â±  0.0008 Tar Wikipedia talk, Arabic ⬤ Communication 1,095,799 1,913,103 1.7310 (dmin = 33) 5.3970 Â±  0.0042 EP Epinions ⬤ Social 131,828 841,372 1.7410 (dmin = 1) 2.1288 Â±  0.0031 RC Reactome ⬤ Metabolic 6,327 147,547 1.7410 (dmin = 17) 1.3645 Â±  0.0046 DF Digg friends ⬤ Social 279,630 1,731,653 1.7510 (dmin = 2) 2.2255 Â±  0.0023 LK Linux kernel mailing list threads ⬤ Interaction 421,599 1,565,683 1.7510 (dmin = 14) 3.7110 Â±  0.0044 OC Occupation ⬤ Affiliation 356,884 250,945 1.7610 (dmin = 13) 4.1454 Â±  0.0066 Dui Delicious ui ⬤ Folksonomy 35,444,383 301,186,579 1.7610 (dmin = 5) 3.6497 Â±  0.0005 Dti Delicious ti ⬤ Folksonomy 42,801,712 301,183,605 4.5570 Â±  0.0006 EN Enron ⬤ Communication 87,273 1,148,072 1.7610 (dmin = 2) 2.6516 Â±  0.0056 TM Teams ⬤ Affiliation 1,836,793 1,366,466 1.7710 (dmin = 21) 5.0982 Â±  0.0042 DV Digg votes ⬤ Rating 282,371 3,018,197 1.7710 (dmin = 25) 1.5724 Â±  0.0015 Cut CiteULike u-t ⬤ Folksonomy 198,707 2,411,819 1.7910 (dmin = 2) 2.8217 Â±  0.0043 M2 MovieLens 1M ⬤ Rating 15,786 1,000,209 1.8010 (dmin = 60) 1.2187 Â±  0.0022 Lb Last.fm band ⬤ Interaction 176,061 19,150,868 1.8110 (dmin = 3) 2.5813 Â±  0.0038 Lk Linux kernel mailing list replies ⬤ Communication 63,399 1,096,440 1.8410 (dmin = 3) 1.8698 Â±  0.0052 M3 MovieLens 10M ⬤ Rating 150,433 10,000,054 1.8510 (dmin = 60) 1.2238 Â±  0.0008 Wpt Wikipedia links, pt ⬤ Hyperlink 1,603,222 49,021,409 1.8510 (dmin = 15) 1.4336 Â±  0.0003 Tru Wikipedia talk, Russian ⬤ Communication 457,017 2,282,055 1.8510 (dmin = 11) 3.6494 Â±  0.0039 J2 Jester 150 ⬤ Rating 101,524 1,728,847 1.8810 (dmin = 8) 1.9279 Â±  0.0041 FX Flixster ⬤ Social 2,523,386 7,918,801 1.9110 (dmin = 2) 2.5941 Â±  0.0010 LI Libimseti.cz ⬤ Social 220,970 17,359,346 1.9110 (dmin = 60) 1.2674 Â±  0.0006 SD Slashdot ⬤ Communication 51,083 140,778 1.9110 (dmin = 1) 2.5189 Â±  0.0067 Ls Last.fm song ⬤ Interaction 1,086,604 19,150,868 1.9210 (dmin = 2) 2.7138 Â±  0.0016 TO Internet topology ⬤ Computer 34,761 171,403 1.9210 (dmin = 5) 2.2334 Â±  0.0066 ER Epinions ⬤ Rating 996,744 13,668,320 1.9510 (dmin = 8) 1.4658 Â±  0.0005 GH Github ⬤ Authorship 233,905 440,237 1.9510 (dmin = 1) 2.6124 Â±  0.0038 But BibSonomy u-t ⬤ Folksonomy 216,261 2,555,080 1.9610 (dmin = 4) 3.6749 Â±  0.0058 HY Hyves ⬤ Social 1,402,673 2,777,419 1.9610 (dmin = 1) 2.6580 Â±  0.0014 HUr Hudong related ⬤ Hyperlink 2,452,715 18,854,882 1.9710 (dmin = 22) 