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KONECT > Statistics > Clustering coefficient

## Clustering coefficient

The term clustering refers to the observation that in almost all networks, nodes tend to form small groups within which many edges are present, and such that only few edges connected different clusters with each other. In a social network for instance, people form groups in which almost every member known the other members. Clustering thus forms one of the primary characteristics of real-world networks, and thus many statistics for measuring it have been defined. The main method for measuring clustering numerically is the clustering coefficient, of which there exist several variants. As a general rule, the clustering coefficient measures to what extent edges in a network tend to form triangles. Since it is based on triangles, it can only be applied to unipartite networks, because bipartite networks do not contain triangles.
The number of triangles $$t$$ itself, as defined in the Section "Count Statistics" of the handbook, is however not a statistic that can be used to measure the clustering in a network, since it correlates with the size and volume of the network. Instead, the clustering coefficients in all its variants can be understood as a count of triangles, normalized in different ways in order to compare several networks with it.
The local clustering coefficient $$c(u)$$ of a node $$u$$ is defined as the probability that two randomly chosen (but distinct) neighbors of $$u$$ are connected [3]. \begin{align} c(u) &= \left\{ \begin{array}{ll} \frac { \{ v, w \in V \mid u \sim v \sim w \sim u \} } { \{ v, w \in V \mid u \sim v \neq w \sim u \} } & \text{when } d(u) > 1 \\ 0 & \text{when } d(u) \leq 1 \end{array} \right. \end{align}
The global clustering of a network can be computed in two ways. The first way defines it as the probability that two incident edges are completed by a third edge to form a triangle [2]. This is also called the transitivity ratio, or simply the transitivity. \begin{align} c &= \frac {|\{ u, v, w \in V \mid u \sim v \sim w \sim u \}|} {|\{ u, v, w \in V \mid u \sim v \neq w \sim u \}|} = \frac {3t} s \end{align} This variant of the global clustering coefficient has values between zero and one, with a value of one denoting that all possible triangles are formed (i.e., the network consists of disconnected cliques), and zero when it is triangle free. Note that the clustering coefficient is trivially zero for bipartite graphs. This clustering coefficient is however not defined when each node has degree zero or one, i.e., when the graph is a disjoint union of edges and unconnected nodes. This is however not a problem in practice.
The second variant variant of the clustering coefficient uses the average of the local clustering coefficients. This second variant was historically the first to be defined. In was defined in 1998 [3] and precedes the first variant by four years. \begin{align} c_2 &= \frac 1 {|V|} \sum_{u \in V} c(u) \end{align} This second variant of the global clustering coefficient is zero when a graph is triangle-free, and one when the graph is a disjoint union of cliques of size at least three. This variant of the global clustering coefficient is defined for all graphs, except for the empty graph, i.e., the graph with zero nodes. A slightly different definition of the second variant computes the average only over nodes with a degree of at least two, as seen for instance in [4].
Because of the arbitrary decision to define $$c(u)$$ as zero when the degree of $$c$$ is zero or one, we recommend to use the first variant of the clustering coefficient. In the following, the extensions to the clustering coefficient we present are all based on the first variant, $$c$$.
For signed graphs, we may define the clustering coefficient to take into account the sign of edges. The signed clustering coefficient is based on balance theory [5]. In a signed network, edges can be positive or negative. For instance in a signed social network, positive edges represent friendship, while negative edges represent enmity. In such networks, balance theory stipulates than triangles tend to be balanced, i.e., that three people are either all friends, or two of them are friends with each other, and enemies with the third. On the other hand, a triangle with two positive and one negative edge, or a triangle with three negative edges is unbalanced. In other words, we can define the sign of a triangle as the product of the three edge signs, which then leads to the stipulation that triangles tend to have positive weight. To extend the clustering coefficient to signed networks, we thus distinguis between balanced and unbalanced triangles, in a way that positive triangles contribute positively to the signed clustering coefficient, and negative triangles contribute negatively to it. For a triangle $$\{u,v,w\}$$, let $$\sigma(u,v,w)=w(u,v)w(v,w)w(w,u)$$ be the sign of the triangle, then the following definition captures the idea: \begin{align} c_{\mathrm s} &= \frac {\sum_{u,v,w\in V} \sigma(u,v,w)} {|\{ u, v, w \in V \mid u \sim v \neq w \sim u \}|} \end{align} Here, the sum is over all triangles $$\{u,v,w\}$$, but can also be taken over all triples of vertices, since $$w(u,v)=0$$ when $$\{u,v\}$$ is not an edge.
