KONECT
KONECT > Statistics > Claw count

## Claw count

Three-stars are defined analogously to two-stars, and their count denoted $$z$$. Three-stars are also called claws and tripins [1]. \begin{align} z = \sum_{u \in V} {d(u) \choose 3} = \sum_{u \in V} \frac 1 6 d(u) (d(u) - 1) (d(u) - 2) \end{align}

 [1] David Gleich and Art Owen. Moment-based estimation of stochastic Kronecker graph parameters. Internet Math., 8(3):232–256, 2012.

 Code Name Category F. W. M. $$n$$ $$m$$ $$z$$ Sw Southern women 2 ⬤ Interaction 15 14 8 SC South African Companies ⬤ Affiliation 17 13 10 CU Contiguous USA ⬤ Infrastructure 49 107 494 HT Highland tribes ⬤ HumanSocial 16 58 777 BC Corporate Leadership ⬤ Affiliation 64 99 1,035 MT Taro exchange ⬤ HumanSocial 22 78 1,076 ZA Zachary karate club ⬤ HumanSocial 34 78 1,764 TF Twitter (MPI) ⬤ Social 52,579,682 1,963,263,821 TW Twitter (WWW) ⬤ Social 41,652,230 1,468,365,182 DO Dolphins ⬤ Animal 62 159 1,861 BM Club membership ⬤ Affiliation 65 95 1,935 ET Euroroad ⬤ Infrastructure 1,174 1,417 1,983 MP PDZBase ⬤ Metabolic 212 244 3,221 MK Kangaroo ⬤ Animal 17 91 3,567 MZ Zebra ⬤ Animal 27 111 3,818 MR Rhesus ⬤ Animal 16 111 8,175 MC Crime ⬤ Interaction 2,209 1,476 12,667 Mt Train bombing ⬤ HumanContact 64 243 14,360 Ml Les Misérables ⬤ Misc 77 254 15,177 CR Chicago ⬤ Infrastructure 1,467 1,298 16,738 MH Highschool ⬤ HumanSocial 70 366 16,957 MA Cattle ⬤ Animal 28 217 19,026 Ms Sampson ⬤ HumanSocial 18 189 26,686 Mc Sheep ⬤ Animal 28 250 28,398 MW Windsurfers ⬤ HumanContact 43 336 36,530 AN David Copperfield ⬤ Lexical 112 425 39,977 MI Physicians ⬤ HumanSocial 241 1,098 50,535 Ar American Revolution ⬤ Affiliation 277 160 58,072 MB Bison ⬤ Animal 26 314 73,357 Mp Protein ⬤ Metabolic 1,870 2,277 75,064 Mv Dutch college ⬤ HumanSocial 32 3,062 77,121 TC Air traffic control ⬤ Infrastructure 1,226 2,615 94,389 MX Seventh graders ⬤ HumanSocial 29 376 99,611 Mh Hens ⬤ Animal 32 496 143,840 If Infectious ⬤ HumanContact 410 17,298 347,591 UL Unicode languages ⬤ Feature 1,122 1,255 521,909 MQ Macaques ⬤ Animal 62 1,187 603,956 ME Adolescent health ⬤ HumanSocial 2,539 12,969 740,457 A@ U. Rovira i Virgili ⬤ Communication 1,133 5,451 817,974 MO Residence hall ⬤ HumanSocial 217 2,672 848,578 FW Florida ecosystem wet ⬤ Trophic 128 2,106 1,380,155 MV Human protein (Vidal) ⬤ Metabolic 3,133 6,726 1,399,841 FD Florida ecosystem dry ⬤ Trophic 128 2,137 1,414,104 JZ Jazz musicians ⬤ HumanSocial 198 2,742 1,583,352 RD Pennsylvania ⬤ Infrastructure 1,088,092 1,541,898 1,707,904 HY Hypertext 2009 ⬤ HumanContact 113 20,818 1,810,498 ML Little Rock Lake ⬤ Trophic 183 2,494 1,985,127 R1 Texas ⬤ Infrastructure 1,379,917 1,921,660 2,004,918 RO California ⬤ Infrastructure 1,965,206 2,766,607 2,952,147 RM