1.4889 Â±  0.0003 M1 MovieLens 100k ⬤ Rating 3,568 100,000 1.9910 (dmin = 39) 1.2852 Â±  0.0056 Mut MovieLens u-t ⬤ Folksonomy 24,546 95,580 2.0010 (dmin = 1) 2.7555 Â±  0.0123 LO Location ⬤ Feature 397,589 293,697 2.0110 (dmin = 9) 3.1762 Â±  0.0046 DNc DNC emails ⬤ Communication 2,029 39,264 2.0110 (dmin = 1) 2.7736 Â±  0.0408 SO Stack Overflow ⬤ Rating 1,187,072 1,301,942 2.0110 (dmin = 1) 2.7977 Â±  0.0022 Bti BibSonomy t-i ⬤ Folksonomy 1,176,793 2,555,080 2.0510 (dmin = 26) 2.2100 Â±  0.0012 BX BookCrossing (implicit) ⬤ Rating 551,079 1,149,739 2.0510 (dmin = 8) 2.6152 Â±  0.0024 AR Amazon ratings ⬤ Rating 5,523,029 5,838,041 2.0710 (dmin = 1) 2.9578 Â±  0.0011 DB DBpedia ⬤ Misc 3,966,924 13,820,853 2.0710 (dmin = 59) 1.9408 Â±  0.0005 Bx BookCrossing (ratings) ⬤ Rating 341,559 433,652 2.0810 (dmin = 2) 3.1466 Â±  0.0042 IN CAIDA ⬤ Computer 26,475 53,381 2.0910 (dmin = 6) 2.5086 Â±  0.0093 J1 Jester 100 ⬤ Rating 146,942 4,136,360 2.0910 (dmin = 23) 1.8492 Â±  0.0031 TR TREC (disks 4–5) ⬤ Text 2,285,379 151,632,178 1.5037 Â±  0.0004 MP PDZBase ⬤ Metabolic 212 244 2.0910 (dmin = 1) 3.0069 Â±  0.1378 AS Route views ⬤ Computer 6,474 13,895 2.1110 (dmin = 8) 2.3363 Â±  0.0166 PS Prosper.com ⬤ Affiliation 14,177 21,017 2.1110 (dmin = 11) 2.4009 Â±  0.0161 nen Wikinews (en) ⬤ Authorship 184,536 901,416 2.1210 (dmin = 1) 3.1110 Â±  0.0051 Sc Catster ⬤ Social 149,700 5,449,275 2.1210 (dmin = 19) 1.3352 Â±  0.0009 CL Actor collaborations ⬤ Misc 382,219 33,115,812 2.1310 (dmin = 49) 1.2816 Â±  0.0005 LM Livemocha ⬤ Social 104,103 2,193,083 2.1310 (dmin = 47) 1.3828 Â±  0.0012 Lj LiveJournal links ⬤ Social 5,204,176 49,174,464 1.5365 Â±  0.0002 Scd Catster/Dogster ⬤ Social 623,766 15,699,276 2.1310 (dmin = 24) 1.3786 Â±  0.0005 SF Stanford ⬤ Hyperlink 281,903 2,312,497 2.1310 (dmin = 5) 1.5378 Â±  0.0010 Wja Wikipedia links, ja ⬤ Hyperlink 1,610,638 71,055,717 2.1310 (dmin = 59) 1.3702 Â±  0.0003 CY Youtube friendship ⬤ Social 1,134,890 2,987,624 2.1410 (dmin = 8) 2.4290 Â±  0.0013 DBT TV Tropes ⬤ Feature 216,508 3,232,134 2.1410 (dmin = 59) 1.5612 Â±  0.0014 LY Youtube links ⬤ Social 1,138,499 4,942,297 2.1410 (dmin = 8) 2.4319 Â±  0.0013 Sd Dogster ⬤ Social 426,820 8,546,581 2.1510 (dmin = 26) 1.3997 Â±  0.0006 ND Notre Dame ⬤ Hyperlink 325,729 1,497,134 2.1510 (dmin = 6) 2.1072 Â±  0.0019 WT Web trackers ⬤ Hyperlink 68,087,704 140,613,762 2.1610 (dmin = 35) 2.2128 Â±  0.0002 