KONECT
KONECT > Statistics > Gini coefficient

## Gini coefficient

The Gini coefficient is a measure of inequality from economics, typically applied to distributions of wealth or income. In KONECT, we apply it to the degree distribution, as described in [1]. The Gini coefficient can either be defined in terms of the Lorenz curve, a type of plot that visualizes the inequality of a distribution, or using the following expression. Let $$d_1 \leq d_2 \leq \dotsb \leq d_{n}$$ be the sorted list of degrees in the network. Then, the Gini coefficient is defined as \begin{align} G &= \frac {2 \sum_{i=1}^{n} i d_i} {n \sum_{i-1}^{n} d_i} - \frac {n+1} {n}. \end{align} The Gini coefficient takes values between zero and one, with zero denoting total equality between degrees, and one denoting the dominance of a single node.

 [1] JÃ©rÃ´me Kunegis and Julia Preusse. Fairness on the web: Alternatives to the power law. In Proc. Web Science Conf., pages 175–184, 2012. [ .pdf ]

 Code Name Category F. W. M. $$n$$ $$m$$ $$G$$ Mh Hens ⬤ Animal 32 496 0% Sw Southern women 2 ⬤ Interaction 15 14 4.29% Ms Sampson ⬤ HumanSocial 18 189 10.3% MQ Macaques ⬤ Animal 62 1,187 11.2% MT Taro exchange ⬤ HumanSocial 22 78 11.8% HT Highland tribes ⬤ HumanSocial 16 58 13.1% Mc Sheep ⬤ Animal 28 250 15.8% MX Seventh graders ⬤ HumanSocial 29 376 18.0% MA Cattle ⬤ Animal 28 217 18.2% MK Kangaroo ⬤ Animal 17 91 18.4% RO California ⬤ Infrastructure 1,965,206 2,766,607 18.6% RD Pennsylvania ⬤ Infrastructure 1,088,092 1,541,898 18.8% R1 Texas ⬤ Infrastructure 1,379,917 1,921,660 18.9% MB Bison ⬤ Animal 26 314 19.2% CU Contiguous USA ⬤ Infrastructure 49 107 20.1% Mv Dutch college ⬤ HumanSocial 32 3,062 20.3% MR Rhesus ⬤ Animal 16 111 20.6% SC South African Companies ⬤ Affiliation 17 13 23.1% MW Windsurfers ⬤ HumanContact 43 336 23.7% ET Euroroad ⬤ Infrastructure 1,174 1,417 24.1% MH Highschool ⬤ HumanSocial 70 366 24.2% MO Residence hall ⬤ HumanSocial 217 2,672 24.4% SW Southern women 1 ⬤ Interaction 50 89 24.5% BC Corporate Leadership ⬤ Affiliation 64 99 25.0% FD Florida ecosystem dry ⬤ Trophic 128 2,137 25.4% FO FOLDOC ⬤ Hyperlink 13,356 125,207 25.4% FW Florida ecosystem wet ⬤ Trophic 128 2,106 25.6% MI Physicians ⬤ HumanSocial 241 1,098 28.5% ME Adolescent health ⬤ HumanSocial 2,539 12,969 30.0% BM Club membership ⬤ Affiliation 65 95 30.1% MZ Zebra ⬤ Animal 27 111 30.8% UG US power grid ⬤ Infrastructure 4,941 6,594 32.5% DO Dolphins ⬤ Animal 62 159 32.5% Am Amazon (TWEB) ⬤ Misc 403,394 3,387,388 33.1% JZ Jazz musicians ⬤ HumanSocial 198 2,742 34.6% ZA Zachary karate club ⬤ HumanSocial 34 78 38.5% TF Twitter (MPI) ⬤ Social 52,579,682 1,963,263,821 TW Twitter (WWW) ⬤ Social 41,652,230 1,468,365,182 CA Amazon (MDS) ⬤ Misc 334,863 925,872 38.6% If Infectious ⬤ HumanContact 410 17,298 39.0% AC arXiv cond-mat ⬤ Authorship 55,467 58,595 39.0% CR Chicago ⬤ Infrastructure 1,467 1,298 40.0% MC