KONECT
KONECT > Statistics > Wedge count

## Wedge count

A star is defined as a graph in which a central node is connected to all other nodes, and no other edges are present. Specifically, a $$k$$-star is defined as a star in which the central node is connected to $$k$$ other nodes. Thus, a 2-star consists of a node connected to two other nodes, or equivalently two incident edges, or a path of length 2. 2-stars are also called wedges. The number of 2-stars can be defined as \begin{align} s = \sum_{u \in V} {d(u) \choose 2} = \sum_{u \in V} \frac 1 2 d(u) (d(u) - 1), \end{align} where $$d(u)$$ is the degree of node $$u$$.

 Code Name Category F. W. M. $$n$$ $$m$$ $$s$$ Sw Southern women 2 ⬤ Interaction 15 14 12 SC South African Companies ⬤ Affiliation 17 13 13 MT Taro exchange ⬤ HumanSocial 22 78 109 HT Highland tribes ⬤ HumanSocial 16 58 387 SW Southern women 1 ⬤ Interaction 50 89 397 CU Contiguous USA ⬤ Infrastructure 49 107 421 BC Corporate Leadership ⬤ Affiliation 64 99 453 ZA Zachary karate club ⬤ HumanSocial 34 78 528 BM Club membership ⬤ Affiliation 65 95 534 MR Rhesus ⬤ Animal 16 111 586 DO Dolphins ⬤ Animal 62 159 923 MK Kangaroo ⬤ Animal 17 91 1,010 MP PDZBase ⬤ Metabolic 212 244 1,049 MZ Zebra ⬤ Animal 27 111 1,108 Ms Sampson ⬤ HumanSocial 18 189 1,683 MH Highschool ⬤ HumanSocial 70 366 2,278 Ml Les Misérables ⬤ Misc 77 254 2,808 Mt Train bombing ⬤ HumanContact 64 243 2,818 ET Euroroad ⬤ Infrastructure 1,174 1,417 2,833 MA Cattle ⬤ Animal 28 217 3,136 Ar American Revolution ⬤ Affiliation 277 160 3,433 MB Bison ⬤ Animal 26 314 3,872 Mc Sheep ⬤ Animal 28 250 4,052 MX Seventh graders ⬤ HumanSocial 29 376 4,476 MC Crime ⬤ Interaction 2,209 1,476 4,816 AN David Copperfield ⬤ Lexical 112 425 5,429 CR Chicago ⬤ Infrastructure 1,467 1,298 5,729 MW Windsurfers ⬤ HumanContact 43 336 5,831 MI Physicians ⬤ HumanSocial 241 1,098 8,026 Mv Dutch college ⬤ HumanSocial 32 3,062 11,098 Mp Protein ⬤ Metabolic 1,870 2,277 12,107 Mh Hens ⬤ Animal 32 496 14,880 TC Air traffic control ⬤ Infrastructure 1,226 2,615 15,307 UG US power grid ⬤ Infrastructure 4,941 6,594 18,933 UL Unicode languages ⬤ Feature 1,122 1,255 21,977 MO Residence hall ⬤ HumanSocial 217 2,672 35,859 MQ Macaques ⬤ Animal 62 1,187 44,463 If Infectious ⬤ HumanContact 410 17,298 48,984 MS Human protein (Stelzl) ⬤ Metabolic 1,706 6,207 49,920 PM Caenorhabditis elegans ⬤ Metabolic 453 4,596 79,173 FW Florida ecosystem wet ⬤ Trophic 128 2,106 81,147 FD Florida ecosystem dry ⬤ Trophic 128 2,137 83,185 MV Human protein (Vidal) ⬤ Metabolic 3,133 6,726 88,809 A@ U. Rovira i Virgili ⬤ Communication 1,133 5,451 96,415 