ZA Zachary karate club ⬤ HumanSocial 34 78 2.1610 (dmin = 2) 1.7810 Â±  0.1339 SZ Slashdot Zoo ⬤ Social 79,120 515,397 2.1810 (dmin = 31) 1.8190 Â±  0.0029 PL Prosper loans ⬤ Interaction 89,269 3,394,979 2.1910 (dmin = 60) 1.3006 Â±  0.0010 Vui vi.sualize.us u-i ⬤ Folksonomy 529,646 2,298,816 2.2010 (dmin = 1) 3.3557 Â±  0.0033 YT YouTube ⬤ Social 3,223,589 9,375,374 2.2110 (dmin = 15) 2.3380 Â±  0.0007 WT TREC WT10g ⬤ Hyperlink 1,601,787 8,063,026 2.2310 (dmin = 55) 1.7449 Â±  0.0006 PR Producers ⬤ Authorship 236,510 207,268 2.2710 (dmin = 5) 3.7639 Â±  0.0064 Wru Wikipedia links, ru ⬤ Hyperlink 2,853,118 82,056,101 2.2710 (dmin = 58) 1.5022 Â±  0.0003 SK Skitter ⬤ Computer 1,696,415 11,095,298 2.2910 (dmin = 48) 1.6108 Â±  0.0005 PW Prosper.com ⬤ Interaction 25,697 35,377 2.2910 (dmin = 1) 3.6436 Â±  0.0171 Wpl Wikipedia links, pl ⬤ Hyperlink 1,529,135 57,489,447 2.2910 (dmin = 55) 1.3657 Â±  0.0003 BAi Baidu internal ⬤ Hyperlink 2,141,300 17,794,839 2.2910 (dmin = 57) 1.6728 Â±  0.0005 HUi Hudong internal ⬤ Hyperlink 1,984,484 14,869,484 2.3010 (dmin = 40) 1.6134 Â±  0.0004 YG YouTube ⬤ Affiliation 218,563 293,360 2.3110 (dmin = 15) 2.4117 Â±  0.0040 Dl Discogs ⬤ Affiliation 3,780,417 14,414,659 2.3210 (dmin = 48) 2.5399 Â±  0.0011 Cti CiteULike t-i ⬤ Folksonomy 1,038,323 2,411,819 2.3310 (dmin = 4) 2.3254 Â±  0.0014 Pa DBLP ⬤ Authorship 6,851,776 8,649,016 2.3310 (dmin = 8) 2.3375 Â±  0.0006 MN Bible ⬤ Lexical 1,773 16,401 2.3410 (dmin = 9) 1.9071 Â±  0.0215 Dj JUNG dependency ⬤ Software 6,120 138,706 2.3410 (dmin = 6) 1.4873 Â±  0.0062 DJ JDK dependency ⬤ Software 6,434 150,985 2.3610 (dmin = 6) 1.4810 Â±  0.0060 DL Wikipedia, English ⬤ Hyperlink 18,268,992 172,183,984 2.3710 (dmin = 58) 2.0977 Â±  0.0003 UL Unicode languages ⬤ Feature 1,122 1,255 2.3710 (dmin = 3) 2.8651 Â±  0.0667 MS Human protein (Stelzl) ⬤ Metabolic 1,706 6,207 2.3810 (dmin = 6) 2.3542 Â±  0.0328 WC Wikipedia (en) ⬤ Feature 3,889,933 3,795,796 2.3810 (dmin = 2) 2.6147 Â±  0.0011 R2 Reuters-21578 ⬤ Text 81,791 1,464,182 2.4010 (dmin = 60) 1.5321 Â±  0.0022 Mui MovieLens u-i ⬤ Folksonomy 15,619 95,580 2.4010 (dmin = 23) 1.8176 Â±  0.0076 Sh Hamsterster full ⬤ Social 2,426 16,631 2.4210 (dmin = 14) 1.5183 Â±  0.0105 Ds Discogs label–style ⬤ Feature 487,911 5,255,950 2.4610 (dmin = 8) 2.0376 Â±  0.0021 Shf Hamsterster friendships ⬤ Social 1,858 12,534 2.4610 (dmin = 20) 1.5382 Â±  0.0125 WK