KONECT
KONECT > Statistics > Reciprocity

## Reciprocity

In a directed network, the reciprocity equals the proportion of edges for which an edge in the opposite direction exists, i.e., that are reciprocated. \begin{align} y = \frac 1 m | \{ (u,v) \in E \mid (v,u) \in E \} | \end{align} The reciprocity can give an idea of the type of network. For instance, citation networks only contain only few pairs of papers that mutually cite each other. On the other hand, an email network will contain many pairs of people who have sent emails to each other. Thus, citation networks typically have low reciprocity, and communnication networks have high reciprocity.

 Code Name Category F. W. M. $$n$$ $$m$$ $$y$$ Mh Hens ⬤ Animal 32 496 0% Ws Twitter (ICWSM) ⬤ Social 465,017 834,797 0.301% Wut Twitter u-t ⬤ Folksonomy 880,846 4,664,605 Wui Twitter u-i ⬤ Folksonomy 9,618,743 12,656,613 Wti Twitter t-i ⬤ Folksonomy 1,773,193 2,635,885 Wen Wikipedia links, en ⬤ Hyperlink 12,150,976 378,142,420 1.13% LI Libimseti.cz ⬤ Social 220,970 17,359,346 1.45% DG Digg ⬤ Communication 30,398 87,627 1.55% HUr Hudong related ⬤ Hyperlink 2,452,715 18,854,882 1.74% Tar Wikipedia talk, Arabic ⬤ Communication 1,095,799 1,913,103 2.92% Wa Twitter ⬤ OnlineContact 2,919,613 12,887,063 3.20% Tzh Wikipedia talk, Chinese ⬤ Communication 1,219,241 2,284,546 4.45% HUi Hudong internal ⬤ Hyperlink 1,984,484 14,869,484 4.67% W2 WikiSigned ⬤ OnlineContact 138,592 740,397 6.58% BAi Baidu internal ⬤ Hyperlink 2,141,300 17,794,839 7.06% Tpt Wikipedia talk, Portuguese ⬤ Communication 541,355 2,424,962 9.50% Tru Wikipedia talk, Russian ⬤ Communication 457,017 2,282,055 11.7% Tfr Wikipedia talk, French ⬤ Communication 1,420,367 4,641,928 14.0% WK Wikipedia, English ⬤ Communication 2,394,385 5,021,410 14.4% Tnl Wikipedia talk, Dutch ⬤ Communication 225,749 1,554,699 16.1% WP Wikipedia, English ⬤ Hyperlink 1,870,709 39,953,145 17.1% Tit Wikipedia talk, Italian ⬤ Communication 863,846 3,067,680 17.4% Ten Wikipedia talk, English ⬤ Communication 2,987,535 24,981,163 21.5% Tde Wikipedia talk, German ⬤ Communication 519,403 6,729,794 22.4% Tes Wikipedia talk, Spanish ⬤ Communication 497,446 2,702,879 25.0% BS Berkeley/Stanford ⬤ Hyperlink 685,230 7,600,595 25.0% Wfr Wikipedia links, fr ⬤ Hyperlink 3,023,165 102,382,410 37.0% Wde Wikipedia links, de ⬤ Hyperlink 3,225,565 81,626,917 38.8% Wja Wikipedia links, ja ⬤ Hyperlink 1,610,638 71,055,717 41.7% Wpt Wikipedia links, pt ⬤ Hyperlink 1,603,222 49,021,409 42.4% Wru Wikipedia links, ru ⬤ Hyperlink 2,853,118 82,056,101 46.3% WD Wikipedia Threads (de) ⬤ Communication 91,340 2,435,731 49.3% Wit Wikipedia links, it ⬤ Hyperlink 