ME Adolescent health ⬤ HumanSocial 2,539 12,969 99,247 ML Little Rock Lake ⬤ Trophic 183 2,494 101,959 HY Hypertext 2009 ⬤ HumanContact 113 20,818 102,182 JZ Jazz musicians ⬤ HumanSocial 198 2,742 103,212 HA Haggle ⬤ HumanContact 274 28,244 118,281 RM Reality Mining ⬤ HumanContact 96 1,086,404 149,335 UF UC Irvine forum ⬤ Interaction 2,320 33,720 174,069 RA Manufacturing emails ⬤ Communication 167 82,927 206,233 DNc DNC emails ⬤ Communication 2,029 39,264 317,905 AC arXiv cond-mat ⬤ Authorship 55,467 58,595 353,433 MF Human protein (Figeys) ⬤ Metabolic 2,239 6,452 353,779 MN Bible ⬤ Lexical 1,773 16,401 368,148 PG Pretty Good Privacy ⬤ OnlineContact 10,680 24,316 434,797 Shf Hamsterster friendships ⬤ Social 1,858 12,534 555,842 Sh Hamsterster full ⬤ Social 2,426 16,631 690,463 UC UC Irvine messages ⬤ Communication 1,899 59,835 755,882 EF Facebook (NIPS) ⬤ Social 2,888 2,981 759,641 OF OpenFlights ⬤ Infrastructure 2,939 30,501 858,032 DN DNC emails co-recipients ⬤ OnlineContact 2,029 136,602 955,910 SX Sexual escorts ⬤ Rating 26,836 50,632 1,055,915 WR Writers ⬤ Authorship 224,925 144,340 1,125,315 OF OpenFlights ⬤ Infrastructure 3,425 67,663 1,221,697 TL Twitter lists ⬤ Social 23,370 33,101 1,231,177 Mg Blogs ⬤ Hyperlink 1,224 19,025 1,341,525 GN Gnutella ⬤ Computer 62,586 147,892 1,568,174 AF US airports ⬤ Infrastructure 1,574 28,236 1,914,691 PW Prosper.com ⬤ Interaction 25,697 35,377 1,969,047 CC Cora citation ⬤ Citation 23,166 91,500 2,022,447 AS Route views ⬤ Computer 6,474 13,895 2,059,364 Pi DBLP ⬤ Citation 12,591 49,743 2,120,079 DG Digg ⬤ Communication 30,398 87,627 2,294,667 Ff Filmtipset ⬤ Social 39,199 87,415 2,566,266 CH Chess ⬤ Interaction 7,301 65,053 2,588,788 PS Prosper.com ⬤ Affiliation 14,177 21,017 2,663,394 FO FOLDOC ⬤ Hyperlink 13,356 125,207 2,762,280 AD Advogato ⬤ Social 6,541 51,127 3,197,651 Mti MovieLens t-i ⬤ Folksonomy 40,657 95,580 3,229,651 ST Movies ⬤ Feature 233,283 281,396 3,240,178 RD Pennsylvania ⬤ Infrastructure 1,088,092 1,541,898 3,390,667 R1 Texas ⬤ Infrastructure 1,379,917 1,921,660 4,128,025 Ow Facebook ⬤ Communication 46,952 876,993 4,331,017 PR Producers ⬤ Authorship 236,510 207,268 4,461,275 RO California ⬤ Infrastructure 1,965,206 2,766,607 5,995,090 Mut MovieLens u-t ⬤ Folksonomy 24,546 95,580 8,091,394 SD Slashdot ⬤ Communication 51,083 140,778 9,392,516 CA Amazon (MDS) ⬤ Misc 334,863 925,872 9,752,186 Mui MovieLens u-i ⬤ Folksonomy 15,619 95,580 10,527,036 DB Douban ⬤ Social 154,908 327,162 11,745,116 AP arXiv astro-ph ⬤ Coauthorship 18,771 198,050 12,749,380 BK Brightkite ⬤ Social 58,228 214,078 13,423,403 EL