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Spectral norm

The spectral norm of a network equals the spectral norm (i.e., the largest absolute eigenvalue) of the network's adjacency matrix \begin{align} | \lambda_1[\mathbf A] | &= \left\| \mathbf A \right\|_2. \end{align} The spectral norm can be understood as an alternative measure of the size of a network.

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 Code Name Category F. W. M. $$n$$ $$m$$ $$| \lambda_1[\mathbf A] |$$ SC South African Companies ⬤ Affiliation 17 13 2.82933 × 100 Sw Southern women 2 ⬤ Interaction 15 14 2.85859 × 100 ET Euroroad ⬤ Infrastructure 1,174 1,417 4.01044 × 100 RD Pennsylvania ⬤ Infrastructure 1,088,092 1,541,898 4.41954 × 100 RO California ⬤ Infrastructure 1,965,206 2,766,607 4.63836 × 100 R1 Texas ⬤ Infrastructure 1,379,917 1,921,660 4.90612 × 100 CR Chicago ⬤ Infrastructure 1,467 1,298 4.91099 × 100 HT Highland tribes ⬤ HumanSocial 16 58 5.04645 × 100 CU Contiguous USA ⬤ Infrastructure 49 107 5.31855 × 100 MC Crime ⬤ Interaction 2,209 1,476 5.58685 × 100 MP PDZBase ⬤ Metabolic 212 244 5.84066 × 100 BC Corporate Leadership ⬤ Affiliation 64 99 6.18250 × 100 BM Club membership ⬤ Affiliation 65 95 6.46551 × 100 ZA Zachary karate club ⬤ HumanSocial 34 78 6.72570 × 100 TF Twitter (MPI) ⬤ Social 52,579,682 1,963,263,821 TW Twitter (WWW) ⬤ Social 41,652,230 1,468,365,182 SW Southern women 1 ⬤ Interaction 50 89 6.74191 × 100 DO Dolphins ⬤ Animal 62 159 7.19361 × 100 UG US power grid ⬤ Infrastructure 4,941 6,594 7.48305 × 100 MT Taro exchange ⬤ HumanSocial 22 78 7.50179 × 100 Mp Protein ⬤ Metabolic 1,870 2,277 7.56190 × 100 UL Unicode languages ⬤ Feature 1,122 1,255 7.93429 × 100 Ar American Revolution ⬤ Affiliation 277 160 7.94968 × 100 Ms Sampson ⬤ HumanSocial 18 189 1.07623 × 101 TC Air traffic control ⬤ Infrastructure 1,226 2,615 1.14548 × 101 AC arXiv cond-mat ⬤ Authorship 55,467 58,595 1.16849 × 101 MZ Zebra ⬤ Animal 27 111 1.22853 × 101 MI Physicians ⬤ HumanSocial 241 1,098 1.28991 × 101 AN David Copperfield ⬤ Lexical 112 425 1.31502 × 101 GN Gnutella ⬤ Computer 62,586 147,892 1.31812 × 101 WR Writers ⬤ Authorship 224,925 144,340 1.66087 × 101 MV Human protein (Vidal) ⬤ Metabolic 3,133 6,726 1.66144 × 101 CH Chess ⬤ Interaction 7,301 65,053 1.88564 × 101 Mt Train bombing ⬤ HumanContact 64 243 1.94863 × 101 PW Prosper.com ⬤ Interaction 25,697 35,377 1.97213 × 101 MH Highschool ⬤ HumanSocial 70 366 2.06981 × 101 A@ U. Rovira i Virgili ⬤ Communication 1,133 5,451 2.07470 × 101 PR Producers ⬤ Authorship 236,510 207,268 2.27438 × 101 CA Amazon (MDS) ⬤ Misc 334,863 925,872 2.39756 × 101 ST Movies ⬤ Feature 233,283 281,396 2.47409 × 101 