Reality Mining ⬤ HumanContact 96 1,086,404 3,073,975 PM Caenorhabditis elegans ⬤ Metabolic 453 4,596 3,352,172 MS Human protein (Stelzl) ⬤ Metabolic 1,706 6,207 5,644,533 PG Pretty Good Privacy ⬤ OnlineContact 10,680 24,316 7,501,208 GN Gnutella ⬤ Computer 62,586 147,892 8,171,989 OR Orkut ⬤ Social 3,072,441 117,184,899 HA Haggle ⬤ HumanContact 274 28,244 9,250,623 CH Chess ⬤ Interaction 7,301 65,053 16,498,559 Shf Hamsterster friendships ⬤ Social 1,858 12,534 17,140,733 MN Bible ⬤ Lexical 1,773 16,401 17,750,527 Sh Hamsterster full ⬤ Social 2,426 16,631 19,926,742 WR Writers ⬤ Authorship 224,925 144,340 20,262,025 MF Human protein (Figeys) ⬤ Metabolic 2,239 6,452 21,373,531 RA Manufacturing emails ⬤ Communication 167 82,927 31,304,118 SX Sexual escorts ⬤ Rating 26,836 50,632 32,662,407 TL Twitter lists ⬤ Social 23,370 33,101 43,439,459 CC Cora citation ⬤ Citation 23,166 91,500 56,729,506 ST Movies ⬤ Feature 233,283 281,396 59,090,368 DNc DNC emails ⬤ Communication 2,029 39,264 59,899,010 DN DNC emails co-recipients ⬤ OnlineContact 2,029 136,602 86,121,142 PW Prosper.com ⬤ Interaction 25,697 35,377 91,785,227 Mg Blogs ⬤ Hyperlink 1,224 19,025 106,210,646 CA Amazon (MDS) ⬤ Misc 334,863 925,872 142,823,893 EF Facebook (NIPS) ⬤ Social 2,888 2,981 160,449,784 Pi DBLP ⬤ Citation 12,591 49,743 171,715,755 FO FOLDOC ⬤ Hyperlink 13,356 125,207 199,487,042 Mti MovieLens t-i ⬤ Folksonomy 40,657 95,580 205,226,828 Ow Facebook ⬤ Communication 46,952 876,993 221,524,187 PR Producers ⬤ Authorship 236,510 207,268 232,308,826 DB Douban ⬤ Social 154,908 327,162 269,719,710 PS Prosper.com ⬤ Affiliation 14,177 21,017 410,799,393 CD DBLP co-authorship ⬤ Coauthorship 317,080 1,049,866 431,568,151 AD Advogato ⬤ Social 6,541 51,127 466,990,179 AP arXiv astro-ph ⬤ Coauthorship 18,771 198,050 545,677,552 Ff Filmtipset ⬤ Social 39,199 87,415 666,823,593 AS Route views ⬤ Computer 6,474 13,895 674,974,421 AM Actor movies ⬤ Affiliation 639,286 1,470,404 1,058,085,710 PHc arXiv hep-ph ⬤ Citation 34,546 421,578 1,344,423,338 BK Brightkite ⬤ Social 58,228 214,078 1,455,808,231 RC Reactome ⬤ Metabolic 6,327 147,547 1,500,721,941 M1 MovieLens 100k ⬤ Rating 3,568 100,000 1,702,768,149 EL Wikipedia elections ⬤ OnlineContact 7,118 103,675 1,728,582,938 EA Edinburgh Associative Thesaurus ⬤ Lexical 23,132 511,764 2,967,734,991 Mui MovieLens u-i ⬤ Folksonomy 15,619 95,580 3,111,884,288 Mut MovieLens u-t ⬤ Folksonomy 24,546 95,580 3,409,576,286 Ol Facebook (WOSN) ⬤ Social 63,731 817,035 4,499,481,578 SD Slashdot ⬤ Communication 51,083 140,778 4,547,184,694 GP Google+ ⬤ Social 23,628 39,242 6,512,607,606 PC US patents ⬤ Citation 3,774,768 16,518,947 6,803,403,509 IN CAIDA ⬤ Computer 26,475 53,381 7,839,606,991 THc arXiv hep-th ⬤ Citation 