Wikipedia, English ⬤ Communication 2,394,385 5,021,410 2.4610 (dmin = 1) 4.2933 Â±  0.0021 TL Twitter lists ⬤ Social 23,370 33,101 2.4710 (dmin = 1) 4.3336 Â±  0.0218 BK Brightkite ⬤ Social 58,228 214,078 2.4810 (dmin = 22) 1.9058 Â±  0.0038 RE Reuters ⬤ Text 1,846,441 96,903,520 2.5110 (dmin = 59) 1.2957 Â±  0.0003 EL Wikipedia elections ⬤ OnlineContact 7,118 103,675 2.5510 (dmin = 57) 1.5365 Â±  0.0064 RL Record labels ⬤ Affiliation 355,095 233,286 2.5710 (dmin = 1) 4.7558 Â±  0.0087 Vti vi.sualize.us t-i ⬤ Folksonomy 659,472 2,298,816 2.5910 (dmin = 6) 2.1745 Â±  0.0015 BS Berkeley/Stanford ⬤ Hyperlink 685,230 7,600,595 2.6010 (dmin = 38) 1.4861 Â±  0.0006 BAr Baidu related ⬤ Hyperlink 415,641 3,284,387 2.6010 (dmin = 15) 1.6311 Â±  0.0010 YS Yahoo songs ⬤ Rating 2,626,941 256,804,235 1.4031 Â±  0.0003 Tes Wikipedia talk, Spanish ⬤ Communication 497,446 2,702,879 1.7810 (dmin = 22) 2.7740 Â±  0.0025 Tit Wikipedia talk, Italian ⬤ Communication 863,846 3,067,680 1.7910 (dmin = 30) 4.2294 Â±  0.0035 Tde Wikipedia talk, German ⬤ Communication 519,403 6,729,794 1.8110 (dmin = 11) 2.5547 Â±  0.0022 Ten Wikipedia talk, English ⬤ Communication 2,987,535 24,981,163 1.8110 (dmin = 22) 2.8271 Â±  0.0011 WO WordNet ⬤ Lexical 146,005 656,999 2.4710 (dmin = 8) 1.6038 Â±  0.0016 Tfr Wikipedia talk, French ⬤ Communication 1,420,367 4,641,928 2.6010 (dmin = 1) 4.8845 Â±  0.0033 YD Yahoo advertisers ⬤ Lexical 653,260 2,931,708 2.6110 (dmin = 8) 2.7988 Â±  0.0022 RM Reality Mining ⬤ HumanContact 96 1,086,404 2.6110 (dmin = 31) 1.3171 Â±  0.0324 PM Caenorhabditis elegans ⬤ Metabolic 453 4,596 2.6210 (dmin = 5) 1.5633 Â±  0.0265 GW Gowalla ⬤ Social 196,591 950,327 2.6510 (dmin = 43) 1.7307 Â±  0.0016 LJ LiveJournal ⬤ Social 4,847,571 68,475,391 2.6510 (dmin = 59) 1.5617 Â±  0.0003 GC Google.com internal ⬤ Hyperlink 15,763 171,206 2.6810 (dmin = 13) 1.4851 Â±  0.0039 Ar American Revolution ⬤ Affiliation 277 160 2.7210 (dmin = 1) 5.5037 Â±  0.3793 WR Writers ⬤ Authorship 224,925 144,340 2.7210 (dmin = 2) 3.3132 Â±  0.0063 CS CiteSeer ⬤ Citation 384,413 1,751,463 2.7310 (dmin = 20) 1.6343 Â±  0.0010 GO Google ⬤ Hyperlink 875,713 5,105,039 2.7310 (dmin = 28) 1.6172 Â±  0.0007 CR Chicago ⬤ Infrastructure 1,467 1,298 2.7610 (dmin = 1) 5.6946 Â±  0.1226 Sw Southern women 2 ⬤ Interaction 15 14 2.8510 (dmin = 2) 4.0829 Â±  0.9749 AP arXiv astro-ph ⬤ Coauthorship 18,771 198,050 2.8610 (dmin = 39) 1.4392 Â±  