1,865,965 91,555,008 51.4% Wpl Wikipedia links, pl ⬤ Hyperlink 1,529,135 57,489,447 53.2% WC Wikipedia (en) ⬤ Feature 3,889,933 3,795,796 CO Wikipedia conflict ⬤ OnlineContact 118,100 2,917,785 WU WebUni Magdeburg ⬤ Text 212,552 3,869,707 SF Stanford ⬤ Hyperlink 281,903 2,312,497 27.7% UL Unicode languages ⬤ Feature 1,122 1,255 ZA Zachary karate club ⬤ HumanSocial 34 78 HT Highland tribes ⬤ HumanSocial 16 58 GO Google ⬤ Hyperlink 875,713 5,105,039 30.7% ND Notre Dame ⬤ Hyperlink 325,729 1,497,134 52.5% BAr Baidu related ⬤ Hyperlink 415,641 3,284,387 55.4% YT YouTube ⬤ Social 3,223,589 9,375,374 LY Youtube links ⬤ Social 1,138,499 4,942,297 79.0% YG YouTube ⬤ Affiliation 218,563 293,360 YS Yahoo songs ⬤ Rating 2,626,941 256,804,235 WO WordNet ⬤ Lexical 146,005 656,999 TF Twitter (MPI) ⬤ Social 52,579,682 1,963,263,821 TW Twitter (WWW) ⬤ Social 41,652,230 1,468,365,182 WT TREC WT10g ⬤ Hyperlink 1,601,787 8,063,026 34.3% WT Web trackers ⬤ Hyperlink 68,087,704 140,613,762 TO Internet topology ⬤ Computer 34,761 171,403 CR Chicago ⬤ Infrastructure 1,467 1,298 DJ JDK dependency ⬤ Software 6,434 150,985 0.868% Dj JUNG dependency ⬤ Software 6,120 138,706 0.970% ET Euroroad ⬤ Infrastructure 1,174 1,417 CC Cora citation ⬤ Citation 23,166 91,500 5.12% SO Stack Overflow ⬤ Rating 1,187,072 1,301,942 SZ Slashdot Zoo ⬤ Social 79,120 515,397 18.5% SD Slashdot ⬤ Communication 51,083 140,778 21.6% R1 Texas ⬤ Infrastructure 1,379,917 1,921,660 RD Pennsylvania ⬤ Infrastructure 1,088,092 1,541,898 RO California ⬤ Infrastructure 1,965,206 2,766,607 RE Reuters ⬤ Text 1,846,441 96,903,520 RC Reactome ⬤ Metabolic 6,327 147,547 PL Prosper loans ⬤ Interaction 89,269 3,394,979 0.0122% RA Manufacturing emails ⬤ Communication 167 82,927 87.6% PW Prosper.com ⬤ Interaction 25,697 35,377 PL Pokec ⬤ Social 1,632,803 30,622,564 54.3% LJ LiveJournal ⬤ Social 4,847,571 68,475,391 74.8% If Infectious ⬤ HumanContact 410 17,298 HY Hypertext 2009 ⬤ HumanContact 113 20,818 ES Epinions ⬤ Social 75,879 508,837 40.5% PS Prosper.com ⬤ Affiliation 14,177 21,017 Vut vi.sualize.us u-t ⬤ Folksonomy 116,279 2,298,816 Vui vi.sualize.us u-i ⬤ Folksonomy 529,646 2,298,816 Vti vi.sualize.us t-i ⬤ Folksonomy 659,472 2,298,816 Sh Hamsterster full ⬤ Social 2,426 16,631 Shf Hamsterster friendships ⬤ Social 1,858 12,534 Sd Dogster ⬤ Social 426,820 8,546,581 Sc Catster ⬤ Social 149,700 5,449,275 Scd Catster/Dogster ⬤ Social 623,766 15,699,276 GN Gnutella ⬤ Computer 62,586 147,892 0% PC US patents ⬤ Citation 3,774,768 16,518,947 0% OR Orkut ⬤ Social 3,072,441 117,184,899 OG Orkut ⬤ Affiliation 14,297,249 327,037,487 UC UC Irvine messages ⬤ Communication 1,899 59,835 