27,770 352,807 8,172,939,577 CS CiteSeer ⬤ Citation 384,413 1,751,463 9,032,698,085 Pa DBLP ⬤ Authorship 6,851,776 8,649,016 10,156,046,544 Am Amazon (TWEB) ⬤ Misc 403,394 3,387,388 12,017,835,784 EN Enron ⬤ Communication 87,273 1,148,072 13,894,959,120 GH Github ⬤ Authorship 233,905 440,237 17,233,019,660 FR Friendster ⬤ Social 68,349,466 2,586,147,869 SZ Slashdot Zoo ⬤ Social 79,120 515,397 18,027,108,870 TO Internet topology ⬤ Computer 34,761 171,403 20,603,857,222 ES Epinions ⬤ Social 75,879 508,837 27,111,469,575 EP Epinions ⬤ Social 131,828 841,372 78,294,267,861 Dj JUNG dependency ⬤ Software 6,120 138,706 85,378,501,686 Lk Linux kernel mailing list replies ⬤ Communication 63,399 1,096,440 90,935,627,152 YG YouTube ⬤ Affiliation 218,563 293,360 92,191,098,295 DJ JDK dependency ⬤ Software 6,434 150,985 92,489,410,361 Pc DBLP ⬤ Coauthorship 1,314,050 18,986,618 117,705,054,352 TM Teams ⬤ Affiliation 1,836,793 1,366,466 117,855,347,259 Bx BookCrossing (ratings) ⬤ Rating 341,559 433,652 141,344,884,260 bfr Wikibooks (fr) ⬤ Authorship 33,881 201,727 149,756,537,416 SO Stack Overflow ⬤ Rating 1,187,072 1,301,942 168,997,476,966 FI Flickr ⬤ Misc 105,938 2,316,948 181,947,878,743 RL Record labels ⬤ Affiliation 355,095 233,286 188,705,350,220 Cut CiteULike u-t ⬤ Folksonomy 198,707 2,411,819 194,428,758,411 Fc Filmtipset ⬤ Interaction 104,890 1,266,753 204,725,098,142 LM Livemocha ⬤ Social 104,103 2,193,083 221,251,722,199 M2 MovieLens 1M ⬤ Rating 15,786 1,000,209 226,612,176,337 EU EU institution ⬤ Communication 265,214 420,045 250,257,426,117 Vut vi.sualize.us u-t ⬤ Folksonomy 116,279 2,298,816 290,844,387,003 LO Location ⬤ Feature 397,589 293,697 324,552,882,549 LX Linux ⬤ Software 30,837 213,954 334,773,756,249 GC Google.com internal ⬤ Hyperlink 15,763 171,206 354,444,098,866 FX Flixster ⬤ Social 2,523,386 7,918,801 370,427,745,071 nfr Wikinews (fr) ⬤ Authorship 27,954 193,618 384,344,920,603 W2 WikiSigned ⬤ OnlineContact 138,592 740,397 393,108,123,126 Us Wikipedia, simple en (dynamic) ⬤ Hyperlink 100,312 1,627,472 422,387,316,406 PL Prosper loans ⬤ Interaction 89,269 3,394,979 455,534,068,547 ND Notre Dame ⬤ Hyperlink 325,729 1,497,134 469,365,457,284 Cui CiteULike u-i ⬤ Folksonomy 777,199 2,411,819 476,035,640,534 Vui vi.sualize.us u-i ⬤ Folksonomy 529,646 2,298,816 582,878,646,237 GO Google ⬤ Hyperlink 875,713 5,105,039 667,827,082,809 AR Amazon ratings ⬤ Rating 5,523,029 5,838,041 704,564,362,291 BX BookCrossing (implicit) ⬤ Rating 551,079 1,149,739 751,050,106,734 WU WebUni Magdeburg ⬤ Text 212,552 3,869,707 779,473,328,511 GW Gowalla ⬤ Social 196,591 950,327 787,564,904,976 DF Digg friends ⬤ Social 279,630 1,731,653 797,470,104,176 PH arXiv hep-ph ⬤ Coauthorship 28,093 4,596,803 862,892,139,927 