KONECT
KONECT > Statistics > Relative edge distribution entropy

Relative edge distribution entropy

The relative edge distribution entropy is a measure of the equality of the degree distribution, and equals one when all degrees are equal, and attains the limit value of zero when all edges attach to a single node [1]. It is defined as \begin{align} H_{\mathrm{er}} &= \frac 1 {\ln n} \sum_{u \in V} - \frac{d(u)}{2m} \ln \frac{d(u)}{2m}. \end{align}

 [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. $$n$$ $$m$$ $$H_{er}$$ Tar Wikipedia talk, Arabic ⬤ Communication 1,095,799 1,913,103 61.5% Da Discogs artist–genre ⬤ Feature 3,509,661 19,033,891 61.8% Dr Discogs label–genre ⬤ Feature 541,557 4,147,665 63.2% mfr Wiktionary (fr) ⬤ Authorship 1,917,281 7,399,298 63.6% Tzh Wikipedia talk, Chinese ⬤ Communication 1,219,241 2,284,546 63.8% Tfr Wikipedia talk, French ⬤ Communication 1,420,367 4,641,928 66.3% Tit Wikipedia talk, Italian ⬤ Communication 863,846 3,067,680 68.2% men Wiktionary (en) ⬤ Authorship 2,163,240 8,998,641 69.2% CN Countries ⬤ Affiliation 1,182,526 637,134 69.7% Tru Wikipedia talk, Russian ⬤ Communication 457,017 2,282,055 70.4% Tpt Wikipedia talk, Portuguese ⬤ Communication 541,355 2,424,962 70.4% Dti Delicious ti ⬤ Folksonomy 42,801,712 301,183,605 70.5% Dt Discogs artist–style ⬤ Feature 3,236,269 24,085,580 70.8% EF Facebook (NIPS) ⬤ Social 2,888 2,981 70.9% mde Wiktionary (de) ⬤ Authorship 157,806 1,229,501 71.9% Tnl Wikipedia talk, Dutch ⬤ Communication 225,749 1,554,699 72.2% Tes Wikipedia talk, Spanish ⬤ Communication 497,446 2,702,879 73.3% Ds Discogs label–style ⬤ Feature 487,911 5,255,950 73.3% Ls Last.fm song ⬤ Interaction 1,086,604 19,150,868 73.8% nfr Wikinews (fr) ⬤ Authorship 27,954 193,618 73.8% Bui BibSonomy u-i ⬤ Folksonomy 779,035 2,555,080 73.8% es Wikipedia (es) ⬤ Authorship 3,623,742 27,011,506 74.6% it Wikipedia (it) ⬤ Authorship 2,531,261 26,241,217 75.2% fr Wikipedia (fr) ⬤ Authorship 4,598,826 46,168,355 75.4% J1 Jester 100 ⬤ Rating 146,942 4,136,360 75.7% EX Wikipedia (en) ⬤ Text 279,519 7,846,807 75.7% nen Wikinews (en) ⬤ Authorship 184,536 901,416 75.8% J2 Jester 150 ⬤ Rating 101,524 1,728,847 75.9% Lb Last.fm band ⬤ Interaction 176,061 19,150,868 76.0% WT Web trackers ⬤ Hyperlink 68,087,704 140,613,762 76.3% Tde Wikipedia talk, German ⬤ Communication 519,403 6,729,794 76.3% GP Google+ ⬤ Social 23,628 39,242 76.7% qen Wikiquote (en) ⬤ Authorship 137,970 549,210 76.8% But BibSonomy u-t ⬤ Folksonomy 216,261 2,555,080 77.2% Ar American Revolution ⬤ Affiliation 277 160 77.3% bfr Wikibooks (fr) ⬤ Authorship 33,881 201,727 77.3% GE DBpedia genre ⬤ Feature 525,651 463,497 77.4% Dut Delicious ut ⬤ Folksonomy 6,178,261 301,186,579 77.8% Ten Wikipedia talk, English ⬤ Communication 2,987,535 24,981,163 78.5% WK