0.0032 Tzh Wikipedia talk, Chinese ⬤ Communication 1,219,241 2,284,546 2.8610 (dmin = 1) 6.2174 Â±  0.0047 BM Club membership ⬤ Affiliation 65 95 2.8710 (dmin = 3) 2.3753 Â±  0.2175 SX Sexual escorts ⬤ Rating 26,836 50,632 2.8810 (dmin = 22) 2.2341 Â±  0.0098 Dt Discogs artist–style ⬤ Feature 3,236,269 24,085,580 2.8910 (dmin = 11) 2.1611 Â±  0.0009 ST Movies ⬤ Feature 233,283 281,396 2.9310 (dmin = 6) 2.1993 Â±  0.0030 EU EU institution ⬤ Communication 265,214 420,045 2.9310 (dmin = 1) 6.6497 Â±  0.0110 Ol Facebook (WOSN) ⬤ Social 63,731 817,035 2.9410 (dmin = 58) 1.4330 Â±  0.0017 Tnl Wikipedia talk, Dutch ⬤ Communication 225,749 1,554,699 2.9610 (dmin = 2) 2.8216 Â±  0.0038 Wit Wikipedia links, it ⬤ Hyperlink 1,865,965 91,555,008 1.3511 Â±  0.0003 Wfr Wikipedia links, fr ⬤ Hyperlink 3,023,165 102,382,410 1.4206 Â±  0.0002 Wen Wikipedia links, en ⬤ Hyperlink 12,150,976 378,142,420 1.4317 Â±  0.0001 Wde Wikipedia links, de ⬤ Hyperlink 3,225,565 81,626,917 2.3810 (dmin = 60) 1.4488 Â±  0.0002 WP Wikipedia, English ⬤ Hyperlink 1,870,709 39,953,145 1.3705 Â±  0.0003 WD Wikipedia Threads (de) ⬤ Communication 91,340 2,435,731 1.7010 (dmin = 2) 1.8160 Â±  0.0027 ML Little Rock Lake ⬤ Trophic 183 2,494 2.9910 (dmin = 22) 1.3456 Â±  0.0255 MV Human protein (Vidal) ⬤ Metabolic 3,133 6,726 3.0310 (dmin = 14) 2.1143 Â±  0.0199 AD Advogato ⬤ Social 6,541 51,127 3.0410 (dmin = 57) 1.6832 Â±  0.0084 PHc arXiv hep-ph ⬤ Citation 34,546 421,578 3.0410 (dmin = 42) 1.3783 Â±  0.0020 Mp Protein ⬤ Metabolic 1,870 2,277 3.0410 (dmin = 5) 2.8698 Â±  0.0432 CH Chess ⬤ Interaction 7,301 65,053 3.0710 (dmin = 24) 1.6176 Â±  0.0075 PL Pokec ⬤ Social 1,632,803 30,622,564 3.0810 (dmin = 59) 1.4048 Â±  0.0003 Dr Discogs label–genre ⬤ Feature 541,557 4,147,665 3.1110 (dmin = 3) 3.6982 Â±  0.0052 THc arXiv hep-th ⬤ Citation 27,770 352,807 3.1210 (dmin = 59) 1.3899 Â±  0.0023 Mti MovieLens t-i ⬤ Folksonomy 40,657 95,580 3.1410 (dmin = 48) 2.1224 Â±  0.0072 Am Amazon (TWEB) ⬤ Misc 403,394 3,387,388 3.1510 (dmin = 29) 1.4474 Â±  0.0007 Mg Blogs ⬤ Hyperlink 1,224 19,025 3.1610 (dmin = 59) 1.4149 Â±  0.0119 SC South African Companies ⬤ Affiliation 17 13 3.2110 (dmin = 2) 2.3040 Â±  0.3932 Pc DBLP ⬤ Coauthorship 1,314,050 18,986,618 3.2210 (dmin = 59) 1.6787 Â±  0.0006 CD DBLP co-authorship ⬤ Coauthorship 317,080 1,049,866 3.2610 (dmin = 29) 1.7200 Â±  0.0013 Cui CiteULike u-i ⬤ Folksonomy 777,199 2,411,819 