Lb Last.fm band ⬤ Interaction 176,061 19,150,868 890,736,635,531 DBT TV Tropes ⬤ Feature 216,508 3,232,134 1,050,242,325,268 EX Wikipedia (en) ⬤ Text 279,519 7,846,807 1,273,176,127,252 OC Occupation ⬤ Affiliation 356,884 250,945 1,306,969,930,352 WC Wikipedia (en) ⬤ Feature 3,889,933 3,795,796 1,363,824,377,144 TH arXiv hep-th ⬤ Coauthorship 22,908 2,673,133 1,506,168,874,130 R2 Reuters-21578 ⬤ Text 81,791 1,464,182 1,978,784,882,823 qen Wikiquote (en) ⬤ Authorship 137,970 549,210 2,427,610,529,024 CO Wikipedia conflict ⬤ OnlineContact 118,100 2,917,785 3,157,750,386,656 PL Pokec ⬤ Social 1,632,803 30,622,564 3,352,153,545,587 But BibSonomy u-t ⬤ Folksonomy 216,261 2,555,080 4,596,638,282,952 Lj LiveJournal links ⬤ Social 5,204,176 49,174,464 4,671,461,810,755 DV Digg votes ⬤ Rating 282,371 3,018,197 5,552,161,405,338 CY Youtube friendship ⬤ Social 1,134,890 2,987,624 5,743,242,041,025 LK Linux kernel mailing list threads ⬤ Interaction 421,599 1,565,683 6,092,500,829,448 GE DBpedia genre ⬤ Feature 525,651 463,497 6,667,061,771,791 LJ LiveJournal ⬤ Social 4,847,571 68,475,391 9,778,896,249,995 HY Hyves ⬤ Social 1,402,673 2,777,419 10,748,028,522,268 nen Wikinews (en) ⬤ Authorship 184,536 901,416 12,674,439,900,034 WT TREC WT10g ⬤ Hyperlink 1,601,787 8,063,026 17,206,337,249,825 CL Actor collaborations ⬤ Misc 382,219 33,115,812 18,499,665,265,236 ben Wikibooks (en) ⬤ Authorship 200,108 1,164,576 20,417,623,992,850 LF Flickr links ⬤ Social 1,715,255 15,551,250 21,493,389,022,491 SF Stanford ⬤ Hyperlink 281,903 2,312,497 25,253,733,860,230 LY Youtube links ⬤ Social 1,138,499 4,942,297 33,377,841,563,982 FG Flickr ⬤ Affiliation 895,589 8,545,307 34,392,804,882,987 Ds Discogs label–style ⬤ Feature 487,911 5,255,950 36,106,246,831,981 LI Libimseti.cz ⬤ Social 220,970 17,359,346 82,085,727,142,249 FL Flickr ⬤ Social 2,302,925 33,140,017 83,140,847,127,775 SK Skitter ⬤ Computer 1,696,415 11,095,298 9.6557738585948000 × 1013 Dui Delicious ui ⬤ Folksonomy 35,444,383 301,186,579 1.0811758274219500 × 1014 Tnl Wikipedia talk, Dutch ⬤ Communication 225,749 1,554,699 1.0891537697120200 × 1014 HUi Hudong internal ⬤ Hyperlink 1,984,484 14,869,484 1.1927487365796300 × 1014 mde Wiktionary (de) ⬤ Authorship 157,806 1,229,501 1.2047598484750800 × 1014 Sd Dogster ⬤ Social 426,820 8,546,581 1.2390919289745700 × 1014 Ls Last.fm song ⬤ Interaction 1,086,604 19,150,868 1.3951627658241600 × 1014 Ud Wikipedia, nl (dynamic) ⬤ Hyperlink 1,039,252 20,070,561 1.6598790901682900 × 1014 M3 MovieLens 10M ⬤ Rating 150,433 10,000,054 1.9238846262663200 × 1014 WK Wikipedia, English ⬤ Communication 2,394,385 5,021,410 1.9480093754887800 × 1014 Dl Discogs ⬤ Affiliation 3,780,417 14,414,659 2.0808614120605700 × 1014 J2 Jester 150 ⬤ Rating 101,524 1,728,847 2.2001768699670900 × 1014 CN Countries ⬤ Affiliation 1,182,526 637,134 2.8881832963124400 × 1014 Ui Wikipedia, it (dynamic) ⬤ Hyperlink 1,204,009 34,826,283 3.7662269970980600 × 1014 Up Wikipedia, pl (dynamic) ⬤ Hyperlink 1,033,050 25,026,208 3.7977023748198600 × 1014 BS Berkeley/Stanford ⬤ Hyperlink 685,230 7,600,595 3.8319893513286100 × 1014 Bui BibSonomy u-i ⬤ Folksonomy 779,035 2,555,080 3.9442471509606700 × 1014 YT YouTube ⬤ Social 3,223,589 9,375,374 4.0939088218680100 × 1014 BAi Baidu internal ⬤ Hyperlink 2,141,300 17,794,839 5.7462575627910900 × 1014 Dr Discogs label–genre ⬤ Feature 541,557 4,147,665 6.4716811928516600 × 1014 Uf Wikipedia, fr (dynamic) ⬤ Hyperlink 2,212,682 59,008,831 6.7355828147194600 × 1014 Ug Wikipedia, de (dynamic) ⬤ Hyperlink 2,166,669 86,337,879 Fr Filmtipset ⬤ Rating 225,153 19,554,219 8.2340252775797500 × 1014 Tru Wikipedia talk, Russian ⬤ Communication 457,017 2,282,055 8.9322969493274200 × 1014 Bti BibSonomy t-i ⬤ Folksonomy 1,176,793 2,555,080 1.0439889254792860 × 1015 Sc Catster ⬤ Social 149,700 5,449,275 1.0847128712973580 × 1015 ER Epinions ⬤ Rating 996,744 13,668,320 1.0920422075268000 × 1015 Scd Catster/Dogster ⬤ Social 623,766 15,699,276 1.2097823266509860 × 1015 Cti CiteULike t-i ⬤ Folksonomy 1,038,323 2,411,819 1.2131930448735180 × 1015 HUr Hudong related ⬤ Hyperlink 2,452,715 18,854,882 1.4391705490541940 × 1015 J1 Jester 100 ⬤ Rating 146,942 4,136,360 1.9072633533446460 × 1015 Vti vi.sualize.us t-i ⬤ Folksonomy 659,472 2,298,816 1.9857996140590940 × 1015 OG Orkut ⬤ Affiliation 14,297,249 327,037,487 SW Southern women 1 ⬤ Interaction 50 89 1,206 UG US power grid ⬤ Infrastructure 4,941 6,594 26,050 AC arXiv cond-mat ⬤ Authorship 55,467 58,595 2,249,330 UF UC Irvine forum ⬤ Interaction 2,320 33,720 2,807,597 DG Digg ⬤ Communication 30,398 87,627 66,161,072 UC UC Irvine messages ⬤ Communication 1,899 59,835 82,140,043 OF OpenFlights ⬤ Infrastructure 2,939 30,501 228,755,628 OF OpenFlights ⬤ Infrastructure 3,425 67,663 383,135,844 AF US airports ⬤ Infrastructure 1,574 28,236 612,363,375 NX Netflix ⬤ Rating 978,148 100,480,507 Ws Twitter (ICWSM) ⬤ Social 465,017 834,797 28,887,087,190 Wa Twitter ⬤ OnlineContact 2,919,613 12,887,063 690,658,257,498 Wui Twitter u-i ⬤ Folksonomy 9,618,743 12,656,613 1,155,590,474,676 Wut Twitter u-t ⬤ Folksonomy 880,846 4,664,605 3,620,991,361,242 Wti Twitter t-i ⬤ Folksonomy 1,773,193 2,635,885 51,877,537,933,158 BAr Baidu related ⬤ Hyperlink 415,641 3,284,387 2.7314000418143890 × 1015 YS Yahoo songs ⬤ Rating 2,626,941 256,804,235 WO WordNet ⬤ Lexical 146,005 656,999 4,063,487,782 Tde Wikipedia talk, German ⬤ Communication 519,403 6,729,794 9.8392640052472300 × 1014 Ten Wikipedia talk, English ⬤ Communication 2,987,535 24,981,163 1.5105691610237420 × 1015 Tes Wikipedia talk, Spanish ⬤ Communication 497,446 2,702,879 2.1340344938231650 × 1015 YD Yahoo advertisers ⬤ Lexical 653,260 2,931,708 2.3032887464275430 × 1015 Wja Wikipedia links, ja ⬤ Hyperlink 1,610,638 71,055,717 3.1429458927244880 × 1015 Wpt Wikipedia links, pt ⬤ Hyperlink 1,603,222 49,021,409 4.7547115643692280 × 1015 Dt Discogs artist–style ⬤ Feature 3,236,269 24,085,580 5.3674926146404490 × 1015 Tpt Wikipedia talk, Portuguese ⬤ Communication 541,355 2,424,962 6.9214955732016490 × 1015 Tit Wikipedia talk, Italian ⬤ Communication 863,846 3,067,680 1.1983312889964536 × 1016 de Wikipedia (de) ⬤ Authorship 4,046,832 57,323,775 1.2663862099328266 × 1016 Wit Wikipedia links, it ⬤ Hyperlink 1,865,965 91,555,008 1.4747978898623198 × 1016 Wfr Wikipedia links, fr ⬤ Hyperlink 3,023,165 102,382,410 1.8197462302868060 × 1016 Wru Wikipedia links, ru ⬤ Hyperlink 2,853,118 82,056,101 1.8849499712571788 × 1016 DB DBpedia ⬤ Misc 3,966,924 13,820,853 1.9647361248950896 × 1016 Wpl Wikipedia links, pl ⬤ Hyperlink 1,529,135 57,489,447 2.0835175308483064 × 1016 Wen Wikipedia links, en ⬤ Hyperlink 12,150,976 378,142,420 WD Wikipedia Threads (de) ⬤ Communication 91,340 2,435,731 189,512,901,727 WP Wikipedia, English ⬤ Hyperlink 1,870,709 39,953,145 3.2063756669194000 × 1015 Wde Wikipedia links, de ⬤ Hyperlink 3,225,565 81,626,917 2.1696265712422924 × 1016 it Wikipedia (it) ⬤ Authorship 2,531,261 26,241,217 2.2557694419732084 × 1016 TR TREC (disks 4–5) ⬤ Text 2,285,379 151,632,178 5.8090382597882208 × 1016 Dut Delicious ut ⬤ Folksonomy 6,178,261 301,186,579 5.8243254727040968 × 1016 DL Wikipedia, English ⬤ Hyperlink 18,268,992 172,183,984 5.8569969947022656 × 1016 RE Reuters ⬤ Text 1,846,441 96,903,520 6.4992574078209184 × 1016 men Wiktionary (en) ⬤ Authorship 2,163,240 8,998,641 8.7858626977810704 × 1016 en Wikipedia (en) ⬤ Authorship 29,143,573 266,769,613 Tar Wikipedia talk, Arabic ⬤ Communication 1,095,799 1,913,103 1.2863343173533914 × 1017 Tzh Wikipedia talk, Chinese ⬤ Communication 1,219,241 2,284,546 1.3764640541547501 × 1017 Da Discogs artist–genre ⬤ Feature 3,509,661 19,033,891 1.5128773521295034 × 1017 fr Wikipedia (fr) ⬤ Authorship 4,598,826 46,168,355 1.6652655027557293 × 1017 es Wikipedia (es) ⬤ Authorship 3,623,742 27,011,506 1.7693089180103901 × 1017 Tfr Wikipedia talk, French ⬤ Communication 1,420,367 4,641,928 2.2009822704717606 × 1017 LG LiveJournal ⬤ Affiliation 13,891,479 112,307,385 3.8340190279099590 × 1017 mfr Wiktionary (fr) ⬤ Authorship 1,917,281 7,399,298 6.0938630825031258 × 1017 Dti Delicious ti ⬤ Folksonomy 42,801,712 301,183,605 8.9995942774935859 × 1017 WT Web trackers ⬤ Hyperlink 68,087,704 140,613,762 2.9634997950810843 × 1020