Crime ⬤ Interaction 2,209 1,476 40.4% AN David Copperfield ⬤ Lexical 112 425 41.7% ML Little Rock Lake ⬤ Trophic 183 2,494 42.7% Mt Train bombing ⬤ HumanContact 64 243 42.8% TC Air traffic control ⬤ Infrastructure 1,226 2,615 42.8% ST Movies ⬤ Feature 233,283 281,396 43.8% MP PDZBase ⬤ Metabolic 212 244 44.2% Mp Protein ⬤ Metabolic 1,870 2,277 44.9% WR Writers ⬤ Authorship 224,925 144,340 45.1% OC Occupation ⬤ Affiliation 356,884 250,945 45.5% HY Hypertext 2009 ⬤ HumanContact 113 20,818 45.8% Ml Les Misérables ⬤ Misc 77 254 46.1% RM Reality Mining ⬤ HumanContact 96 1,086,404 48.8% A@ U. Rovira i Virgili ⬤ Communication 1,133 5,451 49.1% EF Facebook (NIPS) ⬤ Social 2,888 2,981 51.4% PC US patents ⬤ Citation 3,774,768 16,518,947 51.6% CC Cora citation ⬤ Citation 23,166 91,500 52.1% PHc arXiv hep-ph ⬤ Citation 34,546 421,578 52.5% PR Producers ⬤ Authorship 236,510 207,268 52.8% M2 MovieLens 1M ⬤ Rating 15,786 1,000,209 53.3% CN Countries ⬤ Affiliation 1,182,526 637,134 53.5% CD DBLP co-authorship ⬤ Coauthorship 317,080 1,049,866 53.6% MV Human protein (Vidal) ⬤ Metabolic 3,133 6,726 54.1% LO Location ⬤ Feature 397,589 293,697 54.1% Ff Filmtipset ⬤ Social 39,199 87,415 54.2% YD Yahoo advertisers ⬤ Lexical 653,260 2,931,708 54.9% WO WordNet ⬤ Lexical 146,005 656,999 55.1% Ar American Revolution ⬤ Affiliation 277 160 55.2% HUr Hudong related ⬤ Hyperlink 2,452,715 18,854,882 55.5% Pa DBLP ⬤ Authorship 6,851,776 8,649,016 55.6% OR Orkut ⬤ Social 3,072,441 117,184,899 55.9% GN Gnutella ⬤ Computer 62,586 147,892 56.3% THc arXiv hep-th ⬤ Citation 27,770 352,807 57.0% CS CiteSeer ⬤ Citation 384,413 1,751,463 57.9% UL Unicode languages ⬤ Feature 1,122 1,255 58.3% MS Human protein (Stelzl) ⬤ Metabolic 1,706 6,207 58.9% Sh Hamsterster full ⬤ Social 2,426 16,631 58.9% CH Chess ⬤ Interaction 7,301 65,053 59.1% PG Pretty Good Privacy ⬤ OnlineContact 10,680 24,316 59.2% SX Sexual escorts ⬤ Rating 26,836 50,632 59.6% RL Record labels ⬤ Affiliation 355,095 233,286 59.7% GO Google ⬤ Hyperlink 875,713 5,105,039 59.7% M1 MovieLens 100k ⬤ Rating 3,568 100,000 59.8% AS Route views ⬤ Computer 6,474 13,895 60.8% SF Stanford ⬤ Hyperlink 281,903 2,312,497 60.9% AP arXiv astro-ph ⬤ Coauthorship 18,771 198,050 61.1% Shf Hamsterster friendships ⬤ Social 1,858 12,534 61.1% TL Twitter lists ⬤ Social 23,370 33,101 61.3% PM Caenorhabditis elegans ⬤ Metabolic 453 4,596 61.9% RA Manufacturing emails ⬤ Communication 167 82,927 61.9% PL Pokec ⬤ Social 1,632,803 30,622,564 62.1% Wui Twitter u-i ⬤ Folksonomy 9,618,743 12,656,613 62.4% PW Prosper.com ⬤ Interaction 25,697 35,377 62.7% IN CAIDA ⬤ Computer 26,475 53,381 62.8% LX Linux ⬤ Software 30,837 213,954 63.0% DG Digg ⬤ Communication 30,398 87,627 63.2% Mg Blogs ⬤ Hyperlink 1,224 19,025 63.3% GC Google.com internal ⬤ Hyperlink 15,763 171,206 63.6% WT TREC WT10g ⬤ Hyperlink 1,601,787 8,063,026 63.7% WC Wikipedia (en) ⬤ Feature 3,889,933 