The signed clustering coefficient is bounded by the clustering coefficient: \begin{align} | c_{\mathrm s} | \leq c \end{align}
The relative signed clustering coefficient can then be defined as \begin{align} c_{\mathrm r} = \frac {c_{\mathrm s}} c = \frac {\sum_{u,v,w\in V} \sigma(u,v,w)} {|\{ u, v, w \in V \mid u \sim v \sim w \sim u \}|} \end{align} which also equals the proportion of all triangles that are balanced, minus the proportion of edges that are unbalanced.

The clustering coefficient can also be computed for each vertex separately, giving the clustering coefficient distribution.

 [1] JÃ©rÃ´me Kunegis, Andreas Lommatzsch, and Christian Bauckhage. The Slashdot Zoo: Mining a social network with negative edges. In Proc. Int. World Wide Web Conf., pages 741–750, 2009. [ .pdf ] [2] Duncan J. Watts and Steven H. Strogatz. Collective dynamics of `small-world' networks. Nature, 393(1):440–442, 1998. [3] M. E. J. Newman, D. J. Watts, and S. H. Strogatz. Random graph models of social networks. Proc. Natl. Acad. Sci. USA, 99:2566–2572, 2002. [4] Shweta Bansal, Shashank Khandelwal, and Lauren Ancel Meyers. Evolving clustered random networks. CoRR, abs/0808.0509, 2008.

 Code Name Category F. W. M. $$n$$ $$m$$ $$c$$ $$c_{\mathrm r}$$ CR Chicago ⬤ Infrastructure 1,467 1,298 0% Tar Wikipedia talk, Arabic ⬤ Communication 1,095,799 1,913,103 0.000331% Tzh Wikipedia talk, Chinese ⬤ Communication 1,219,241 2,284,546 0.000837% Tfr Wikipedia talk, French ⬤ Communication 1,420,367 4,641,928 0.00233% Tpt Wikipedia talk, Portuguese ⬤ Communication 541,355 2,424,962 0.00896% Tit Wikipedia talk, Italian ⬤ Communication 863,846 3,067,680 0.00900% Tes Wikipedia talk, Spanish ⬤ Communication 497,446 2,702,879 0.0210% Tru Wikipedia talk, Russian ⬤ Communication 457,017 2,282,055 0.0218% BAr Baidu related ⬤ Hyperlink 415,641 3,284,387 0.0663% TW Twitter (WWW) ⬤ Social 41,652,230 1,468,365,182 0.0846% Tnl Wikipedia talk, Dutch ⬤ Communication 225,749 1,554,699 0.0928% TF Twitter (MPI) ⬤ Social 52,579,682 1,963,263,821 0.0937% HUr Hudong related ⬤ Hyperlink 2,452,715 18,854,882 0.117% Tde Wikipedia talk, German ⬤ Communication 519,403 6,729,794 0.129% YT YouTube ⬤ Social 3,223,589 9,375,374 0.138% WK Wikipedia, English ⬤ Communication 2,394,385 5,021,410 0.219% Ten Wikipedia talk, English ⬤ Communication 2,987,535 24,981,163 0.220% BAi Baidu internal ⬤ Hyperlink 2,141,300 17,794,839 0.245% MP PDZBase ⬤ Metabolic 212 244 0.286% WP Wikipedia, English ⬤ Hyperlink 1,870,709 39,953,145 0.309% PL Prosper loans ⬤ Interaction 89,269 3,394,979 0.312% HUi Hudong internal ⬤ Hyperlink 1,984,484 14,869,484 0.346% Uf Wikipedia, fr (dynamic) ⬤ Hyperlink 2,212,682 59,008,831 0.494% Ui Wikipedia, it (dynamic) ⬤ Hyperlink 1,204,009 34,826,283 0.507% Up Wikipedia, pl (dynamic) ⬤ Hyperlink 1,033,050 25,026,208 0.508% Ud Wikipedia, nl (dynamic) ⬤ Hyperlink 1,039,252 20,070,561 0.545% MS Human protein (Stelzl) ⬤ Metabolic 1,706 6,207 0.577% LY Youtube links ⬤ Social 