Wikipedia elections ⬤ OnlineContact 7,118 103,675 14,524,030 GP Google+ ⬤ Social 23,628 39,242 14,738,751 IN CAIDA ⬤ Computer 26,475 53,381 14,906,270 M1 MovieLens 100k ⬤ Rating 3,568 100,000 18,367,254 RC Reactome ⬤ Metabolic 6,327 147,547 20,746,788 CD DBLP co-authorship ⬤ Coauthorship 317,080 1,049,866 21,780,889 PHc arXiv hep-ph ⬤ Citation 34,546 421,578 26,298,866 EA Edinburgh Associative Thesaurus ⬤ Lexical 23,132 511,764 30,388,904 TO Internet topology ⬤ Computer 34,761 171,403 34,304,301 WO WordNet ⬤ Lexical 146,005 656,999 35,863,116 THc arXiv hep-th ⬤ Citation 27,770 352,807 37,101,609 AM Actor movies ⬤ Affiliation 639,286 1,470,404 39,482,206 EN Enron ⬤ Communication 87,273 1,148,072 49,424,399 Dj JUNG dependency ⬤ Software 6,120 138,706 49,825,722 DJ JDK dependency ⬤ Software 6,434 150,985 52,676,393 GH Github ⬤ Authorship 233,905 440,237 53,048,506 SZ Slashdot Zoo ⬤ Social 79,120 515,397 67,962,178 YG YouTube ⬤ Affiliation 218,563 293,360 70,180,198 ES Epinions ⬤ Social 75,879 508,837 74,201,120 Ws Twitter (ICWSM) ⬤ Social 465,017 834,797 187,988,707 SO Stack Overflow ⬤ Rating 1,187,072 1,301,942 205,586,615 Vut vi.sualize.us u-t ⬤ Folksonomy 116,279 2,298,816 211,070,075 WD Wikipedia Threads (de) ⬤ Communication 91,340 2,435,731 235,942,901 W2 WikiSigned ⬤ OnlineContact 138,592 740,397 235,954,939 ND Notre Dame ⬤ Hyperlink 325,729 1,497,134 304,881,174 PC US patents ⬤ Citation 3,774,768 16,518,947 335,781,273 Vui vi.sualize.us u-i ⬤ Folksonomy 529,646 2,298,816 489,164,625 M2 MovieLens 1M ⬤ Rating 15,786 1,000,209 602,009,923 Wui Twitter u-i ⬤ Folksonomy 9,618,743 12,656,613 708,995,210 GO Google ⬤ Hyperlink 875,713 5,105,039 727,417,224 Wa Twitter ⬤ OnlineContact 2,919,613 12,887,063 736,717,625 WC Wikipedia (en) ⬤ Feature 3,889,933 3,795,796 898,164,591 Wut Twitter u-t ⬤ Folksonomy 880,846 4,664,605 1,006,768,611 PL Prosper loans ⬤ Interaction 89,269 3,394,979 1,112,425,463 WU WebUni Magdeburg ⬤ Text 212,552 3,869,707 1,353,078,618 CO Wikipedia conflict ⬤ OnlineContact 118,100 2,917,785 1,394,925,925 LY Youtube links ⬤ Social 1,138,499 4,942,297 1,472,987,114 PL Pokec ⬤ Social 1,632,803 30,622,564 2,086,073,558 SF Stanford ⬤ Hyperlink 281,903 2,312,497 3,944,069,093 WT TREC WT10g ⬤ Hyperlink 1,601,787 8,063,026 4,375,162,265 Wti Twitter t-i ⬤ Folksonomy 1,773,193 2,635,885 4,418,323,415 Tnl Wikipedia talk, Dutch ⬤ Communication 225,749 1,554,699 6,058,956,301 LJ LiveJournal ⬤ Social 4,847,571 68,475,391 7,269,503,753 WK Wikipedia, English ⬤ Communication 2,394,385 5,021,410 12,593,522,422 Sd Dogster ⬤ Social 426,820 8,546,581 17,554,438,218 HUi