KONECT
KONECT > Statistics > Square count

## Square count

A square is a cycle of length four, and the number of squares in a graph is denoted $$q$$. \begin{align} q = | \{ u, v, w, x \mid u \sim v \sim w \sim x \sim u \} | \;/\; 8 \end{align} The factor 8 ensures that squares are counted regardless of their edge labeling. Multiple edges are ignored in these count statistics, and edges in patterns are not allowed to overlap.

 Code Name Category F. W. M. $$n$$ $$m$$ $$q$$ CR Chicago ⬤ Infrastructure 1,467 1,298 0 Sw Southern women 2 ⬤ Interaction 15 14 4 SC South African Companies ⬤ Affiliation 17 13 4 MT Taro exchange ⬤ HumanSocial 22 78 4 ET Euroroad ⬤ Infrastructure 1,174 1,417 41 Ar American Revolution ⬤ Affiliation 277 160 64 CU Contiguous USA ⬤ Infrastructure 49 107 70 MP PDZBase ⬤ Metabolic 212 244 122 MC Crime ⬤ Interaction 2,209 1,476 143 ZA Zachary karate club ⬤ HumanSocial 34 78 154 BC Corporate Leadership ⬤ Affiliation 64 99 195 BM Club membership ⬤ Affiliation 65 95 212 HT Highland tribes ⬤ HumanSocial 16 58 283 TF Twitter (MPI) ⬤ Social 52,579,682 1,963,263,821 TW Twitter (WWW) ⬤ Social 41,652,230 1,468,365,182 Mp Protein ⬤ Metabolic 1,870 2,277 461 MR Rhesus ⬤ Animal 16 111 724 TC Air traffic control ⬤ Infrastructure 1,226 2,615 1,103 EF Facebook (NIPS) ⬤ Social 2,888 2,981 1,261 UL Unicode languages ⬤ Feature 1,122 1,255 1,266 MH Highschool ⬤ HumanSocial 70 366 1,277 MK Kangaroo ⬤ Animal 17 91 2,114 MZ Zebra ⬤ Animal 27 111 2,325 AN David Copperfield ⬤ Lexical 112 425 2,579 Ml Les Misérables ⬤ Misc 77 254 2,672 MI Physicians ⬤ HumanSocial 241 1,098 3,165 Mt Train bombing ⬤ HumanContact 64 243 3,672 Ms Sampson ⬤ HumanSocial 18 189 4,449 MA Cattle ⬤ Animal 28 217 7,216 Mv Dutch college ⬤ HumanSocial 32 3,062 7,783 MV Human protein (Vidal) ⬤ Metabolic 3,133 6,726 10,216 Mc Sheep ⬤ Animal 28 250 12,006 MW Windsurfers ⬤ HumanContact 43 336 12,034 MB Bison ⬤ Animal 26 314 12,388 MX Seventh graders ⬤ HumanSocial 29 376 13,524 MS Human protein (Stelzl) ⬤ Metabolic 1,706 6,207 15,969 ME Adolescent health ⬤ HumanSocial 2,539 12,969 17,977 PW Prosper.com ⬤ Interaction 25,697 35,377 35,039 MO Residence hall ⬤ HumanSocial 217 2,672 35,657 GN Gnutella ⬤ Computer 62,586 147,892 42,466 A@ U. Rovira i Virgili ⬤ Communication 1,133 5,451 43,591 PM Caenorhabditis elegans ⬤ Metabolic 453 4,596 50,289 If Infectious ⬤ HumanContact 410 17,298 81,287 Mh Hens ⬤ Animal 32 496 107,880 WR Writers ⬤ Authorship 224,925 144,340 126,753 RD Pennsylvania ⬤ Infrastructure 1,088,092 1,541,898 157,802 TL Twitter lists ⬤ Social 23,370 33,101 165,762 MF Human protein (Figeys) ⬤ Metabolic 2,239 6,452 166,681 SX Sexual escorts ⬤ Rating 26,836 50,632 179,910 R1 Texas ⬤ Infrastructure 1,379,917 1,921,660 183,252 DNc DNC emails ⬤ Communication 2,029 39,264 209,206 ST Movies ⬤ Feature 233,283 281,396 221,363 RO California ⬤ Infrastructure 1,965,206 2,766,607 262,339 RE Reuters ⬤ Text 1,846,441 96,903,520 PR Producers ⬤ Authorship 236,510 207,268 266,983 MQ Macaques ⬤ Animal 62 1,187 270,724 AS Route views ⬤ Computer 6,474 13,895 288,840 FW Florida ecosystem wet ⬤ Trophic 128 2,106 318,981 MN Bible ⬤ Lexical 1,773 16,401 321,883 CH Chess ⬤ Interaction 7,301 65,053 324,301 FD Florida ecosystem dry ⬤ Trophic 128 2,137 335,189 Ff Filmtipset ⬤ Social 39,199 87,415 403,278 JZ Jazz musicians ⬤ HumanSocial 198 2,742 406,441 ML Little Rock Lake ⬤ Trophic 183 2,494 456,289 SD Slashdot ⬤ Communication 51,083 140,778 549,661 HY Hypertext 2009 ⬤ HumanContact 113 20,818 558,736 FO FOLDOC ⬤ Hyperlink 13,356 125,207 739,721 CC Cora citation ⬤ Citation 23,166 91,500 779,838 Pi DBLP ⬤ Citation 12,591 49,743 784,677 HA Haggle ⬤ HumanContact 274 28,244 848,067 Mti MovieLens t-i ⬤ Folksonomy 40,657 95,580 959,491 Cui CiteULike u-i ⬤ Folksonomy 777,199 2,411,819 962,735 PG Pretty Good Privacy ⬤ OnlineContact 10,680 24,316 1,010,957 RL Record labels ⬤ Affiliation 355,095 233,286 1,086,886 Ow Facebook ⬤ Communication 46,952 876,993 1,265,222 Bx BookCrossing (ratings) ⬤ Rating 341,559 433,652 1,457,330 PS Prosper.com ⬤ Affiliation 14,177 21,017 1,474,982 RM Reality Mining ⬤ HumanContact 96 1,086,404 1,534,878 Mut MovieLens u-t ⬤ Folksonomy 24,546 95,580 1,580,737 RA Manufacturing emails ⬤ Communication 167 82,927 1,622,683 IN CAIDA ⬤ Computer 26,475 53,381 2,287,349 GP Google+ ⬤ Social 23,628 39,242 2,358,832 Bui BibSonomy u-i ⬤ Folksonomy 779,035 2,555,080 2,794,766 CA Amazon (MDS) ⬤ Misc 334,863 925,872 3,125,323 AM Actor movies ⬤ Affiliation 639,286 1,470,404 3,503,276 AD Advogato ⬤ Social 6,541 51,127 3,571,636 LO Location ⬤ Feature 397,589 293,697 3,761,594 Mg Blogs ⬤ Hyperlink 1,224 19,025 5,171,257 Mui MovieLens u-i ⬤ Folksonomy 15,619 95,580 7,490,391 DN DNC emails co-recipients ⬤ OnlineContact 2,029 136,602 10,408,369 TM Teams ⬤ Affiliation 1,836,793 1,366,466 10,778,376 LK Linux kernel mailing list threads ⬤ Interaction 421,599 1,565,683 11,033,932 SO Stack Overflow ⬤ Rating 1,187,072 1,301,942 18,293,548 EU EU institution ⬤ Communication 265,214 420,045 18,421,946 Vui vi.sualize.us u-i ⬤ Folksonomy 529,646 2,298,816 19,336,325 Pa DBLP ⬤ Authorship 6,851,776 8,649,016 21,040,464 BK Brightkite ⬤ Social 58,228 214,078 23,380,701 OC Occupation ⬤ Affiliation 356,884 250,945 24,509,245 HY Hyves ⬤ Social 1,402,673 2,777,419 47,825,228 SZ Slashdot Zoo ⬤ Social 79,120 515,397 48,414,095 EL Wikipedia elections ⬤ OnlineContact 7,118 103,675 57,518,620 TO Internet topology ⬤ Computer 34,761 171,403 79,912,964 Dj JUNG dependency ⬤ Software 6,120 138,706 80,032,387 DJ JDK dependency ⬤ Software 6,434 150,985 82,893,262 EN Enron ⬤ Communication 87,273 1,148,072 92,985,807 GW Gowalla ⬤ Social 196,591 950,327 146,652,712 Ol Facebook (WOSN) ⬤ Social 63,731 817,035 151,719,237 WC Wikipedia (en) ⬤ Feature 3,889,933 3,795,796 160,976,541 ES Epinions ⬤ Social 75,879 508,837 166,635,817 M1 MovieLens 100k ⬤ Rating 3,568 100,000 220,548,028 