1,138,499 4,942,297 0.621% YG YouTube ⬤ Affiliation 218,563 293,360 YS Yahoo songs ⬤ Rating 2,626,941 256,804,235 LI Libimseti.cz ⬤ Social 220,970 17,359,346 0.734% Ug Wikipedia, de (dynamic) ⬤ Hyperlink 2,166,669 86,337,879 0.734% MF Human protein (Figeys) ⬤ Metabolic 2,239 6,452 0.761% Wde Wikipedia links, de ⬤ Hyperlink 3,225,565 81,626,917 0.883% Dj JUNG dependency ⬤ Software 6,120 138,706 1.10% Wpl Wikipedia links, pl ⬤ Hyperlink 1,529,135 57,489,447 1.10% DJ JDK dependency ⬤ Software 6,434 150,985 1.11% LM Livemocha ⬤ Social 104,103 2,193,083 1.41% WT TREC WT10g ⬤ Hyperlink 1,601,787 8,063,026 1.44% WT Web trackers ⬤ Hyperlink 68,087,704 140,613,762 Wfr Wikipedia links, fr ⬤ Hyperlink 3,023,165 102,382,410 1.50% Wru Wikipedia links, ru ⬤ Hyperlink 2,853,118 82,056,101 1.54% Wen Wikipedia links, en ⬤ Hyperlink 12,150,976 378,142,420 1.63% Us Wikipedia, simple en (dynamic) ⬤ Hyperlink 100,312 1,627,472 1.89% Wja Wikipedia links, ja ⬤ Hyperlink 1,610,638 71,055,717 2.14% Wpt Wikipedia links, pt ⬤ Hyperlink 1,603,222 49,021,409 2.23% GW Gowalla ⬤ Social 196,591 950,327 2.35% Wit Wikipedia links, it ⬤ Hyperlink 1,865,965 91,555,008 2.43% ET Euroroad ⬤ Infrastructure 1,174 1,417 3.39% MV Human protein (Vidal) ⬤ Metabolic 3,133 6,726 3.54% W2 WikiSigned ⬤ OnlineContact 138,592 740,397 3.79% TO Internet topology ⬤ Computer 34,761 171,403 4.85% TC Air traffic control ⬤ Infrastructure 1,226 2,615 6.39% WD Wikipedia Threads (de) ⬤ Communication 91,340 2,435,731 7.28% WC Wikipedia (en) ⬤ Feature 3,889,933 3,795,796 CO Wikipedia conflict ⬤ OnlineContact 118,100 2,917,785 2.98% WU WebUni Magdeburg ⬤ Text 212,552 3,869,707 BS Berkeley/Stanford ⬤ Hyperlink 685,230 7,600,595 0.694% SF Stanford ⬤ Hyperlink 281,903 2,312,497 0.862% GO Google ⬤ Hyperlink 875,713 5,105,039 5.52% ND Notre Dame ⬤ Hyperlink 325,729 1,497,134 8.77% UL Unicode languages ⬤ Feature 1,122 1,255 CC Cora citation ⬤ Citation 23,166 91,500 11.7% ZA Zachary karate club ⬤ HumanSocial 34 78 25.6% HT Highland tribes ⬤ HumanSocial 16 58 52.7% SO Stack Overflow ⬤ Rating 1,187,072 1,301,942 PL Pokec ⬤ Social 1,632,803 30,622,564 4.68% WO WordNet ⬤ Lexical 146,005 656,999 9.58% LJ LiveJournal ⬤ Social 4,847,571 68,475,391 11.8% If Infectious ⬤ HumanContact 410 17,298 43.6% PW Prosper.com ⬤ Interaction 25,697 35,377 PS Prosper.com ⬤ Affiliation 14,177 21,017 Vut vi.sualize.us u-t ⬤ Folksonomy 116,279 2,298,816 SD Slashdot ⬤ Communication 51,083 140,778 0.605% SZ Slashdot Zoo ⬤ Social 79,120 515,397 2.37% RD Pennsylvania ⬤ Infrastructure 1,088,092 1,541,898 5.94% R1 Texas ⬤ Infrastructure 1,379,917 1,921,660 6.02% RO California ⬤ Infrastructure 1,965,206 2,766,607 6.04% ES Epinions ⬤ Social 75,879 508,837 6.57% HY Hypertext 2009 ⬤ HumanContact 113 20,818 49.5% RE Reuters ⬤ Text 1,846,441 96,903,520 RA Manufacturing emails ⬤ Communication 167 82,927 54.1% RC Reactome ⬤ Metabolic 6,327 147,547 60.6% Vui vi.sualize.us u-i ⬤ Folksonomy 529,646 2,298,816 Vti vi.sualize.us t-i ⬤ Folksonomy 