TL Twitter lists ⬤ Social 23,370 33,101 2.52098 × 101 EF Facebook (NIPS) ⬤ Social 2,888 2,981 2.78031 × 101 Mh Hens ⬤ Animal 32 496 3.10000 × 101 MF Human protein (Figeys) ⬤ Metabolic 2,239 6,452 3.15812 × 101 Pa DBLP ⬤ Authorship 6,851,776 8,649,016 3.15840 × 101 CC Cora citation ⬤ Citation 23,166 91,500 3.22245 × 101 MS Human protein (Stelzl) ⬤ Metabolic 1,706 6,207 3.50124 × 101 EL Wikipedia elections ⬤ OnlineContact 7,118 103,675 3.51750 × 101 JZ Jazz musicians ⬤ HumanSocial 198 2,742 4.00274 × 101 Ff Filmtipset ⬤ Social 39,199 87,415 4.03796 × 101 DG Digg ⬤ Communication 30,398 87,627 4.04000 × 101 DB Douban ⬤ Social 154,908 327,162 4.19682 × 101 AM Actor movies ⬤ Affiliation 639,286 1,470,404 4.22519 × 101 PG Pretty Good Privacy ⬤ OnlineContact 10,680 24,316 4.24355 × 101 Pi DBLP ⬤ Citation 12,591 49,743 4.29998 × 101 ML Little Rock Lake ⬤ Trophic 183 2,494 4.33868 × 101 MA Cattle ⬤ Animal 28 217 4.50445 × 101 Shf Hamsterster friendships ⬤ Social 1,858 12,534 4.61623 × 101 AS Route views ⬤ Computer 6,474 13,895 4.74766 × 101 Sh Hamsterster full ⬤ Social 2,426 16,631 5.00215 × 101 PS Prosper.com ⬤ Affiliation 14,177 21,017 5.15691 × 101 SZ Slashdot Zoo ⬤ Social 79,120 515,397 5.21833 × 101 FO FOLDOC ⬤ Hyperlink 13,356 125,207 5.45925 × 101 M1 MovieLens 100k ⬤ Rating 3,568 100,000 5.78015 × 101 CS CiteSeer ⬤ Citation 384,413 1,751,463 5.86534 × 101 Am Amazon (TWEB) ⬤ Misc 403,394 3,387,388 5.89578 × 101 ME Adolescent health ⬤ HumanSocial 2,539 12,969 5.91679 × 101 MX Seventh graders ⬤ HumanSocial 29 376 5.96258 × 101 Mc Sheep ⬤ Animal 28 250 5.98919 × 101 GP Google+ ⬤ Social 23,628 39,242 6.35954 × 101 Ml Les Misérables ⬤ Misc 77 254 6.50263 × 101 W2 WikiSigned ⬤ OnlineContact 138,592 740,397 6.78129 × 101 IN CAIDA ⬤ Computer 26,475 53,381 6.96434 × 101 WO WordNet ⬤ Lexical 146,005 656,999 6.99344 × 101 TM Teams ⬤ Affiliation 1,836,793 1,366,466 7.13124 × 101 SX Sexual escorts ⬤ Rating 26,836 50,632 7.14733 × 101 AD Advogato ⬤ Social 6,541 51,127 7.55579 × 101 PHc arXiv hep-ph ⬤ Citation 34,546 421,578 7.66411 × 101 Ws Twitter (ICWSM) ⬤ Social 465,017 834,797 8.15997 × 101 MQ Macaques ⬤ Animal 62 1,187 8.58363 × 101 Mti MovieLens t-i ⬤ Folksonomy 40,657 95,580 8.64401 × 101 RL Record labels ⬤ Affiliation 355,095 233,286 8.70748 × 101 EP Epinions ⬤ Social 131,828 841,372 8.72001 × 101 MB Bison ⬤ Animal 26 314 8.84386 × 101 YG YouTube ⬤ Affiliation 218,563 293,360 9.03775 × 101 Mg Blogs ⬤ Hyperlink 1,224 19,025 9.07402 × 101 SD Slashdot ⬤ Communication 51,083 140,778 9.15029 × 101 AP arXiv astro-ph ⬤ Coauthorship 18,771 198,050 9.44296 × 101 Mv Dutch college ⬤ HumanSocial 32 3,062 9.96060 × 101 SO Stack Overflow ⬤ Rating 