Wikipedia, English ⬤ Communication 2,394,385 5,021,410 78.7% WU WebUni Magdeburg ⬤ Text 212,552 3,869,707 78.9% DNc DNC emails ⬤ Communication 2,029 39,264 79.0% en Wikipedia (en) ⬤ Authorship 29,143,573 266,769,613 79.1% de Wikipedia (de) ⬤ Authorship 4,046,832 57,323,775 79.4% HA Haggle ⬤ HumanContact 274 28,244 79.5% Vti vi.sualize.us t-i ⬤ Folksonomy 659,472 2,298,816 79.7% Lk Linux kernel mailing list replies ⬤ Communication 63,399 1,096,440 79.8% EU EU institution ⬤ Communication 265,214 420,045 79.8% TO Internet topology ⬤ Computer 34,761 171,403 80.8% LK Linux kernel mailing list threads ⬤ Interaction 421,599 1,565,683 80.8% TR TREC (disks 4–5) ⬤ Text 2,285,379 151,632,178 80.9% Vut vi.sualize.us u-t ⬤ Folksonomy 116,279 2,298,816 81.1% ben Wikibooks (en) ⬤ Authorship 200,108 1,164,576 81.3% DF Digg friends ⬤ Social 279,630 1,731,653 81.5% DV Digg votes ⬤ Rating 282,371 3,018,197 82.1% LG LiveJournal ⬤ Affiliation 13,891,479 112,307,385 82.1% LF Flickr links ⬤ Social 1,715,255 15,551,250 82.2% PS Prosper.com ⬤ Affiliation 14,177 21,017 82.2% Ws Twitter (ICWSM) ⬤ Social 465,017 834,797 82.3% Dj JUNG dependency ⬤ Software 6,120 138,706 82.5% RE Reuters ⬤ Text 1,846,441 96,903,520 82.6% Sc Catster ⬤ Social 149,700 5,449,275 82.6% WD Wikipedia Threads (de) ⬤ Communication 91,340 2,435,731 82.7% EN Enron ⬤ Communication 87,273 1,148,072 82.8% Cut CiteULike u-t ⬤ Folksonomy 198,707 2,411,819 82.8% FL Flickr ⬤ Social 2,302,925 33,140,017 82.8% ER Epinions ⬤ Rating 996,744 13,668,320 82.9% DJ JDK dependency ⬤ Software 6,434 150,985 83.0% EP Epinions ⬤ Social 131,828 841,372 83.1% RL Record labels ⬤ Affiliation 355,095 233,286 83.6% NX Netflix ⬤ Rating 978,148 100,480,507 83.7% IN CAIDA ⬤ Computer 26,475 53,381 83.8% Vui vi.sualize.us u-i ⬤ Folksonomy 529,646 2,298,816 83.8% AF US airports ⬤ Infrastructure 1,574 28,236 84.2% Mut MovieLens u-t ⬤ Folksonomy 24,546 95,580 84.2% DN DNC emails co-recipients ⬤ OnlineContact 2,029 136,602 84.2% Dui Delicious ui ⬤ Folksonomy 35,444,383 301,186,579 84.3% ES Epinions ⬤ Social 75,879 508,837 84.5% Fr Filmtipset ⬤ Rating 225,153 19,554,219 84.6% Cti CiteULike t-i ⬤ Folksonomy 1,038,323 2,411,819 84.7% Cui CiteULike u-i ⬤ Folksonomy 777,199 2,411,819 84.8% Mui MovieLens u-i ⬤ Folksonomy 15,619 95,580 84.9% W2 WikiSigned ⬤ OnlineContact 138,592 740,397 85.0% BAr Baidu related ⬤ Hyperlink 415,641 3,284,387 85.1% Fc Filmtipset ⬤ Interaction 104,890 1,266,753 85.1% OG Orkut ⬤ Affiliation 14,297,249 327,037,487 85.4% TM Teams ⬤ Affiliation 1,836,793 1,366,466 85.4% AS Route views ⬤ Computer 6,474 13,895 85.4% MF Human protein (Figeys) ⬤ Metabolic 2,239 6,452 85.5% BX BookCrossing (implicit) ⬤ Rating 551,079 1,149,739 85.5% R2 Reuters-21578 ⬤ Text 81,791 1,464,182 85.7% Bti BibSonomy t-i ⬤ Folksonomy 1,176,793 2,555,080 85.7% Dl