Lk Linux kernel mailing list replies ⬤ Communication 63,399 1,096,440 306,703,924 Vut vi.sualize.us u-t ⬤ Folksonomy 116,279 2,298,816 519,071,489 RC Reactome ⬤ Metabolic 6,327 147,547 521,539,475 GO Google ⬤ Hyperlink 875,713 5,105,039 539,575,204 EP Epinions ⬤ Social 131,828 841,372 715,390,258 ND Notre Dame ⬤ Hyperlink 325,729 1,497,134 884,960,527 PL Pokec ⬤ Social 1,632,803 30,622,564 953,891,791 LM Livemocha ⬤ Social 104,103 2,193,083 1,282,771,394 Vti vi.sualize.us t-i ⬤ Folksonomy 659,472 2,298,816 2,199,351,548 PL Prosper loans ⬤ Interaction 89,269 3,394,979 3,930,622,348 OR Orkut ⬤ Social 3,072,441 117,184,899 Shf Hamsterster friendships ⬤ Social 1,858 12,534 780,549 Sh Hamsterster full ⬤ Social 2,426 16,631 1,234,177 PC US patents ⬤ Citation 3,774,768 16,518,947 341,906,226 CO Wikipedia conflict ⬤ OnlineContact 118,100 2,917,785 7,362,208,309 WT TREC WT10g ⬤ Hyperlink 1,601,787 8,063,026 12,596,865,743 SF Stanford ⬤ Hyperlink 281,903 2,312,497 13,316,840,570 M2 MovieLens 1M ⬤ Rating 15,786 1,000,209 16,671,201,295 WU WebUni Magdeburg ⬤ Text 212,552 3,869,707 21,431,485,810 LJ LiveJournal ⬤ Social 4,847,571 68,475,391 51,520,572,777 Sd Dogster ⬤ Social 426,820 8,546,581 68,359,711,169 BS Berkeley/Stanford ⬤ Hyperlink 685,230 7,600,595 127,118,333,411 WT Web trackers ⬤ Hyperlink 68,087,704 140,613,762 W2 WikiSigned ⬤ OnlineContact 138,592 740,397 255,775,680 Tnl Wikipedia talk, Dutch ⬤ Communication 225,749 1,554,699 1,925,439,105 WK Wikipedia, English ⬤ Communication 2,394,385 5,021,410 2,152,013,141 Wru Wikipedia links, ru ⬤ Hyperlink 2,853,118 82,056,101 HUr Hudong related ⬤ Hyperlink 2,452,715 18,854,882 3,135,310,038 Tru Wikipedia talk, Russian ⬤ Communication 457,017 2,282,055 4,632,803,687 HUi Hudong internal ⬤ Hyperlink 1,984,484 14,869,484 7,069,486,215 Tar Wikipedia talk, Arabic ⬤ Communication 1,095,799 1,913,103 8,084,744,426 Tpt Wikipedia talk, Portuguese ⬤ Communication 541,355 2,424,962 13,588,648,746 BAr Baidu related ⬤ Hyperlink 415,641 3,284,387 235,529,921,685 BAi Baidu internal ⬤ Hyperlink 2,141,300 17,794,839 YG YouTube ⬤ Affiliation 218,563 293,360 12,540,261 LY Youtube links ⬤ Social 1,138,499 4,942,297 467,434,016 YT YouTube ⬤ Social 3,223,589 9,375,374 9,915,671,458 YS Yahoo songs ⬤ Rating 2,626,941 256,804,235 WO WordNet ⬤ Lexical 146,005 656,999 32,926,054 Ten Wikipedia talk, English ⬤ Communication 2,987,535 24,981,163 Tit Wikipedia talk, Italian ⬤ Communication 863,846 3,067,680 6,154,887,250 Tzh Wikipedia talk, Chinese ⬤ Communication 1,219,241 2,284,546 6,675,967,773 Tfr Wikipedia talk, French ⬤ Communication 1,420,367 4,641,928 11,749,091,667 Tde Wikipedia talk, German ⬤ Communication 519,403 6,729,794 12,355,986,906 Tes Wikipedia talk, Spanish ⬤ Communication 497,446 2,702,879 17,513,494,039 Wpt Wikipedia links, pt ⬤ Hyperlink 1,603,222 49,021,409 681,168,760,896 Wpl Wikipedia links, pl ⬤ Hyperlink 1,529,135 57,489,447 Wja Wikipedia links, ja ⬤ Hyperlink 1,610,638 71,055,717 488,448,691,023 Wit Wikipedia links, it ⬤ Hyperlink 1,865,965 91,555,008 Wfr Wikipedia links, fr ⬤ Hyperlink 3,023,165 102,382,410 Wen Wikipedia links, en ⬤ Hyperlink 12,150,976 378,142,420 Wde Wikipedia links, de ⬤ Hyperlink 3,225,565 81,626,917 WP Wikipedia, English ⬤ Hyperlink 1,870,709 39,953,145 WD Wikipedia Threads (de) ⬤ Communication 91,340 2,435,731 1,088,430,251 Sc Catster ⬤ Social 149,700 5,449,275 427,574,757,984 Scd Catster/Dogster ⬤ Social 623,766 15,699,276 770,091,837,319 OG Orkut ⬤ Affiliation 14,297,249 327,037,487 SW Southern women 1 ⬤ Interaction 50 89 341 UG US power grid ⬤ Infrastructure 4,941 6,594 979 AC arXiv cond-mat ⬤ Authorship 55,467 58,595 70,549 UF UC Irvine forum ⬤ Interaction 2,320 33,720 76,095 DG Digg ⬤ Communication 30,398 87,627 78,931 UC UC Irvine messages ⬤ Communication 1,899 59,835 729,064 OF OpenFlights ⬤ Infrastructure 2,939 30,501 2,642,153 OF OpenFlights ⬤ Infrastructure 3,425 67,663 4,243,727 AF US airports ⬤ Infrastructure 1,574 28,236 19,604,634 NX Netflix ⬤ Rating 978,148 100,480,507 Ws Twitter (ICWSM) ⬤ Social 465,017 834,797 21,828,900 Wui Twitter u-i ⬤ Folksonomy 9,618,743 12,656,613 53,711,135 Wti Twitter t-i ⬤ Folksonomy 1,773,193 2,635,885 70,327,726 Wa Twitter ⬤ OnlineContact 2,919,613 12,887,063 81,161,696 Wut Twitter u-t ⬤ Folksonomy 880,846 4,664,605 206,508,691 M3 MovieLens 10M ⬤ Rating 150,433 10,000,054 1,197,019,065,804 Lj LiveJournal links ⬤ Social 5,204,176 49,174,464 LG LiveJournal ⬤ Affiliation 13,891,479 112,307,385 LX Linux ⬤ Software 30,837 213,954 153,045,006 Us Wikipedia, simple en (dynamic) ⬤ Hyperlink 100,312 1,627,472 278,060,062 Up Wikipedia, pl (dynamic) ⬤ Hyperlink 1,033,050 25,026,208 Fc Filmtipset ⬤ Interaction 104,890 1,266,753 2,724,858,975 Ud Wikipedia, nl (dynamic) ⬤ Hyperlink 1,039,252 20,070,561 9,487,566,269 Ui Wikipedia, it (dynamic) ⬤ Hyperlink 1,204,009 34,826,283 Uf Wikipedia, fr (dynamic) ⬤ Hyperlink 2,212,682 59,008,831 Ug Wikipedia, de (dynamic) ⬤ Hyperlink 2,166,669 86,337,879 TR TREC (disks 4–5) ⬤ Text 2,285,379 151,632,178 GH Github ⬤ Authorship 233,905 440,237 50,894,505 YD Yahoo advertisers ⬤ Lexical 653,260 2,931,708 395,269,117 Lb Last.fm band ⬤ Interaction 176,061 19,150,868 4,419,565,780 Ls Last.fm song ⬤ Interaction 1,086,604 19,150,868 32,357,367,219 LI Libimseti.cz ⬤ Social 220,970 17,359,346 252,125,304,066 J2 Jester 150 ⬤ Rating 101,524 1,728,847 266,934,299,745 J1 Jester 100 ⬤ Rating 146,942 4,136,360 2,599,984,203,310 FR Friendster ⬤ Social 68,349,466 2,586,147,869 FX Flixster ⬤ Social 2,523,386 7,918,801 454,368,595 R2 Reuters-21578 ⬤ Text 81,791 1,464,182 2,502,669,891 FI Flickr ⬤ Misc 105,938 2,316,948 34,729,244,373 FG Flickr ⬤ Affiliation 895,589 8,545,307 35,258,013,095 EX Wikipedia (en) ⬤ Text 279,519 7,846,807 113,573,615,622 ER Epinions ⬤ Rating 996,744 13,668,320 170,303,771,005 LF Flickr links ⬤ Social 1,715,255 15,551,250 428,143,604,855 