3.2810 (dmin = 1) 9.0729 Â±  0.0093 CC Cora citation ⬤ Citation 23,166 91,500 3.3010 (dmin = 30) 1.6455 Â±  0.0042 Pi DBLP ⬤ Citation 12,591 49,743 3.3610 (dmin = 25) 1.8374 Â±  0.0075 Da Discogs artist–genre ⬤ Feature 3,509,661 19,033,891 3.3610 (dmin = 3) 3.5369 Â±  0.0019 CA Amazon (MDS) ⬤ Misc 334,863 925,872 3.5810 (dmin = 22) 1.6912 Â±  0.0012 AN David Copperfield ⬤ Lexical 112 425 3.6210 (dmin = 10) 1.5896 Â±  0.0557 AM Actor movies ⬤ Affiliation 639,286 1,470,404 3.6310 (dmin = 45) 2.0750 Â±  0.0015 Ff Filmtipset ⬤ Social 39,199 87,415 3.6610 (dmin = 21) 2.0210 Â±  0.0052 BC Corporate Leadership ⬤ Affiliation 64 99 3.6910 (dmin = 5) 2.5255 Â±  0.2300 TC Air traffic control ⬤ Infrastructure 1,226 2,615 3.7010 (dmin = 9) 1.9053 Â±  0.0259 LG LiveJournal ⬤ Affiliation 13,891,479 112,307,385 1.8584 Â±  0.0003 LX Linux ⬤ Software 30,837 213,954 1.9910 (dmin = 45) 1.5369 Â±  0.0031 Us Wikipedia, simple en (dynamic) ⬤ Hyperlink 100,312 1,627,472 2.3010 (dmin = 12) 1.5961 Â±  0.0019 Uf Wikipedia, fr (dynamic) ⬤ Hyperlink 2,212,682 59,008,831 2.3910 (dmin = 53) 1.6149 Â±  0.0004 Up Wikipedia, pl (dynamic) ⬤ Hyperlink 1,033,050 25,026,208 2.4210 (dmin = 37) 1.4974 Â±  0.0005 Ug Wikipedia, de (dynamic) ⬤ Hyperlink 2,166,669 86,337,879 1.4997 Â±  0.0003 Ui Wikipedia, it (dynamic) ⬤ Hyperlink 1,204,009 34,826,283 2.4110 (dmin = 59) 1.4820 Â±  0.0004 Ud Wikipedia, nl (dynamic) ⬤ Hyperlink 1,039,252 20,070,561 2.4310 (dmin = 34) 1.5299 Â±  0.0005 FR Friendster ⬤ Social 68,349,466 2,586,147,869 FO FOLDOC ⬤ Hyperlink 13,356 125,207 2.8910 (dmin = 52) 1.7368 Â±  0.0064 MC Crime ⬤ Interaction 2,209 1,476 3.9010 (dmin = 7) 3.0082 Â±  0.0541 PC US patents ⬤ Citation 3,774,768 16,518,947 4.0010 (dmin = 47) 1.6087 Â±  0.0003 Mt Train bombing ⬤ HumanContact 64 243 4.0410 (dmin = 10) 1.6029 Â±  0.0754 Ml Les Misérables ⬤ Misc 77 254 4.1210 (dmin = 10) 1.6911 Â±  0.0788 HY Hypertext 2009 ⬤ HumanContact 113 20,818 4.1710 (dmin = 39) 1.2839 Â±  0.0267 PG Pretty Good Privacy ⬤ OnlineContact 10,680 24,316 4.2610 (dmin = 36) 2.1092 Â±  0.0107 MH Highschool ⬤ HumanSocial 70 366 4.3810 (dmin = 8) 1.7939 Â±  0.0949 Ow Facebook ⬤ Communication 46,952 876,993 4.4310 (dmin = 50) 1.7049 Â±  0.0033 CN Countries ⬤ Affiliation 1,182,526 637,134 4.5110 (dmin = 1) 25.393 Â±  0.032 RA Manufacturing emails ⬤ Communication 167 82,927 4.6110 (dmin = 53) 1.3326 Â±  0.0257 MI Physicians ⬤ HumanSocial 241 1,098 