Hudong internal ⬤ Hyperlink 1,984,484 14,869,484 18,725,710,519 Tde Wikipedia talk, German ⬤ Communication 519,403 6,729,794 22,215,138,984 Tru Wikipedia talk, Russian ⬤ Communication 457,017 2,282,055 25,135,039,055 YT YouTube ⬤ Social 3,223,589 9,375,374 26,535,309,102 BS Berkeley/Stanford ⬤ Hyperlink 685,230 7,600,595 27,982,987,280 Vti vi.sualize.us t-i ⬤ Folksonomy 659,472 2,298,816 30,601,838,083 BAi Baidu internal ⬤ Hyperlink 2,141,300 17,794,839 30,884,847,288 HUr Hudong related ⬤ Hyperlink 2,452,715 18,854,882 30,913,972,903 Tes Wikipedia talk, Spanish ⬤ Communication 497,446 2,702,879 36,007,011,621 M3 MovieLens 10M ⬤ Rating 150,433 10,000,054 40,053,435,221 OR Orkut ⬤ Social 3,072,441 117,184,899 45,625,361,722 Sc Catster ⬤ Social 149,700 5,449,275 50,615,774,277 Ten Wikipedia talk, English ⬤ Communication 2,987,535 24,981,163 57,066,712,805 BAr Baidu related ⬤ Hyperlink 415,641 3,284,387 64,694,677,166 Scd Catster/Dogster ⬤ Social 623,766 15,699,276 69,385,263,164 Tpt Wikipedia talk, Portuguese ⬤ Communication 541,355 2,424,962 75,046,674,318 Tit Wikipedia talk, Italian ⬤ Communication 863,846 3,067,680 111,830,205,348 WP Wikipedia, English ⬤ Hyperlink 1,870,709 39,953,145 122,966,873,340 Wpt Wikipedia links, pt ⬤ Hyperlink 1,603,222 49,021,409 170,705,225,779 Wja Wikipedia links, ja ⬤ Hyperlink 1,610,638 71,055,717 180,195,944,461 Wpl Wikipedia links, pl ⬤ Hyperlink 1,529,135 57,489,447 308,975,533,785 Wde Wikipedia links, de ⬤ Hyperlink 3,225,565 81,626,917 328,404,251,068 Wru Wikipedia links, ru ⬤ Hyperlink 2,853,118 82,056,101 370,052,519,879 Wit Wikipedia links, it ⬤ Hyperlink 1,865,965 91,555,008 388,152,455,834 Tar Wikipedia talk, Arabic ⬤ Communication 1,095,799 1,913,103 440,266,628,953 Tzh Wikipedia talk, Chinese ⬤ Communication 1,219,241 2,284,546 454,139,500,995 Wfr Wikipedia links, fr ⬤ Hyperlink 3,023,165 102,382,410 455,085,682,943 Tfr Wikipedia talk, French ⬤ Communication 1,420,367 4,641,928 623,970,181,277 RE Reuters ⬤ Text 1,846,441 96,903,520 1,546,388,153,215 Wen Wikipedia links, en ⬤ Hyperlink 12,150,976 378,142,420 2,157,209,765,149 OG Orkut ⬤ Affiliation 14,297,249 327,037,487 2,528,039,357,274 NX Netflix ⬤ Rating 978,148 100,480,507 2,856,821,221,128 YS Yahoo songs ⬤ Rating 2,626,941 256,804,235 4,627,224,528,654 WT Web trackers ⬤ Hyperlink 68,087,704 140,613,762 106,441,673,202,003 TW Twitter (WWW) ⬤ Social 41,652,230 1,468,365,182 123,435,589,564,841 TF Twitter (MPI) ⬤ Social 52,579,682 1,963,263,821 177,464,933,477,000 FR Friendster ⬤ Social 68,349,466 2,586,147,869 Lk Linux kernel mailing list replies ⬤ Communication 63,399 