659,472 2,298,816 GN Gnutella ⬤ Computer 62,586 147,892 0.387% Sc Catster ⬤ Social 149,700 5,449,275 1.10% Sd Dogster ⬤ Social 426,820 8,546,581 1.43% Scd Catster/Dogster ⬤ Social 623,766 15,699,276 2.84% OR Orkut ⬤ Social 3,072,441 117,184,899 4.13% PC US patents ⬤ Citation 3,774,768 16,518,947 6.71% OG Orkut ⬤ Affiliation 14,297,249 327,037,487 UC UC Irvine messages ⬤ Communication 1,899 59,835 5.68% Shf Hamsterster friendships ⬤ Social 1,858 12,534 9.04% Sh Hamsterster full ⬤ Social 2,426 16,631 23.1% AF US airports ⬤ Infrastructure 1,574 28,236 38.4% UF UC Irvine forum ⬤ Interaction 2,320 33,720 SW Southern women 1 ⬤ Interaction 50 89 Ws Twitter (ICWSM) ⬤ Social 465,017 834,797 0.0613% UG US power grid ⬤ Infrastructure 4,941 6,594 10.3% OF OpenFlights ⬤ Infrastructure 3,425 67,663 24.8% NX Netflix ⬤ Rating 978,148 100,480,507 OF OpenFlights ⬤ Infrastructure 2,939 30,501 25.5% AC arXiv cond-mat ⬤ Authorship 55,467 58,595 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 DG Digg ⬤ Communication 30,398 87,627 0.560% Wa Twitter ⬤ OnlineContact 2,919,613 12,887,063 0.590% 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 Mp Protein ⬤ Metabolic 1,870 2,277 5.50% Lk Linux kernel mailing list replies ⬤ Communication 63,399 1,096,440 10.6% BK Brightkite ⬤ Social 58,228 214,078 11.1% LK Linux kernel mailing list threads ⬤ Interaction 421,599 1,565,683 Lj LiveJournal links ⬤ Social 5,204,176 49,174,464 12.4% LG LiveJournal ⬤ Affiliation 13,891,479 112,307,385 LX Linux ⬤ Software 30,837 213,954 0.282% ME Adolescent health ⬤ HumanSocial 2,539 12,969 14.2% MN Bible ⬤ Lexical 1,773 16,401 16.3% Mg Blogs ⬤ Hyperlink 1,224 19,025 22.6% MI Physicians ⬤ HumanSocial 241 1,098 25.1% MT Taro exchange ⬤ HumanSocial 22 78 27.5% MO Residence hall ⬤ HumanSocial 217 2,672 30.4% ML Little Rock Lake ⬤ Trophic 183 2,494 33.2% MH Highschool ⬤ HumanSocial 70 366 40.4% Ml Les Misérables ⬤ Misc 77 254 49.9% Mt Train bombing ⬤ HumanContact 64 243 56.1% MW Windsurfers ⬤ HumanContact 43 336 56.4% MQ Macaques ⬤ Animal 62 1,187 66.0% MR Rhesus ⬤ Animal 16 111 67.1% RM Reality Mining ⬤ HumanContact 96 1,086,404 72.5% Mc Sheep ⬤ Animal 28 250 72.8% MX Seventh graders ⬤ HumanSocial 29 376 73.4% MB Bison ⬤ Animal 26 314 78.9% MK Kangaroo ⬤ Animal 17 91 84.1% MZ Zebra ⬤ Animal 27 111 84.5% Ms Sampson ⬤ HumanSocial 18 189 85.4% Mv Dutch college ⬤ HumanSocial 32 3,062 90.4% Mh Hens ⬤ Animal 32 496 100% MC Crime ⬤ Interaction 2,209 1,476 MA Cattle ⬤ Animal 28 217 64.9% Ls Last.fm song ⬤ Interaction 1,086,604 19,150,868 Lb Last.fm band ⬤ Interaction 176,061 19,150,868 YD Yahoo advertisers ⬤ Lexical 653,260 2,931,708 0.000516% 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 0.156% 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 FX Flixster ⬤ Social 2,523,386 7,918,801 1.37% FL Flickr ⬤ Social 2,302,925 33,140,017 10.8% LF Flickr links ⬤ Social 1,715,255 15,551,250 11.2% FO FOLDOC ⬤ Hyperlink 13,356 125,207 11.3% FG Flickr ⬤ Affiliation 895,589 8,545,307 