63.6% AF US airports ⬤ Infrastructure 1,574 28,236 78.1% UF UC Irvine forum ⬤ Interaction 2,320 33,720 SW Southern women 1 ⬤ Interaction 50 89 UG US power grid ⬤ Infrastructure 4,941 6,594 OF OpenFlights ⬤ Infrastructure 2,939 30,501 97.2% AC arXiv cond-mat ⬤ Authorship 55,467 58,595 OF OpenFlights ⬤ Infrastructure 3,425 67,663 97.6% NX Netflix ⬤ Rating 978,148 100,480,507 M2 MovieLens 1M ⬤ Rating 15,786 1,000,209 Mut MovieLens u-t ⬤ Folksonomy 24,546 95,580 Mui MovieLens u-i ⬤ Folksonomy 15,619 95,580 Mti MovieLens t-i ⬤ Folksonomy 40,657 95,580 M3 MovieLens 10M ⬤ Rating 150,433 10,000,054 M1 MovieLens 100k ⬤ Rating 3,568 100,000 MZ Zebra ⬤ Animal 27 111 Mc Sheep ⬤ Animal 28 250 12.0% Ms Sampson ⬤ HumanSocial 18 189 66.7% MX Seventh graders ⬤ HumanSocial 29 376 67.0% Mv Dutch college ⬤ HumanSocial 32 3,062 68.4% Mt Train bombing ⬤ HumanContact 64 243 Mg Blogs ⬤ Hyperlink 1,224 19,025 24.3% ME Adolescent health ⬤ HumanSocial 2,539 12,969 38.8% MC Crime ⬤ Interaction 2,209 1,476 MA Cattle ⬤ Animal 28 217 11.1% MB Bison ⬤ Animal 26 314 58.6% MW Windsurfers ⬤ HumanContact 43 336 RM Reality Mining ⬤ HumanContact 96 1,086,404 MV Human protein (Vidal) ⬤ Metabolic 3,133 6,726 MF Human protein (Figeys) ⬤ Metabolic 2,239 6,452 0.620% TC Air traffic control ⬤ Infrastructure 1,226 2,615 15.8% MS Human protein (Stelzl) ⬤ Metabolic 1,706 6,207 97.8% MP PDZBase ⬤ Metabolic 212 244 ML Little Rock Lake ⬤ Trophic 183 2,494 4.09% GW Gowalla ⬤ Social 196,591 950,327 BK Brightkite ⬤ Social 58,228 214,078 Lk Linux kernel mailing list replies ⬤ Communication 63,399 1,096,440 65.9% LK Linux kernel mailing list threads ⬤ Interaction 421,599 1,565,683 LM Livemocha ⬤ Social 104,103 2,193,083 Lj LiveJournal links ⬤ Social 5,204,176 49,174,464 LG LiveJournal ⬤ Affiliation 13,891,479 112,307,385 LX Linux ⬤ Software 30,837 213,954 0.441% Us Wikipedia, simple en (dynamic) ⬤ Hyperlink 100,312 1,627,472 12.7% Ui Wikipedia, it (dynamic) ⬤ Hyperlink 1,204,009 34,826,283 15.0% Up Wikipedia, pl (dynamic) ⬤ Hyperlink 1,033,050 25,026,208 17.5% Ud Wikipedia, nl (dynamic) ⬤ Hyperlink 1,039,252 20,070,561 17.9% MR Rhesus ⬤ Animal 16 111 75.7% MT Taro exchange ⬤ HumanSocial 22 78 100% Mp Protein ⬤ Metabolic 1,870 2,277 MO Residence hall ⬤ HumanSocial 217 2,672 62.4% MN Bible ⬤ Lexical 1,773 16,401 MQ Macaques ⬤ Animal 62 1,187 3.37% Ml Les Misérables ⬤ Misc 77 254 MK Kangaroo ⬤ Animal 17 91 MI Physicians ⬤ HumanSocial 241 1,098 31.9% MH Highschool ⬤ HumanSocial 70 366 50.3% Ls Last.fm song ⬤ Interaction 1,086,604 19,150,868 Uf Wikipedia, fr (dynamic) ⬤ Hyperlink 2,212,682 59,008,831 15.5% Ug Wikipedia, de (dynamic) ⬤ Hyperlink 2,166,669 86,337,879 