Discogs ⬤ Affiliation 3,780,417 14,414,659 85.8% Wen Wikipedia links, en ⬤ Hyperlink 12,150,976 378,142,420 85.8% LX Linux ⬤ Software 30,837 213,954 85.9% FG Flickr ⬤ Affiliation 895,589 8,545,307 85.9% OC Occupation ⬤ Affiliation 356,884 250,945 85.9% PW Prosper.com ⬤ Interaction 25,697 35,377 85.9% YT YouTube ⬤ Social 3,223,589 9,375,374 86.0% Scd Catster/Dogster ⬤ Social 623,766 15,699,276 86.0% LY Youtube links ⬤ Social 1,138,499 4,942,297 86.2% OF OpenFlights ⬤ Infrastructure 3,425 67,663 86.4% FX Flixster ⬤ Social 2,523,386 7,918,801 86.4% Wti Twitter t-i ⬤ Folksonomy 1,773,193 2,635,885 86.4% CO Wikipedia conflict ⬤ OnlineContact 118,100 2,917,785 86.5% Sd Dogster ⬤ Social 426,820 8,546,581 86.7% TL Twitter lists ⬤ Social 23,370 33,101 86.8% OF OpenFlights ⬤ Infrastructure 2,939 30,501 86.9% DL Wikipedia, English ⬤ Hyperlink 18,268,992 172,183,984 87.1% SZ Slashdot Zoo ⬤ Social 79,120 515,397 87.1% YS Yahoo songs ⬤ Rating 2,626,941 256,804,235 87.1% EL Wikipedia elections ⬤ OnlineContact 7,118 103,675 87.2% GH Github ⬤ Authorship 233,905 440,237 87.4% FR Friendster ⬤ Social 68,349,466 2,586,147,869 DB DBpedia ⬤ Misc 3,966,924 13,820,853 87.4% M3 MovieLens 10M ⬤ Rating 150,433 10,000,054 87.5% YD Yahoo advertisers ⬤ Lexical 653,260 2,931,708 87.5% DBT TV Tropes ⬤ Feature 216,508 3,232,134 87.5% ND Notre Dame ⬤ Hyperlink 325,729 1,497,134 87.6% FI Flickr ⬤ Misc 105,938 2,316,948 87.6% CY Youtube friendship ⬤ Social 1,134,890 2,987,624 87.7% YG YouTube ⬤ Affiliation 218,563 293,360 87.8% GC Google.com internal ⬤ Hyperlink 15,763 171,206 87.9% BAi Baidu internal ⬤ Hyperlink 2,141,300 17,794,839 88.1% Up Wikipedia, pl (dynamic) ⬤ Hyperlink 1,033,050 25,026,208 88.1% HUi Hudong internal ⬤ Hyperlink 1,984,484 14,869,484 88.2% SD Slashdot ⬤ Communication 51,083 140,778 88.2% Wut Twitter u-t ⬤ Folksonomy 880,846 4,664,605 88.3% Uf Wikipedia, fr (dynamic) ⬤ Hyperlink 2,212,682 59,008,831 88.3% Wpt Wikipedia links, pt ⬤ Hyperlink 1,603,222 49,021,409 88.6% BS Berkeley/Stanford ⬤ Hyperlink 685,230 7,600,595 88.6% Wru Wikipedia links, ru ⬤ Hyperlink 2,853,118 82,056,101 88.7% Ui Wikipedia, it (dynamic) ⬤ Hyperlink 1,204,009 34,826,283 88.7% Us Wikipedia, simple en (dynamic) ⬤ Hyperlink 100,312 1,627,472 88.8% AD Advogato ⬤ Social 6,541 51,127 88.9% LO Location ⬤ Feature 397,589 293,697 88.9% UL Unicode languages ⬤ Feature 1,122 1,255 88.9% SK Skitter ⬤ Computer 1,696,415 11,095,298 88.9% UC UC Irvine messages ⬤ Communication 1,899 59,835 89.0% DB Douban ⬤ Social 154,908 327,162 89.0% SO Stack Overflow ⬤ Rating 1,187,072 1,301,942 89.1% Wfr Wikipedia links, fr ⬤ Hyperlink 3,023,165 102,382,410 89.1% Ud Wikipedia, nl (dynamic) ⬤ Hyperlink 1,039,252 20,070,561 89.2% SF Stanford ⬤ Hyperlink 281,903 2,312,497 89.4% Wa Twitter ⬤ OnlineContact 2,919,613 12,887,063 