4.6210 (dmin = 9) 1.5248 Â±  0.0338 Mh Hens ⬤ Animal 32 496 Bui BibSonomy u-i ⬤ Folksonomy 779,035 2,555,080 4.6910 (dmin = 1) 29.251 Â±  0.032 GN Gnutella ⬤ Computer 62,586 147,892 4.8310 (dmin = 13) 2.0629 Â±  0.0042 OR Orkut ⬤ Social 3,072,441 117,184,899 1.2724 Â±  0.0002 OG Orkut ⬤ Affiliation 14,297,249 327,037,487 1.4949 Â±  0.0001 OF OpenFlights ⬤ Infrastructure 3,425 67,663 1.7410 (dmin = 2) 1.7159 Â±  0.0122 OF OpenFlights ⬤ Infrastructure 2,939 30,501 1.7410 (dmin = 2) 1.7227 Â±  0.0133 AF US airports ⬤ Infrastructure 1,574 28,236 1.8510 (dmin = 13) 1.5469 Â±  0.0138 AC arXiv cond-mat ⬤ Authorship 55,467 58,595 2.8110 (dmin = 3) 2.2448 Â±  0.0063 UC UC Irvine messages ⬤ Communication 1,899 59,835 2.8310 (dmin = 35) 1.5629 Â±  0.0129 UF UC Irvine forum ⬤ Interaction 2,320 33,720 3.3010 (dmin = 22) 1.5846 Â±  0.0155 SW Southern women 1 ⬤ Interaction 50 89 4.6910 (dmin = 7) 2.1135 Â±  0.1968 UG US power grid ⬤ Infrastructure 4,941 6,594 7.6310 (dmin = 10) 2.2468 Â±  0.0177 NX Netflix ⬤ Rating 978,148 100,480,507 1.2150 Â±  0.0003 Wa Twitter ⬤ OnlineContact 2,919,613 12,887,063 1.8610 (dmin = 2) 2.8453 Â±  0.0011 Wti Twitter t-i ⬤ Folksonomy 1,773,193 2,635,885 1.9410 (dmin = 11) 3.7925 Â±  0.0023 Ws Twitter (ICWSM) ⬤ Social 465,017 834,797 2.4710 (dmin = 1) 4.3583 Â±  0.0049 Wut Twitter u-t ⬤ Folksonomy 880,846 4,664,605 2.6010 (dmin = 34) 2.4605 Â±  0.0017 DG Digg ⬤ Communication 30,398 87,627 2.6910 (dmin = 16) 1.9875 Â±  0.0057 Wui Twitter u-i ⬤ Folksonomy 9,618,743 12,656,613 3.2610 (dmin = 1) 8.9456 Â±  0.0026 FW Florida ecosystem wet ⬤ Trophic 128 2,106 4.8710 (dmin = 35) 1.3753 Â±  0.0332 FD Florida ecosystem dry ⬤ Trophic 128 2,137 5.0210 (dmin = 37) 1.3732 Â±  0.0330 en Wikipedia (en) ⬤ Authorship 29,143,573 266,769,613 2.2136 Â±  0.0002 ben Wikibooks (en) ⬤ Authorship 200,108 1,164,576 2.3910 (dmin = 5) 2.4691 Â±  0.0036 qen Wikiquote (en) ⬤ Authorship 137,970 549,210 2.4310 (dmin = 7) 3.1969 Â±  0.0065 es Wikipedia (es) ⬤ Authorship 3,623,742 27,011,506 2.4510 (dmin = 19) 2.4711 Â±  0.0008 it Wikipedia (it) ⬤ Authorship 2,531,261 26,241,217 2.5910 (dmin = 14) 2.0222 Â±  0.0007 men Wiktionary (en) ⬤ Authorship 2,163,240 8,998,641 2.6210 (dmin = 12) 2.4743 Â±  0.0010 GP Google+ ⬤ Social 23,628 39,242 2.6210 (dmin = 2) 3.9822 Â±  0.0194 bfr Wikibooks (fr) ⬤ Authorship 33,881 201,727 2.6710 (dmin = 4) 2.5700 Â±  0.0090 nfr Wikinews (fr) ⬤ Authorship 27,954 