1,187,072 1,301,942 9.99772 × 101 BK Brightkite ⬤ Social 58,228 214,078 1.01491 × 102 MO Residence hall ⬤ HumanSocial 217 2,672 1.07958 × 102 LO Location ⬤ Feature 397,589 293,697 1.11155 × 102 THc arXiv hep-th ⬤ Citation 27,770 352,807 1.11322 × 102 PC US patents ⬤ Citation 3,774,768 16,518,947 1.13040 × 102 CD DBLP co-authorship ⬤ Coauthorship 317,080 1,049,866 1.15847 × 102 GO Google ⬤ Hyperlink 875,713 5,105,039 1.16964 × 102 GH Github ⬤ Authorship 233,905 440,237 1.20273 × 102 MR Rhesus ⬤ Animal 16 111 1.22605 × 102 OF OpenFlights ⬤ Infrastructure 2,939 30,501 1.24591 × 102 MK Kangaroo ⬤ Animal 17 91 1.24790 × 102 MW Windsurfers ⬤ HumanContact 43 336 1.25530 × 102 Ol Facebook (WOSN) ⬤ Social 63,731 817,035 1.32568 × 102 OC Occupation ⬤ Affiliation 356,884 250,945 1.38395 × 102 WC Wikipedia (en) ⬤ Feature 3,889,933 3,795,796 1.47912 × 102 BX BookCrossing (implicit) ⬤ Rating 551,079 1,149,739 1.47958 × 102 EU EU institution ⬤ Communication 265,214 420,045 1.52046 × 102 Bx BookCrossing (ratings) ⬤ Rating 341,559 433,652 1.52914 × 102 PM Caenorhabditis elegans ⬤ Metabolic 453 4,596 1.62930 × 102 GW Gowalla ⬤ Social 196,591 950,327 1.70939 × 102 LX Linux ⬤ Software 30,837 213,954 1.71851 × 102 GE DBpedia genre ⬤ Feature 525,651 463,497 1.71978 × 102 M2 MovieLens 1M ⬤ Rating 15,786 1,000,209 1.77579 × 102 GC Google.com internal ⬤ Hyperlink 15,763 171,206 1.78018 × 102 EA Edinburgh Associative Thesaurus ⬤ Lexical 23,132 511,764 1.89271 × 102 Us Wikipedia, simple en (dynamic) ⬤ Hyperlink 100,312 1,627,472 1.99284 × 102 RC Reactome ⬤ Metabolic 6,327 147,547 2.08170 × 102 If Infectious ⬤ HumanContact 410 17,298 2.10048 × 102 CY Youtube friendship ⬤ Social 1,134,890 2,987,624 2.10395 × 102 ER Epinions ⬤ Rating 996,744 13,668,320 2.45159 × 102 ES Epinions ⬤ Social 75,879 508,837 2.45999 × 102 PL Pokec ⬤ Social 1,632,803 30,622,564 2.47819 × 102 LM Livemocha ⬤ Social 104,103 2,193,083 2.75173 × 102 MN Bible ⬤ Lexical 1,773 16,401 2.91251 × 102 Mui MovieLens u-i ⬤ Folksonomy 15,619 95,580 3.07003 × 102 ND Notre Dame ⬤ Hyperlink 325,729 1,497,134 3.14060 × 102 CN Countries ⬤ Affiliation 1,182,526 637,134 3.35937 × 102 PL Prosper loans ⬤ Interaction 89,269 3,394,979 3.47590 × 102 WT TREC WT10g ⬤ Hyperlink 1,601,787 8,063,026 3.49929 × 102 DBT TV Tropes ⬤ Feature 216,508 3,232,134 3.52306 × 102 OF OpenFlights ⬤ Infrastructure 3,425 67,663 3.53415 × 102 Fc Filmtipset ⬤ Interaction 104,890 1,266,753 3.58889 × 102 UF UC Irvine forum ⬤ Interaction 2,320 33,720 3.70755 × 102 UC UC Irvine messages ⬤ Communication 1,899 59,835 3.84619 × 102 LY Youtube links ⬤ Social 1,138,499 4,942,297 3.92305 × 102 TO Internet topology ⬤ Computer 34,761 171,403 