FW Florida ecosystem wet ⬤ Trophic 128 2,106 31.2% FD Florida ecosystem dry ⬤ Trophic 128 2,137 31.4% FI Flickr ⬤ Misc 105,938 2,316,948 40.2% Fr Filmtipset ⬤ Rating 225,153 19,554,219 Ff Filmtipset ⬤ Social 39,199 87,415 8.20% Fc Filmtipset ⬤ Interaction 104,890 1,266,753 EF Facebook (NIPS) ⬤ Social 2,888 2,981 0.0359% GP Google+ ⬤ Social 23,628 39,242 0.371% it Wikipedia (it) ⬤ Authorship 2,531,261 26,241,217 mfr Wiktionary (fr) ⬤ Authorship 1,917,281 7,399,298 EU EU institution ⬤ Communication 265,214 420,045 0.411% CY Youtube friendship ⬤ Social 1,134,890 2,987,624 0.622% TL Twitter lists ⬤ Social 23,370 33,101 2.15% Pi DBLP ⬤ Citation 12,591 49,743 6.20% EN Enron ⬤ Communication 87,273 1,148,072 7.16% Ow Facebook ⬤ Communication 46,952 876,993 8.51% DNc DNC emails ⬤ Communication 2,029 39,264 8.90% THc arXiv hep-th ⬤ Citation 27,770 352,807 12.0% EL Wikipedia elections ⬤ OnlineContact 7,118 103,675 12.5% PHc arXiv hep-ph ⬤ Citation 34,546 421,578 14.6% Cut CiteULike u-t ⬤ Folksonomy 198,707 2,411,819 Cui CiteULike u-i ⬤ Folksonomy 777,199 2,411,819 Ol Facebook (WOSN) ⬤ Social 63,731 817,035 14.8% SX Sexual escorts ⬤ Rating 26,836 50,632 ER Epinions ⬤ Rating 996,744 13,668,320 EP Epinions ⬤ Social 131,828 841,372 8.08% 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 DB Douban ⬤ Social 154,908 327,162 1.04% EA Edinburgh Associative Thesaurus ⬤ Lexical 23,132 511,764 4.04% Pc DBLP ⬤ Coauthorship 1,314,050 18,986,618 17.0% DO Dolphins ⬤ Animal 62 159 30.9% Pa DBLP ⬤ Authorship 6,851,776 8,649,016 CA Amazon (MDS) ⬤ Misc 334,863 925,872 20.5% CD DBLP co-authorship ⬤ Coauthorship 317,080 1,049,866 30.6% CU Contiguous USA ⬤ Infrastructure 49 107 40.6% DN DNC emails co-recipients ⬤ OnlineContact 2,029 136,602 54.8% 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 6.14% 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 0.169% 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 0.0143% HA Haggle ⬤ HumanContact 274 28,244 56.6% Cti CiteULike t-i ⬤ Folksonomy 1,038,323 2,411,819 GC Google.com internal ⬤ Hyperlink 15,763 171,206 1.33% CS CiteSeer ⬤ Citation 384,413 1,751,463 4.96% AD Advogato ⬤ Social 6,541 51,127 9.22% PM Caenorhabditis elegans ⬤ Metabolic 453 4,596 12.4% CH Chess ⬤ Interaction 7,301 65,053 12.6% AN David Copperfield ⬤ Lexical 112 425 15.7% TH arXiv hep-th ⬤ Coauthorship 22,908 2,673,133 26.9% PH arXiv hep-ph ⬤ Coauthorship 28,093 4,596,803 28.0% AP arXiv astro-ph ⬤ Coauthorship 18,771 198,050 31.8% 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 0.539% IN CAIDA ⬤ Computer 26,475 53,381 0.732% AS Route views ⬤ Computer 6,474 13,895 0.959% PG Pretty Good Privacy ⬤ OnlineContact 10,680 24,316 37.8% AM Actor movies ⬤ Affiliation 639,286 1,470,404 CL Actor collaborations ⬤ Misc 382,219 33,115,812 16.6% A@ U. Rovira i Virgili ⬤ Communication 1,133 5,451 16.6% JZ Jazz musicians ⬤ HumanSocial 198 2,742 52.0% AR Amazon ratings ⬤ Rating 5,523,029 5,838,041 Am Amazon (TWEB) ⬤ Misc 403,394 3,387,388 16.6%