89.4% Bx BookCrossing (ratings) ⬤ Rating 341,559 433,652 89.4% Mti MovieLens t-i ⬤ Folksonomy 40,657 95,580 89.5% Mg Blogs ⬤ Hyperlink 1,224 19,025 89.8% MS Human protein (Stelzl) ⬤ Metabolic 1,706 6,207 89.8% PM Caenorhabditis elegans ⬤ Metabolic 453 4,596 89.9% Wde Wikipedia links, de ⬤ Hyperlink 3,225,565 81,626,917 90.0% LM Livemocha ⬤ Social 104,103 2,193,083 90.0% Wit Wikipedia links, it ⬤ Hyperlink 1,865,965 91,555,008 90.0% Wja Wikipedia links, ja ⬤ Hyperlink 1,610,638 71,055,717 90.1% WP Wikipedia, English ⬤ Hyperlink 1,870,709 39,953,145 90.2% BK Brightkite ⬤ Social 58,228 214,078 90.2% WC Wikipedia (en) ⬤ Feature 3,889,933 3,795,796 90.2% Ug Wikipedia, de (dynamic) ⬤ Hyperlink 2,166,669 86,337,879 90.4% GW Gowalla ⬤ Social 196,591 950,327 90.4% Wpl Wikipedia links, pl ⬤ Hyperlink 1,529,135 57,489,447 90.4% LI Libimseti.cz ⬤ Social 220,970 17,359,346 90.6% HY Hyves ⬤ Social 1,402,673 2,777,419 90.6% Wui Twitter u-i ⬤ Folksonomy 9,618,743 12,656,613 90.6% Shf Hamsterster friendships ⬤ Social 1,858 12,534 90.8% Pi DBLP ⬤ Citation 12,591 49,743 90.8% SX Sexual escorts ⬤ Rating 26,836 50,632 91.1% EA Edinburgh Associative Thesaurus ⬤ Lexical 23,132 511,764 91.2% RC Reactome ⬤ Metabolic 6,327 147,547 91.2% WT TREC WT10g ⬤ Hyperlink 1,601,787 8,063,026 91.3% HUr Hudong related ⬤ Hyperlink 2,452,715 18,854,882 91.3% MN Bible ⬤ Lexical 1,773 16,401 91.5% TH arXiv hep-th ⬤ Coauthorship 22,908 2,673,133 91.5% AR Amazon ratings ⬤ Rating 5,523,029 5,838,041 91.7% Ml Les Misérables ⬤ Misc 77 254 91.7% Sh Hamsterster full ⬤ Social 2,426 16,631 91.8% DG Digg ⬤ Communication 30,398 87,627 92.0% PG Pretty Good Privacy ⬤ OnlineContact 10,680 24,316 92.2% ZA Zachary karate club ⬤ HumanSocial 34 78 92.5% MP PDZBase ⬤ Metabolic 212 244 92.5% RA Manufacturing emails ⬤ Communication 167 82,927 92.6% MV Human protein (Vidal) ⬤ Metabolic 3,133 6,726 92.6% M1 MovieLens 100k ⬤ Rating 3,568 100,000 92.7% Mt Train bombing ⬤ HumanContact 64 243 92.7% UF UC Irvine forum ⬤ Interaction 2,320 33,720 92.7% CR Chicago ⬤ Infrastructure 1,467 1,298 92.8% CH Chess ⬤ Interaction 7,301 65,053 92.9% PL Prosper loans ⬤ Interaction 89,269 3,394,979 92.9% LJ LiveJournal ⬤ Social 4,847,571 68,475,391 93.0% M2 MovieLens 1M ⬤ Rating 15,786 1,000,209 93.1% Ol Facebook (WOSN) ⬤ Social 63,731 817,035 93.1% AP arXiv astro-ph ⬤ Coauthorship 18,771 198,050 93.1% CL Actor collaborations ⬤ Misc 382,219 33,115,812 93.1% Lj LiveJournal links ⬤ Social 5,204,176 49,174,464 93.2% AM Actor movies ⬤ Affiliation 639,286 1,470,404 93.3% PH arXiv hep-ph ⬤ Coauthorship 28,093 4,596,803 93.5% AN David Copperfield ⬤ Lexical 112 425 93.5% PR Producers ⬤ Authorship 236,510 207,268 93.5% THc arXiv hep-th ⬤ Citation 27,770 352,807 93.8% Ow Facebook ⬤ Communication 46,952 876,993 93.9% WO WordNet ⬤ Lexical 146,005 