FL Flickr ⬤ Social 2,302,925 33,140,017 712,355,262,231 Fr Filmtipset ⬤ Rating 225,153 19,554,219 8,728,909,858,170 it Wikipedia (it) ⬤ Authorship 2,531,261 26,241,217 bfr Wikibooks (fr) ⬤ Authorship 33,881 201,727 12,962,442 ben Wikibooks (en) ⬤ Authorship 200,108 1,164,576 93,226,753 nen Wikinews (en) ⬤ Authorship 184,536 901,416 95,011,761 en Wikipedia (en) ⬤ Authorship 29,143,573 266,769,613 qen Wikiquote (en) ⬤ Authorship 137,970 549,210 108,810,979 mde Wiktionary (de) ⬤ Authorship 157,806 1,229,501 7,023,812,795 men Wiktionary (en) ⬤ Authorship 2,163,240 8,998,641 113,806,587,655 de Wikipedia (de) ⬤ Authorship 4,046,832 57,323,775 DO Dolphins ⬤ Animal 62 159 278 DB Douban ⬤ Social 154,908 327,162 750,163 EA Edinburgh Associative Thesaurus ⬤ Lexical 23,132 511,764 16,682,968 mfr Wiktionary (fr) ⬤ Authorship 1,917,281 7,399,298 586,810,603,830 es Wikipedia (es) ⬤ Authorship 3,623,742 27,011,506 nfr Wikinews (fr) ⬤ Authorship 27,954 193,618 43,535,318 fr Wikipedia (fr) ⬤ Authorship 4,598,826 46,168,355 DL Wikipedia, English ⬤ Hyperlink 18,268,992 172,183,984 CS CiteSeer ⬤ Citation 384,413 1,751,463 25,382,500 Am Amazon (TWEB) ⬤ Misc 403,394 3,387,388 35,661,461 AR Amazon ratings ⬤ Rating 5,523,029 5,838,041 35,849,304 PHc arXiv hep-ph ⬤ Citation 34,546 421,578 39,015,537 AP arXiv astro-ph ⬤ Coauthorship 18,771 198,050 44,916,549 GE DBpedia genre ⬤ Feature 525,651 463,497 54,299,350 CD DBLP co-authorship ⬤ Coauthorship 317,080 1,049,866 55,107,655 THc arXiv hep-th ⬤ Citation 27,770 352,807 63,698,507 CN Countries ⬤ Affiliation 1,182,526 637,134 66,757,428 BX BookCrossing (implicit) ⬤ Rating 551,079 1,149,739 93,843,300 Cut CiteULike u-t ⬤ Folksonomy 198,707 2,411,819 146,940,165 GC Google.com internal ⬤ Hyperlink 15,763 171,206 196,281,177 Pc DBLP ⬤ Coauthorship 1,314,050 18,986,618 245,372,935 But BibSonomy u-t ⬤ Folksonomy 216,261 2,555,080 305,062,057 Cti CiteULike t-i ⬤ Folksonomy 1,038,323 2,411,819 383,860,055 CY Youtube friendship ⬤ Social 1,134,890 2,987,624 468,774,021 Bti BibSonomy t-i ⬤ Folksonomy 1,176,793 2,555,080 636,346,469 Dr Discogs label–genre ⬤ Feature 541,557 4,147,665 2,880,892,476 Dl Discogs ⬤ Affiliation 3,780,417 14,414,659 3,261,758,502 DBT TV Tropes ⬤ Feature 216,508 3,232,134 4,209,628,681 DF Digg friends ⬤ Social 279,630 1,731,653 4,925,314,153 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 Ds Discogs label–style ⬤ Feature 487,911 5,255,950 5,232,874,697 DV Digg votes ⬤ Rating 282,371 3,018,197 29,370,076,933 DB DBpedia ⬤ Misc 3,966,924 13,820,853 31,569,203,235 SK Skitter ⬤ Computer 1,696,415 11,095,298 62,769,198,018 PH arXiv hep-ph ⬤ Coauthorship 28,093 4,596,803 69,676,915,730 Dt Discogs artist–style ⬤ Feature 3,236,269 24,085,580 77,383,418,076 CL Actor collaborations ⬤ Misc 382,219 33,115,812 86,624,264,954 TH arXiv hep-th ⬤ Coauthorship 22,908 2,673,133 92,607,592,200 Da Discogs artist–genre ⬤ Feature 3,509,661 19,033,891 111,241,556,929