17.5% Lb Last.fm band ⬤ Interaction 176,061 19,150,868 YD Yahoo advertisers ⬤ Lexical 653,260 2,931,708 0.000614% J2 Jester 150 ⬤ Rating 101,524 1,728,847 J1 Jester 100 ⬤ Rating 146,942 4,136,360 HY Hyves ⬤ Social 1,402,673 2,777,419 TR TREC (disks 4–5) ⬤ Text 2,285,379 151,632,178 R2 Reuters-21578 ⬤ Text 81,791 1,464,182 EX Wikipedia (en) ⬤ Text 279,519 7,846,807 GH Github ⬤ Authorship 233,905 440,237 FR Friendster ⬤ Social 68,349,466 2,586,147,869 FD Florida ecosystem dry ⬤ Trophic 128 2,137 2.90% FW Florida ecosystem wet ⬤ Trophic 128 2,106 2.94% FO FOLDOC ⬤ Hyperlink 13,356 125,207 47.9% FX Flixster ⬤ Social 2,523,386 7,918,801 LF Flickr links ⬤ Social 1,715,255 15,551,250 FL Flickr ⬤ Social 2,302,925 33,140,017 62.2% FG Flickr ⬤ Affiliation 895,589 8,545,307 FI Flickr ⬤ Misc 105,938 2,316,948 Fr Filmtipset ⬤ Rating 225,153 19,554,219 Ff Filmtipset ⬤ Social 39,199 87,415 Fc Filmtipset ⬤ Interaction 104,890 1,266,753 GP Google+ ⬤ Social 23,628 39,242 0.245% Ow Facebook ⬤ Communication 46,952 876,993 62.5% Ol Facebook (WOSN) ⬤ Social 63,731 817,035 SX Sexual escorts ⬤ Rating 26,836 50,632 ER Epinions ⬤ Rating 996,744 13,668,320 EN Enron ⬤ Communication 87,273 1,148,072 14.6% EU EU institution ⬤ Communication 265,214 420,045 26.2% EP Epinions ⬤ Social 131,828 841,372 30.9% EF Facebook (NIPS) ⬤ Social 2,888 2,981 it Wikipedia (it) ⬤ Authorship 2,531,261 26,241,217 mfr Wiktionary (fr) ⬤ Authorship 1,917,281 7,399,298 nfr Wikinews (fr) ⬤ Authorship 27,954 193,618 fr Wikipedia (fr) ⬤ Authorship 4,598,826 46,168,355 bfr Wikibooks (fr) ⬤ Authorship 33,881 201,727 es Wikipedia (es) ⬤ Authorship 3,623,742 27,011,506 men Wiktionary (en) ⬤ Authorship 2,163,240 8,998,641 qen Wikiquote (en) ⬤ Authorship 137,970 549,210 nen Wikinews (en) ⬤ Authorship 184,536 901,416 en Wikipedia (en) ⬤ Authorship 29,143,573 266,769,613 ben Wikibooks (en) ⬤ Authorship 200,108 1,164,576 mde Wiktionary (de) ⬤ Authorship 157,806 1,229,501 de Wikipedia (de) ⬤ Authorship 4,046,832 57,323,775 EA Edinburgh Associative Thesaurus ⬤ Lexical 23,132 511,764 9.57% DB Douban ⬤ Social 154,908 327,162 DO Dolphins ⬤ Animal 62 159 DNc DNC emails ⬤ Communication 2,029 39,264 41.9% DN DNC emails co-recipients ⬤ OnlineContact 2,029 136,602 Dt Discogs artist–style ⬤ Feature 3,236,269 24,085,580 Ds Discogs label–style ⬤ Feature 487,911 5,255,950 Dr Discogs label–genre ⬤ Feature 541,557 4,147,665 Da Discogs artist–genre ⬤ Feature 3,509,661 19,033,891 Dl Discogs ⬤ Affiliation 3,780,417 14,414,659 DV Digg votes ⬤ Rating 282,371 3,018,197 DF Digg friends ⬤ Social 279,630 1,731,653 21.2% Dut Delicious ut ⬤ Folksonomy 6,178,261 301,186,579 Dui Delicious ui ⬤ Folksonomy 35,444,383 301,186,579 Dti Delicious ti ⬤ Folksonomy 42,801,712 301,183,605 DBT TV Tropes ⬤ Feature 216,508 3,232,134 WR Writers ⬤ Authorship 224,925 144,340 TM Teams ⬤ Affiliation 1,836,793 1,366,466 ST Movies ⬤ Feature 233,283 281,396 RL Record labels ⬤ Affiliation 355,095 233,286 PR Producers ⬤ Authorship 236,510 207,268 OC Occupation ⬤ Affiliation 356,884 250,945 LO Location ⬤ Feature 397,589 293,697 DL Wikipedia, English ⬤ Hyperlink 18,268,992 172,183,984 14.1% GE DBpedia genre ⬤ Feature 525,651 463,497 CN Countries ⬤ Affiliation 1,182,526 637,134 DB DBpedia ⬤ Misc 3,966,924 13,820,853 3.88% Pc DBLP ⬤ Coauthorship 1,314,050 18,986,618 Pi DBLP ⬤ Citation 12,591 49,743 0.464% Pa DBLP ⬤ Authorship 6,851,776 8,649,016 CU Contiguous USA ⬤ Infrastructure 49 107 HA Haggle ⬤ HumanContact 274 28,244 CY Youtube friendship ⬤ Social 1,134,890 2,987,624 CD DBLP co-authorship ⬤ Coauthorship 317,080 1,049,866 CA Amazon (MDS) ⬤ Misc 334,863 925,872 THc arXiv hep-th ⬤ Citation 27,770 352,807 0.285% PHc arXiv hep-ph ⬤ Citation 34,546 421,578 0.322% Cut CiteULike u-t ⬤ Folksonomy 198,707 2,411,819 Cui CiteULike u-i ⬤ Folksonomy 777,199 2,411,819 Cti CiteULike t-i ⬤ Folksonomy 1,038,323 2,411,819 CS CiteSeer ⬤ Citation 384,413 1,751,463 1.36% TL Twitter lists ⬤ Social 23,370 33,101 1.63% EL Wikipedia elections ⬤ OnlineContact 7,118 103,675 5.70% CH Chess ⬤ Interaction 7,301 65,053 7.13% GC Google.com internal ⬤ Hyperlink 15,763 171,206 25.9% TH arXiv hep-th ⬤ Coauthorship 22,908 2,673,133 PH arXiv hep-ph ⬤ Coauthorship 28,093 4,596,803 AP arXiv astro-ph ⬤ Coauthorship 18,771 198,050 SC South African Companies ⬤ Affiliation 17 13 Ar American Revolution ⬤ Affiliation 277 160 BC Corporate Leadership ⬤ Affiliation 64 99 Sw Southern women 2 ⬤ Interaction 15 14 BM Club membership ⬤ Affiliation 65 95 Bx BookCrossing (ratings) ⬤ Rating 341,559 433,652 BX BookCrossing (implicit) ⬤ Rating 551,079 1,149,739 But BibSonomy u-t ⬤ Folksonomy 216,261 2,555,080 Bui BibSonomy u-i ⬤ Folksonomy 779,035 2,555,080 Bti BibSonomy t-i ⬤ Folksonomy 1,176,793 2,555,080 SK Skitter ⬤ Computer 1,696,415 11,095,298 IN CAIDA ⬤ Computer 26,475 53,381 AS Route views ⬤ Computer 6,474 13,895 PG Pretty Good Privacy ⬤ OnlineContact 10,680 24,316 PM Caenorhabditis elegans ⬤ Metabolic 453 4,596 JZ Jazz musicians ⬤ HumanSocial 198 2,742 A@ U. Rovira i Virgili ⬤ Communication 1,133 5,451 AR Amazon ratings ⬤ Rating 5,523,029 5,838,041 AD Advogato ⬤ Social 6,541 51,127 38.5% Am Amazon (TWEB) ⬤ Misc 403,394 3,387,388 55.7% AN David Copperfield ⬤ Lexical 112 425 AM Actor movies ⬤ Affiliation 639,286 1,470,404 CL Actor collaborations ⬤ Misc 382,219 33,115,812