4.25817 × 102 Bti BibSonomy t-i ⬤ Folksonomy 1,176,793 2,555,080 4.30870 × 102 Cti CiteULike t-i ⬤ Folksonomy 1,038,323 2,411,819 4.36053 × 102 SF Stanford ⬤ Hyperlink 281,903 2,312,497 4.49572 × 102 HUr Hudong related ⬤ Hyperlink 2,452,715 18,854,882 4.62636 × 102 YT YouTube ⬤ Social 3,223,589 9,375,374 4.64866 × 102 Ud Wikipedia, nl (dynamic) ⬤ Hyperlink 1,039,252 20,070,561 4.79901 × 102 BAi Baidu internal ⬤ Hyperlink 2,141,300 17,794,839 4.85196 × 102 WK Wikipedia, English ⬤ Communication 2,394,385 5,021,410 4.93096 × 102 M3 MovieLens 10M ⬤ Rating 150,433 10,000,054 4.96970 × 102 DF Digg friends ⬤ Social 279,630 1,731,653 5.18890 × 102 Lj LiveJournal links ⬤ Social 5,204,176 49,174,464 5.40675 × 102 HUi Hudong internal ⬤ Hyperlink 1,984,484 14,869,484 5.58805 × 102 Ug Wikipedia, de (dynamic) ⬤ Hyperlink 2,166,669 86,337,879 5.79773 × 102 FG Flickr ⬤ Affiliation 895,589 8,545,307 5.87208 × 102 DV Digg votes ⬤ Rating 282,371 3,018,197 6.04628 × 102 FI Flickr ⬤ Misc 105,938 2,316,948 6.15564 × 102 Mut MovieLens u-t ⬤ Folksonomy 24,546 95,580 6.40915 × 102 SK Skitter ⬤ Computer 1,696,415 11,095,298 6.70349 × 102 Uf Wikipedia, fr (dynamic) ⬤ Hyperlink 2,212,682 59,008,831 6.77907 × 102 Up Wikipedia, pl (dynamic) ⬤ Hyperlink 1,033,050 25,026,208 6.80257 × 102 Ui Wikipedia, it (dynamic) ⬤ Hyperlink 1,204,009 34,826,283 6.96272 × 102 BS Berkeley/Stanford ⬤ Hyperlink 685,230 7,600,595 6.97551 × 102 DB DBpedia ⬤ Misc 3,966,924 13,820,853 7.31842 × 102 Sd Dogster ⬤ Social 426,820 8,546,581 7.42714 × 102 AR Amazon ratings ⬤ Rating 5,523,029 5,838,041 7.45697 × 102 LJ LiveJournal ⬤ Social 4,847,571 68,475,391 7.60849 × 102 OR Orkut ⬤ Social 3,072,441 117,184,899 7.82151 × 102 WP Wikipedia, English ⬤ Hyperlink 1,870,709 39,953,145 8.48572 × 102 Dj JUNG dependency ⬤ Software 6,120 138,706 9.13941 × 102 BAr Baidu related ⬤ Hyperlink 415,641 3,284,387 1.00837 × 103 Vui vi.sualize.us u-i ⬤ Folksonomy 529,646 2,298,816 1.01277 × 103 DJ JDK dependency ⬤ Software 6,434 150,985 1.06214 × 103 Pc DBLP ⬤ Coauthorship 1,314,050 18,986,618 1.07869 × 103 Wa Twitter ⬤ OnlineContact 2,919,613 12,887,063 1.11449 × 103 Sc Catster ⬤ Social 149,700 5,449,275 1.18157 × 103 Scd Catster/Dogster ⬤ Social 623,766 15,699,276 1.19093 × 103 TH arXiv hep-th ⬤ Coauthorship 22,908 2,673,133 1.22532 × 103 HA Haggle ⬤ HumanContact 274 28,244 1.23103 × 103 LF Flickr links ⬤ Social 1,715,255 15,551,250 1.24026 × 103 HY Hypertext 2009 ⬤ HumanContact 113 20,818 1.29172 × 103 Cui CiteULike u-i ⬤ Folksonomy 777,199 2,411,819 1.44825 × 103 NX Netflix ⬤ Rating 978,148 100,480,507 1.54505 × 103 Vti vi.sualize.us t-i ⬤ Folksonomy 659,472 2,298,816 1.54834 × 103 DNc DNC emails ⬤ Communication 2,029 39,264 1.56651 × 103 Wru Wikipedia links, ru ⬤ Hyperlink 2,853,118 82,056,101 1.64710 × 103 Wde Wikipedia links, de ⬤ Hyperlink 3,225,565 81,626,917 1.66352 × 103 Wpl Wikipedia links, pl ⬤ Hyperlink 1,529,135 57,489,447 1.67932 × 103 Wja Wikipedia links, ja ⬤ Hyperlink 1,610,638 71,055,717 1.70841 × 103 Wui Twitter u-i ⬤ Folksonomy 9,618,743 12,656,613 1.71376 × 103 Ow Facebook ⬤ Communication 46,952 876,993 1.71763 × 103 Wit Wikipedia links, it ⬤ Hyperlink 1,865,965 91,555,008 1.73418 × 103 Bui BibSonomy u-i ⬤ Folksonomy 779,035 2,555,080 1.76775 × 103 mde Wiktionary (de) ⬤ Authorship 157,806 1,229,501 1.79735 × 103 LK Linux kernel mailing list threads ⬤ Interaction 421,599 1,565,683 1.89558 × 103 LG LiveJournal ⬤ Affiliation 13,891,479 112,307,385 1.91207 × 103 PH arXiv hep-ph ⬤ Coauthorship 28,093 4,596,803 1.92146 × 103 Wpt Wikipedia links, pt ⬤ Hyperlink 1,603,222 49,021,409 2.08703 × 103 FL Flickr ⬤ Social 2,302,925 33,140,017 2.14447 × 103 Wfr Wikipedia links, fr ⬤ Hyperlink 3,023,165 102,382,410 2.15978 × 103 Wut Twitter u-t ⬤ Folksonomy 880,846 4,664,605 2.21648 × 103 bfr Wikibooks (fr) ⬤ Authorship 33,881 201,727 2.34248 × 103 OG Orkut ⬤ Affiliation 14,297,249 327,037,487 3.03736 × 103 WU WebUni Magdeburg ⬤ Text 212,552 3,869,707 3.18160 × 103 CL Actor collaborations ⬤ Misc 382,219 33,115,812 3.27861 × 103 ben Wikibooks (en) ⬤ Authorship 200,108 1,164,576 3.35117 × 103 DN DNC emails co-recipients ⬤ OnlineContact 2,029 136,602 3.52212 × 103 qen Wikiquote (en) ⬤ Authorship 137,970 549,210 3.58015 × 103 RA Manufacturing emails ⬤ Communication 167 82,927 3.58116 × 103 DL Wikipedia, English ⬤ Hyperlink 18,268,992 172,183,984 3.59975 × 103 Dui Delicious ui ⬤ Folksonomy 35,444,383 301,186,579 3.69459 × 103 WT Web trackers ⬤ Hyperlink 68,087,704 140,613,762 3.79086 × 103 mfr Wiktionary (fr) ⬤ Authorship 1,917,281 7,399,298 3.82799 × 103 WD Wikipedia Threads (de) ⬤ Communication 91,340 2,435,731 4.59030 × 103 Tzh Wikipedia talk, Chinese ⬤ Communication 1,219,241 2,284,546 4.65272 × 103 CO Wikipedia conflict ⬤ OnlineContact 118,100 2,917,785 4.81078 × 103 Wen Wikipedia links, en ⬤ Hyperlink 12,150,976 378,142,420 5.06927 × 103 RE Reuters ⬤ Text 1,846,441 96,903,520 6.50210 × 103 Tpt Wikipedia talk, Portuguese ⬤ Communication 541,355 2,424,962 6.90626 × 103 Tar Wikipedia talk, Arabic ⬤ Communication 1,095,799 1,913,103 7.06188 × 103 Tes Wikipedia talk, Spanish ⬤ Communication 497,446 2,702,879 7.53802 × 103 Fr Filmtipset ⬤ Rating 225,153 19,554,219 7.65324 × 103 EN Enron ⬤ Communication 87,273 1,148,072 7.80815 × 103 Tit Wikipedia talk, Italian ⬤ Communication 863,846 3,067,680 9.31844 × 103 Lk Linux kernel