1,096,440 53,774,357 Ol Facebook (WOSN) ⬤ Social 63,731 817,035 71,097,140 Am Amazon (TWEB) ⬤ Misc 403,394 3,387,388 72,209,687 Bx BookCrossing (ratings) ⬤ Rating 341,559 433,652 80,944,469 CS CiteSeer ⬤ Citation 384,413 1,751,463 81,727,579 bfr Wikibooks (fr) ⬤ Authorship 33,881 201,727 87,215,966 LO Location ⬤ Feature 397,589 293,697 122,892,989 GC Google.com internal ⬤ Hyperlink 15,763 171,206 133,820,601 RL Record labels ⬤ Affiliation 355,095 233,286 144,874,235 nfr Wikinews (fr) ⬤ Authorship 27,954 193,618 147,753,076 LX Linux ⬤ Software 30,837 213,954 181,572,103 EP Epinions ⬤ Social 131,828 841,372 182,193,467 Pa DBLP ⬤ Authorship 6,851,776 8,649,016 184,560,080 Cut CiteULike u-t ⬤ Folksonomy 198,707 2,411,819 192,371,639 EU EU institution ⬤ Communication 265,214 420,045 195,288,557 Pc DBLP ⬤ Coauthorship 1,314,050 18,986,618 214,677,486 GW Gowalla ⬤ Social 196,591 950,327 290,400,040 Us Wikipedia, simple en (dynamic) ⬤ Hyperlink 100,312 1,627,472 320,147,664 OC Occupation ⬤ Affiliation 356,884 250,945 335,154,441 TM Teams ⬤ Affiliation 1,836,793 1,366,466 336,279,376 Cui CiteULike u-i ⬤ Folksonomy 777,199 2,411,819 343,677,541 BX BookCrossing (implicit) ⬤ Rating 551,079 1,149,739 465,125,366 Fc Filmtipset ⬤ Interaction 104,890 1,266,753 493,367,139 AR Amazon ratings ⬤ Rating 5,523,029 5,838,041 627,186,651 qen Wikiquote (en) ⬤ Authorship 137,970 549,210 633,690,320 DF Digg friends ⬤ Social 279,630 1,731,653 695,297,099 LM Livemocha ⬤ Social 104,103 2,193,083 716,316,150 FI Flickr ⬤ Misc 105,938 2,316,948 806,678,787 R2 Reuters-21578 ⬤ Text 81,791 1,464,182 821,566,836 Lb Last.fm band ⬤ Interaction 176,061 19,150,868 889,895,853 But BibSonomy u-t ⬤ Folksonomy 216,261 2,555,080 991,843,705 LK Linux kernel mailing list threads ⬤ Interaction 421,599 1,565,683 1,002,436,389 GE DBpedia genre ⬤ Feature 525,651 463,497 1,331,590,538 nen Wikinews (en) ⬤ Authorship 184,536 901,416 1,412,247,639 HY Hyves ⬤ Social 1,402,673 2,777,419 1,447,128,030 CY Youtube friendship ⬤ Social 1,134,890 2,987,624 1,474,482,560 DBT TV Tropes ⬤ Feature 216,508 3,232,134 1,494,276,935 ben Wikibooks (en) ⬤ Authorship 200,108 1,164,576 1,568,255,430 FX Flixster ⬤ Social 2,523,386 7,918,801 1,735,571,393 PH arXiv hep-ph ⬤ Coauthorship 28,093 4,596,803 2,097,593,926 TH arXiv hep-th ⬤ Coauthorship 22,908 2,673,133 2,134,203,872 EX Wikipedia (en) ⬤ Text 279,519 7,846,807 2,707,057,869 DV Digg votes ⬤ Rating 282,371 3,018,197 3,452,748,079 Ds Discogs label–style ⬤ Feature 487,911 5,255,950 5,820,293,288 CL Actor collaborations ⬤ Misc 382,219 33,115,812 6,266,209,411 Lj LiveJournal links ⬤ Social 5,204,176 49,174,464 7,518,595,106 mde Wiktionary (de) ⬤ Authorship 157,806 1,229,501 8,353,603,342 FG Flickr ⬤ Affiliation 895,589 8,545,307 9,755,612,929 CN Countries ⬤ Affiliation 1,182,526 637,134 11,166,368,856 Bui BibSonomy u-i ⬤ Folksonomy 779,035 2,555,080 12,835,279,754 Dl Discogs ⬤ Affiliation 3,780,417 14,414,659 13,051,812,272 LF Flickr links ⬤ Social 1,715,255 15,551,250 14,660,775,057 SK Skitter ⬤ Computer 1,696,415 11,095,298 16,021,665,681 Dr Discogs label–genre ⬤ Feature 541,557 4,147,665 18,190,840,285 J2 Jester 150 ⬤ Rating 101,524 1,728,847 19,185,429,458 Bti BibSonomy t-i ⬤ Folksonomy 1,176,793 2,555,080 19,526,902,897 Ud Wikipedia, nl (dynamic) ⬤ Hyperlink 1,039,252 20,070,561 21,187,791,948 Cti CiteULike t-i ⬤ Folksonomy 1,038,323 2,411,819 21,880,206,884 Ls Last.fm song ⬤ Interaction 1,086,604 19,150,868 22,053,978,162 FL Flickr ⬤ Social 2,302,925 33,140,017 23,342,941,288 LI Libimseti.cz ⬤ Social 220,970 17,359,346 28,261,600,655 YD Yahoo advertisers ⬤ Lexical 653,260 2,931,708 39,072,502,469 Up Wikipedia, pl (dynamic) ⬤ Hyperlink 1,033,050 25,026,208 42,876,854,599 Ui Wikipedia, it (dynamic) ⬤ Hyperlink 1,204,009 34,826,283 58,316,691,930 ER Epinions ⬤ Rating 996,744 13,668,320 69,245,866,714 Dui Delicious ui ⬤ Folksonomy 35,444,383 301,186,579 69,264,303,940 Ug Wikipedia, de (dynamic) ⬤ Hyperlink 2,166,669 86,337,879 69,396,476,987 Uf Wikipedia, fr (dynamic) ⬤ Hyperlink 2,212,682 59,008,831 84,717,021,383 J1 Jester 100 ⬤ Rating 146,942 4,136,360 102,339,759,934 Fr Filmtipset ⬤ Rating 225,153 19,554,219 113,150,077,280 Dt Discogs artist–style ⬤ Feature 3,236,269 24,085,580 166,393,512,911 DB DBpedia ⬤ Misc 3,966,924 13,820,853 174,275,329,593 de Wikipedia (de) ⬤ Authorship 4,046,832 57,323,775 338,064,857,067 it Wikipedia (it) ⬤ Authorship 2,531,261 26,241,217 361,590,072,626 men Wiktionary (en) ⬤ Authorship 2,163,240 8,998,641 549,925,395,663 DL Wikipedia, English ⬤ Hyperlink 18,268,992 172,183,984 583,124,689,932 Da Discogs artist–genre ⬤ Feature 3,509,661 19,033,891 713,800,298,659 es Wikipedia (es) ⬤ Authorship 3,623,742 27,011,506 766,722,417,754 fr Wikipedia (fr) ⬤ Authorship 4,598,826 46,168,355 1,093,651,554,833 Dut Delicious ut ⬤ Folksonomy 6,178,261 301,186,579 1,445,587,961,389 TR TREC (disks 4–5) ⬤ Text 2,285,379 151,632,178 1,604,790,310,718 mfr Wiktionary (fr) ⬤ Authorship 1,917,281 7,399,298 1,663,287,100,001 LG LiveJournal ⬤ Affiliation 13,891,479 112,307,385 2,703,813,727,685 Dti Delicious ti ⬤ Folksonomy 42,801,712 301,183,605 6,122,567,080,440 en Wikipedia (en) ⬤ Authorship 29,143,573 266,769,613 6,299,863,981,390