3,795,796 64.0% BAr Baidu related ⬤ Hyperlink 415,641 3,284,387 64.0% Ol Facebook (WOSN) ⬤ Social 63,731 817,035 64.3% PL Prosper loans ⬤ Interaction 89,269 3,394,979 64.4% TM Teams ⬤ Affiliation 1,836,793 1,366,466 64.6% J1 Jester 100 ⬤ Rating 146,942 4,136,360 64.6% GE DBpedia genre ⬤ Feature 525,651 463,497 64.6% HY Hyves ⬤ Social 1,402,673 2,777,419 65.0% AR Amazon ratings ⬤ Rating 5,523,029 5,838,041 65.1% RC Reactome ⬤ Metabolic 6,327 147,547 65.7% Pi DBLP ⬤ Citation 12,591 49,743 65.8% BS Berkeley/Stanford ⬤ Hyperlink 685,230 7,600,595 65.9% GP Google+ ⬤ Social 23,628 39,242 66.0% DB DBpedia ⬤ Misc 3,966,924 13,820,853 66.2% Bx BookCrossing (ratings) ⬤ Rating 341,559 433,652 66.3% EU EU institution ⬤ Communication 265,214 420,045 66.3% Bti BibSonomy t-i ⬤ Folksonomy 1,176,793 2,555,080 66.7% CL Actor collaborations ⬤ Misc 382,219 33,115,812 66.9% PH arXiv hep-ph ⬤ Coauthorship 28,093 4,596,803 67.1% Wti Twitter t-i ⬤ Folksonomy 1,773,193 2,635,885 67.1% MF Human protein (Figeys) ⬤ Metabolic 2,239 6,452 67.2% RE Reuters ⬤ Text 1,846,441 96,903,520 68.0% UF UC Irvine forum ⬤ Interaction 2,320 33,720 68.2% GW Gowalla ⬤ Social 196,591 950,327 68.3% TH arXiv hep-th ⬤ Coauthorship 22,908 2,673,133 68.4% BK Brightkite ⬤ Social 58,228 214,078 68.5% AM Actor movies ⬤ Affiliation 639,286 1,470,404 68.7% MN Bible ⬤ Lexical 1,773 16,401 68.9% Tar Wikipedia talk, Arabic ⬤ Communication 1,095,799 1,913,103 68.9% AD Advogato ⬤ Social 6,541 51,127 69.1% YG YouTube ⬤ Affiliation 218,563 293,360 69.3% DB Douban ⬤ Social 154,908 327,162 69.4% Ws Twitter (ICWSM) ⬤ Social 465,017 834,797 69.5% Us Wikipedia, simple en (dynamic) ⬤ Hyperlink 100,312 1,627,472 69.5% SK Skitter ⬤ Computer 1,696,415 11,095,298 69.6% EA Edinburgh Associative Thesaurus ⬤ Lexical 23,132 511,764 69.7% Pc DBLP ⬤ Coauthorship 1,314,050 18,986,618 69.7% Lj LiveJournal links ⬤ Social 5,204,176 49,174,464 70.2% SO Stack Overflow ⬤ Rating 1,187,072 1,301,942 70.6% Cti CiteULike t-i ⬤ Folksonomy 1,038,323 2,411,819 70.7% Ud Wikipedia, nl (dynamic) ⬤ Hyperlink 1,039,252 20,070,561 70.8% LI Libimseti.cz ⬤ Social 220,970 17,359,346 71.0% OF OpenFlights ⬤ Infrastructure 2,939 30,501 71.1% SD Slashdot ⬤ Communication 51,083 140,778 71.2% Tzh Wikipedia talk, Chinese ⬤ Communication 1,219,241 2,284,546 71.4% CY Youtube friendship ⬤ Social 1,134,890 2,987,624 71.4% LJ LiveJournal ⬤ Social 4,847,571 68,475,391 71.6% LM Livemocha ⬤ Social 104,103 2,193,083 72.1% Up Wikipedia, pl (dynamic) ⬤ Hyperlink 1,033,050 25,026,208 72.3% HUi Hudong internal ⬤ Hyperlink 1,984,484 14,869,484 72.6% M3 MovieLens 10M ⬤ Rating 150,433 10,000,054 72.8% YT YouTube ⬤ Social 3,223,589 9,375,374 72.9% Bui BibSonomy u-i ⬤ Folksonomy 779,035 2,555,080 73.0% Ug Wikipedia, de (dynamic) ⬤ Hyperlink 2,166,669 86,337,879 73.0% Wpl Wikipedia links, pl ⬤ Hyperlink 1,529,135 57,489,447 73.1% WT Web trackers ⬤ Hyperlink 68,087,704 140,613,762 