mailing list replies ⬤ Communication 63,399 1,096,440 1.10037 × 104 FR Friendster ⬤ Social 68,349,466 2,586,147,869 FX Flixster ⬤ Social 2,523,386 7,918,801 1.48325 × 102 HY Hyves ⬤ Social 1,402,673 2,777,419 1.79347 × 102 FD Florida ecosystem dry ⬤ Trophic 128 2,137 4.35201 × 102 YD Yahoo advertisers ⬤ Lexical 653,260 2,931,708 4.74580 × 102 FW Florida ecosystem wet ⬤ Trophic 128 2,106 5.93416 × 102 R2 Reuters-21578 ⬤ Text 81,791 1,464,182 6.85707 × 102 LI Libimseti.cz ⬤ Social 220,970 17,359,346 1.12741 × 103 J2 Jester 150 ⬤ Rating 101,524 1,728,847 1.86319 × 103 J1 Jester 100 ⬤ Rating 146,942 4,136,360 3.00763 × 103 EX Wikipedia (en) ⬤ Text 279,519 7,846,807 4.78882 × 103 Ls Last.fm song ⬤ Interaction 1,086,604 19,150,868 7.51629 × 103 Dl Discogs ⬤ Affiliation 3,780,417 14,414,659 1.10731 × 104 it Wikipedia (it) ⬤ Authorship 2,531,261 26,241,217 1.18256 × 104 Cut CiteULike u-t ⬤ Folksonomy 198,707 2,411,819 1.24181 × 104 de Wikipedia (de) ⬤ Authorship 4,046,832 57,323,775 1.29454 × 104 Tru Wikipedia talk, Russian ⬤ Communication 457,017 2,282,055 1.69053 × 104 nfr Wikinews (fr) ⬤ Authorship 27,954 193,618 1.81375 × 104 Vut vi.sualize.us u-t ⬤ Folksonomy 116,279 2,298,816 1.89915 × 104 men Wiktionary (en) ⬤ Authorship 2,163,240 8,998,641 2.13944 × 104 Tde Wikipedia talk, German ⬤ Communication 519,403 6,729,794 2.27424 × 104 Wti Twitter t-i ⬤ Folksonomy 1,773,193 2,635,885 2.38533 × 104 es Wikipedia (es) ⬤ Authorship 3,623,742 27,011,506 2.41717 × 104 Ds Discogs label–style ⬤ Feature 487,911 5,255,950 2.74608 × 104 Lb Last.fm band ⬤ Interaction 176,061 19,150,868 2.78113 × 104 Dti Delicious ti ⬤ Folksonomy 42,801,712 301,183,605 2.93146 × 104 nen Wikinews (en) ⬤ Authorship 184,536 901,416 3.01617 × 104 Tnl Wikipedia talk, Dutch ⬤ Communication 225,749 1,554,699 3.84348 × 104 fr Wikipedia (fr) ⬤ Authorship 4,598,826 46,168,355 4.21606 × 104 TR TREC (disks 4–5) ⬤ Text 2,285,379 151,632,178 4.41170 × 104 Dut Delicious ut ⬤ Folksonomy 6,178,261 301,186,579 5.57535 × 104 RM Reality Mining ⬤ HumanContact 96 1,086,404 6.18019 × 104 But BibSonomy u-t ⬤ Folksonomy 216,261 2,555,080 6.23914 × 104 Dr Discogs label–genre ⬤ Feature 541,557 4,147,665 7.37824 × 104 Dt Discogs artist–style ⬤ Feature 3,236,269 24,085,580 8.92741 × 104 Ten Wikipedia talk, English ⬤ Communication 2,987,535 24,981,163 9.08162 × 104 Tfr Wikipedia talk, French ⬤ Communication 1,420,367 4,641,928 1.10219 × 105 YS Yahoo songs ⬤ Rating 2,626,941 256,804,235 1.30625 × 105 Da Discogs artist–genre ⬤ Feature 3,509,661 19,033,891 2.21106 × 105 en Wikipedia (en) ⬤ Authorship 29,143,573 266,769,613 3.08364 × 105 AF US airports ⬤ Infrastructure 1,574 28,236 2.38376 × 107