656,999 94.0% ML Little Rock Lake ⬤ Trophic 183 2,494 94.1% GO Google ⬤ Hyperlink 875,713 5,105,039 94.1% A@ U. Rovira i Virgili ⬤ Communication 1,133 5,451 94.3% Ff Filmtipset ⬤ Social 39,199 87,415 94.3% Mp Protein ⬤ Metabolic 1,870 2,277 94.3% MZ Zebra ⬤ Animal 27 111 94.4% CS CiteSeer ⬤ Citation 384,413 1,751,463 94.5% Pc DBLP ⬤ Coauthorship 1,314,050 18,986,618 94.7% CC Cora citation ⬤ Citation 23,166 91,500 94.8% GN Gnutella ⬤ Computer 62,586 147,892 94.8% PL Pokec ⬤ Social 1,632,803 30,622,564 95.1% TC Air traffic control ⬤ Infrastructure 1,226 2,615 95.1% PHc arXiv hep-ph ⬤ Citation 34,546 421,578 95.2% BM Club membership ⬤ Affiliation 65 95 95.5% CD DBLP co-authorship ⬤ Coauthorship 317,080 1,049,866 95.5% ST Movies ⬤ Feature 233,283 281,396 95.6% MC Crime ⬤ Interaction 2,209 1,476 95.7% DO Dolphins ⬤ Animal 62 159 95.7% Pa DBLP ⬤ Authorship 6,851,776 8,649,016 95.8% OR Orkut ⬤ Social 3,072,441 117,184,899 95.8% WR Writers ⬤ Authorship 224,925 144,340 95.8% BC Corporate Leadership ⬤ Affiliation 64 99 95.8% JZ Jazz musicians ⬤ HumanSocial 198 2,742 96.2% SC South African Companies ⬤ Affiliation 17 13 96.4% SW Southern women 1 ⬤ Interaction 50 89 96.5% AC arXiv cond-mat ⬤ Authorship 55,467 58,595 96.6% If Infectious ⬤ HumanContact 410 17,298 96.8% MK Kangaroo ⬤ Animal 17 91 96.8% PC US patents ⬤ Citation 3,774,768 16,518,947 96.9% MR Rhesus ⬤ Animal 16 111 97.3% MI Physicians ⬤ HumanSocial 241 1,098 97.5% HY Hypertext 2009 ⬤ HumanContact 113 20,818 97.6% CA Amazon (MDS) ⬤ Misc 334,863 925,872 97.7% MW Windsurfers ⬤ HumanContact 43 336 97.7% FW Florida ecosystem wet ⬤ Trophic 128 2,106 97.7% MH Highschool ⬤ HumanSocial 70 366 97.7% FD Florida ecosystem dry ⬤ Trophic 128 2,137 97.7% UG US power grid ⬤ Infrastructure 4,941 6,594 97.8% MA Cattle ⬤ Animal 28 217 97.9% MB Bison ⬤ Animal 26 314 97.9% ME Adolescent health ⬤ HumanSocial 2,539 12,969 98.1% Mv Dutch college ⬤ HumanSocial 32 3,062 98.1% MO Residence hall ⬤ HumanSocial 217 2,672 98.2% RM Reality Mining ⬤ HumanContact 96 1,086,404 98.3% CU Contiguous USA ⬤ Infrastructure 49 107 98.3% MX Seventh graders ⬤ HumanSocial 29 376 98.3% Am Amazon (TWEB) ⬤ Misc 403,394 3,387,388 98.3% Mc Sheep ⬤ Animal 28 250 98.3% FO FOLDOC ⬤ Hyperlink 13,356 125,207 98.4% ET Euroroad ⬤ Infrastructure 1,174 1,417 98.5% HT Highland tribes ⬤ HumanSocial 16 58 98.8% TF Twitter (MPI) ⬤ Social 52,579,682 1,963,263,821 TW Twitter (WWW) ⬤ Social 41,652,230 1,468,365,182 MT Taro exchange ⬤ HumanSocial 22 78 99.0% Ms Sampson ⬤ HumanSocial 18 189 99.3% RD Pennsylvania ⬤ Infrastructure 1,088,092 1,541,898 99.5% R1 Texas ⬤ Infrastructure 1,379,917 1,921,660 99.5% MQ Macaques ⬤ Animal 62 1,187 99.5% RO California ⬤ Infrastructure 1,965,206 2,766,607 99.5% Sw Southern women 2 ⬤ Interaction 15 14 99.5% Mh Hens ⬤ Animal 32 496 100%