193,618 3.3310 (dmin = 4) 2.2545 Â±  0.0077 fr Wikipedia (fr) ⬤ Authorship 4,598,826 46,168,355 2.0882 Â±  0.0005 mfr Wiktionary (fr) ⬤ Authorship 1,917,281 7,399,298 3.4210 (dmin = 5) 2.3851 Â±  0.0010 mde Wiktionary (de) ⬤ Authorship 157,806 1,229,501 3.4510 (dmin = 8) 1.8228 Â±  0.0021 EF Facebook (NIPS) ⬤ Social 2,888 2,981 4.5210 (dmin = 1) 25.589 Â±  0.458 de Wikipedia (de) ⬤ Authorship 4,046,832 57,323,775 1.8727 Â±  0.0005 DB Douban ⬤ Social 154,908 327,162 2.0810 (dmin = 1) 2.9706 Â±  0.0050 EA Edinburgh Associative Thesaurus ⬤ Lexical 23,132 511,764 3.2110 (dmin = 49) 1.4697 Â±  0.0031 MW Windsurfers ⬤ HumanContact 43 336 5.0210 (dmin = 17) 2.1579 Â±  0.1766 JZ Jazz musicians ⬤ HumanSocial 198 2,742 5.2710 (dmin = 39) 1.3293 Â±  0.0234 MA Cattle ⬤ Animal 28 217 5.4110 (dmin = 14) 1.3888 Â±  0.0735 MQ Macaques ⬤ Animal 62 1,187 5.7810 (dmin = 33) 2.2925 Â±  0.1641 MK Kangaroo ⬤ Animal 17 91 6.0710 (dmin = 11) 1.4515 Â±  0.1095 MO Residence hall ⬤ HumanSocial 217 2,672 6.3210 (dmin = 24) 1.4928 Â±  0.0335 ET Euroroad ⬤ Infrastructure 1,174 1,417 6.4010 (dmin = 5) 2.2899 Â±  0.0376 If Infectious ⬤ HumanContact 410 17,298 6.4210 (dmin = 23) 1.4241 Â±  0.0209 A@ U. Rovira i Virgili ⬤ Communication 1,133 5,451 6.7710 (dmin = 35) 1.5611 Â±  0.0167 Mv Dutch college ⬤ HumanSocial 32 3,062 7.1010 (dmin = 17) 2.4100 Â±  0.2532 DO Dolphins ⬤ Animal 62 159 7.7110 (dmin = 9) 1.7085 Â±  0.0900 MX Seventh graders ⬤ HumanSocial 29 376 7.8110 (dmin = 18) 2.1884 Â±  0.2207 ME Adolescent health ⬤ HumanSocial 2,539 12,969 8.2510 (dmin = 17) 1.5141 Â±  0.0102 R1 Texas ⬤ Infrastructure 1,379,917 1,921,660 8.9010 (dmin = 7) 2.0737 Â±  0.0009 CU Contiguous USA ⬤ Infrastructure 49 107 8.9910 (dmin = 6) 1.7154 Â±  0.1022 MB Bison ⬤ Animal 26 314 8.9910 (dmin = 19) 2.0077 Â±  0.1976 MR Rhesus ⬤ Animal 16 111 8.9910 (dmin = 10) 2.0096 Â±  0.2524 Ms Sampson ⬤ HumanSocial 18 189 8.9910 (dmin = 14) 2.4776 Â±  0.3483 Mc Sheep ⬤ Animal 28 250 8.9910 (dmin = 19) 1.7331 Â±  0.1385 MT Taro exchange ⬤ HumanSocial 22 78 8.9910 (dmin = 5) 8.2748 Â±  1.5510 RO California ⬤ Infrastructure 1,965,206 2,766,607 8.9910 (dmin = 5) 2.0557 Â±  0.0008 RD Pennsylvania ⬤ Infrastructure 1,088,092 1,541,898 8.9910 (dmin = 5) 2.0528 Â±  0.0010 HT Highland tribes ⬤ HumanSocial 16 58 8.9910 (dmin = 8) 2.1828 Â±  0.2957 TF Twitter (MPI) ⬤ Social 52,579,682 1,963,263,821 TW Twitter (WWW) ⬤ Social 41,652,230 1,468,365,182