73.5% Ow Facebook ⬤ Communication 46,952 876,993 73.5% Ui Wikipedia, it (dynamic) ⬤ Hyperlink 1,204,009 34,826,283 73.6% WK Wikipedia, English ⬤ Communication 2,394,385 5,021,410 73.6% J2 Jester 150 ⬤ Rating 101,524 1,728,847 73.8% PS Prosper.com ⬤ Affiliation 14,177 21,017 73.8% Mti MovieLens t-i ⬤ Folksonomy 40,657 95,580 74.3% GH Github ⬤ Authorship 233,905 440,237 74.5% Mui MovieLens u-i ⬤ Folksonomy 15,619 95,580 74.7% Cui CiteULike u-i ⬤ Folksonomy 777,199 2,411,819 74.8% Sd Dogster ⬤ Social 426,820 8,546,581 75.0% DJ JDK dependency ⬤ Software 6,434 150,985 75.1% EL Wikipedia elections ⬤ OnlineContact 7,118 103,675 75.2% BX BookCrossing (implicit) ⬤ Rating 551,079 1,149,739 75.2% Dj JUNG dependency ⬤ Software 6,120 138,706 75.3% YS Yahoo songs ⬤ Rating 2,626,941 256,804,235 75.3% AF US airports ⬤ Infrastructure 1,574 28,236 75.3% UC UC Irvine messages ⬤ Communication 1,899 59,835 75.4% Wja Wikipedia links, ja ⬤ Hyperlink 1,610,638 71,055,717 75.7% mfr Wiktionary (fr) ⬤ Authorship 1,917,281 7,399,298 75.7% Tpt Wikipedia talk, Portuguese ⬤ Communication 541,355 2,424,962 76.3% Wfr Wikipedia links, fr ⬤ Hyperlink 3,023,165 102,382,410 76.3% ND Notre Dame ⬤ Hyperlink 325,729 1,497,134 76.4% Vti vi.sualize.us t-i ⬤ Folksonomy 659,472 2,298,816 76.5% Wit Wikipedia links, it ⬤ Hyperlink 1,865,965 91,555,008 76.5% Wen Wikipedia links, en ⬤ Hyperlink 12,150,976 378,142,420 WP Wikipedia, English ⬤ Hyperlink 1,870,709 39,953,145 68.4% Wde Wikipedia links, de ⬤ Hyperlink 3,225,565 81,626,917 74.2% Fr Filmtipset ⬤ Rating 225,153 19,554,219 76.7% Scd Catster/Dogster ⬤ Social 623,766 15,699,276 76.8% ER Epinions ⬤ Rating 996,744 13,668,320 76.9% Wru Wikipedia links, ru ⬤ Hyperlink 2,853,118 82,056,101 77.0% mde Wiktionary (de) ⬤ Authorship 157,806 1,229,501 77.1% Sc Catster ⬤ Social 149,700 5,449,275 77.1% SZ Slashdot Zoo ⬤ Social 79,120 515,397 77.4% Uf Wikipedia, fr (dynamic) ⬤ Hyperlink 2,212,682 59,008,831 77.4% LY Youtube links ⬤ Social 1,138,499 4,942,297 77.5% BAi Baidu internal ⬤ Hyperlink 2,141,300 17,794,839 77.6% Vui vi.sualize.us u-i ⬤ Folksonomy 529,646 2,298,816 77.7% FI Flickr ⬤ Misc 105,938 2,316,948 78.0% OF OpenFlights ⬤ Infrastructure 3,425 67,663 78.1% men Wiktionary (en) ⬤ Authorship 2,163,240 8,998,641 78.7% nfr Wikinews (fr) ⬤ Authorship 27,954 193,618 79.0% NX Netflix ⬤ Rating 978,148 100,480,507 79.2% LK Linux kernel mailing list threads ⬤ Interaction 421,599 1,565,683 79.3% DBT TV Tropes ⬤ Feature 216,508 3,232,134 79.5% Wpt Wikipedia links, pt ⬤ Hyperlink 1,603,222 49,021,409 79.6% Wa Twitter ⬤ OnlineContact 2,919,613 12,887,063 79.8% W2 WikiSigned ⬤ OnlineContact 138,592 740,397 79.9% Fc Filmtipset ⬤ Interaction 104,890 1,266,753 80.3% TO Internet topology ⬤ Computer 34,761 171,403 80.8% CO Wikipedia conflict ⬤ OnlineContact 118,100 2,917,785 81.0% ES Epinions ⬤ Social 75,879 508,837 81.4% Tes Wikipedia talk, Spanish ⬤ Communication 497,446 2,702,879 81.9% ben Wikibooks (en) ⬤ Authorship 200,108 1,164,576 82.3% bfr Wikibooks (fr) ⬤ Authorship 33,881 201,727 82.4% Tfr Wikipedia talk, French ⬤ Communication 1,420,367 4,641,928 82.6% Mut MovieLens u-t ⬤ Folksonomy 24,546 95,580 82.9% Tit Wikipedia talk, Italian ⬤ Communication 863,846 3,067,680 83.3% EP Epinions ⬤ Social 131,828 841,372 83.6% HA Haggle ⬤ HumanContact 274 28,244 84.2% Wut Twitter u-t ⬤ Folksonomy 880,846 4,664,605 84.3% qen Wikiquote (en) ⬤ Authorship 137,970 549,210 84.6% FG Flickr ⬤ Affiliation 895,589 8,545,307 84.9% DF Digg friends ⬤ Social 279,630 1,731,653 85.2% LG LiveJournal ⬤ Affiliation 13,891,479 112,307,385 85.3% TR TREC (disks 4–5) ⬤ Text 2,285,379 151,632,178 85.4% nen Wikinews (en) ⬤ Authorship 184,536 901,416 85.8% DL Wikipedia, English ⬤ Hyperlink 18,268,992 172,183,984 86.1% Dl Discogs ⬤ Affiliation 3,780,417 14,414,659 86.2% Tru Wikipedia talk, Russian ⬤ Communication 457,017 2,282,055 86.6% it Wikipedia (it) ⬤ Authorship 2,531,261 26,241,217 86.9% OG Orkut ⬤ Affiliation 14,297,249 327,037,487 87.4% Tnl Wikipedia talk, Dutch ⬤ Communication 225,749 1,554,699 87.7% de Wikipedia (de) ⬤ Authorship 4,046,832 57,323,775 87.7% fr Wikipedia (fr) ⬤ Authorship 4,598,826 46,168,355 87.9% Dui Delicious ui ⬤ Folksonomy 35,444,383 301,186,579 87.9% FL Flickr ⬤ Social 2,302,925 33,140,017 88.0% DV Digg votes ⬤ Rating 282,371 3,018,197 88.2% LF Flickr links ⬤ Social 1,715,255 15,551,250 88.2% es Wikipedia (es) ⬤ Authorship 3,623,742 27,011,506 88.5% Dti Delicious ti ⬤ Folksonomy 42,801,712 301,183,605 88.9% DN DNC emails co-recipients ⬤ OnlineContact 2,029 136,602 88.9% en Wikipedia (en) ⬤ Authorship 29,143,573 266,769,613 89.0% Da Discogs artist–genre ⬤ Feature 3,509,661 19,033,891 89.2% Dt Discogs artist–style ⬤ Feature 3,236,269 24,085,580 89.5% Ten Wikipedia talk, English ⬤ Communication 2,987,535 24,981,163 90.0% WD Wikipedia Threads (de) ⬤ Communication 91,340 2,435,731 90.5% EN Enron ⬤ Communication 87,273 1,148,072 90.8% Ls Last.fm song ⬤ Interaction 1,086,604 19,150,868 90.9% DNc DNC emails ⬤ Communication 2,029 39,264 91.1% Cut CiteULike u-t ⬤ Folksonomy 198,707 2,411,819 91.3% Tde Wikipedia talk, German ⬤ Communication 519,403 6,729,794 91.7% Ds Discogs label–style ⬤ Feature 487,911 5,255,950 92.1% Dr Discogs label–genre ⬤ Feature 541,557 4,147,665 92.4% But BibSonomy u-t ⬤ Folksonomy 216,261 2,555,080 92.6% Lk Linux kernel mailing list replies ⬤ Communication 63,399 1,096,440 93.5% WU WebUni Magdeburg ⬤ Text 212,552 3,869,707 93.8% Vut vi.sualize.us u-t ⬤ Folksonomy 116,279 2,298,816 94.0% Dut Delicious ut ⬤ Folksonomy 6,178,261 301,186,579 95.9% Lb Last.fm band ⬤ Interaction 176,061 19,150,868 96.4% FR Friendster ⬤ Social 68,349,466 2,586,147,869 R2 Reuters-21578 ⬤ Text 81,791 1,464,182 75.4% FX Flixster ⬤ Social 2,523,386 7,918,801 77.6% EX Wikipedia (en) ⬤ Text 279,519 7,846,807 95.5%