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Preferential attachment exponent

The term preferential attachment refers to the observation that in networks that grow over time, the probability that an edge is added to a node with \(d\) neighbors is proportional to \(d\). This linear relationship lies at the heart of Barabási and Albert's scale-free network model [6], and has been used in a vast number of subsequent work to model networks, online and offline. The scale-free network model results in a distribution of degrees, i.e., number of neighbors of individual nodes, that follows a power law with negative exponent. In other words, the number of nodes with degree \(d\) is proportional to \(d^{-\gamma}\) in these networks, for a constant \(\gamma>1\).
In basic preferential attachment, the probability that an edge attached to a vertex \(u\) is propertional to its degree \(d(u)\). An extension of this basic model uses a probability that is a power of the degree, i.e., \(d(u)^\beta\). The exponent \(\beta\) is a positive number, and can be measured empirically from a dataset [9]. The value of \(\beta\) then determines the type of preferential attachment:

  1. Constant case \(\beta=0\). This case is equivalent to a constant probability of attachment, and thus this graph growth model results in networks in which each edge is equally likely and independent from other edges. This is the Erdős–Rényi model of random graphs [3].
  2. Sublinear case \(0 < \beta < 1\). In this case, the preferential attachment function is sublinear. This model gives rise to a stretched exponential degree distribution [4], whose exact expression is complex and given in [5].
  3. Linear case \(\beta=1\). This is the scale-free network model of Barabási and Albert [6], in which attachment is proportional to the degree. This gives a power law degree distribution.
  4. Superlinear case \(\beta > 1\). In this case, a single node will acquire 100% of all edges asymptotically [7]. Networks with this behavior will however display power law degree distributions in the pre-asymptotic regime [8].
The following minimization problem gives an estimate for the exponent \(\beta\) [9]. \begin{align} \min_{\alpha,\beta} \sum_{u\in V} \left( \alpha + \beta \ln[1 + d_1(u)] - \ln[\lambda + d_2(u)] \right)^2 \label{eq:min} \end{align} The resulting value of \(\beta\) is the estimated preferential attachment exponent. To measure the error of the fit, the root-mean-square logarithmic error \(\epsilon\) can be defined in the following way: \begin{align*} \epsilon &= \exp\left\{ \sqrt{ \frac 1 {|V|} \sum_{u \in V} \left(\alpha + \beta \ln[1 + d_1(u)] - \ln[\lambda + d_2(u)]\right)^2 } \right\} \end{align*} This gives the average factor by which the actual new number of edges differs from the predicted value, computed logarithmically. The value of \(\epsilon\) is larger or equal to one by construction.

[1] Jérôme Kunegis, Marcel Blattner, and Christine Moser. Preferential attachment in online networks: Measurement and explanations. In Proc. Web Science Conf., pages 205–214, 2013. [ .pdf ]
[2] Albert-László Barabási and Réka Albert. Emergence of scaling in random networks. Science, 286(5439):509–512, 1999.
[3] Paul Erdős and Alfréd Rényi. On random graphs I. Publ. Math. Debrecen, 6:290–297, 1959.
[4] Steffen Dereich and Peter Mörters. Random networks with sublinear preferential attachment: Degree evolutions. Electrical J. of Probability, 14:1222–1267, 2009.
[5] Anna Rudas, Bálint Tóth, and Benedek Valkó. Random trees and general branching processes. Random Struct. Algorithms, 31(2):186–202, 2007.
[6] Paul L. Krapivsky and Dmitri Krioukov. Scale-free networks as preasymptotic regimes of superlinear preferential attachment. Phys. Rev. E, 78:026114, 2008.
[7] S. N. Dorogovtsev and J. F. F. Mendes. Evolution of networks. Adv. Phys., 51:1079–1187, 2002.



Scatter plot of Preferential attachment exponent statistic

CodeName Category F. W. M.\(n\) \(m\) \(\beta\)
HUr Hudong relatedHyperlink Hyperlink 2Directed: Edges are directed 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
1
2,452,715
18,854,882
HUi Hudong internalHyperlink Hyperlink 2Directed: Edges are directed 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
1
1,984,484
14,869,484
BAr Baidu relatedHyperlink Hyperlink 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
Loops:  An edge may connect a node with itself
1
415,641
3,284,387
BAi Baidu internalHyperlink Hyperlink 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
Loops:  An edge may connect a node with itself
1
2,141,300
17,794,839
LK Linux kernel mailing list threadsInteraction Interaction 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
421,599
1,565,683
1.58109 × 10–2 (ε = 1.16245 × 100)
Bui BibSonomy u-iFolksonomy Folksonomy 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
Entity metadata:  Nodes are annotated with metadata
2
779,035
2,555,080
4.40401 × 10–2 (ε = 1.26467 × 100)
Bti BibSonomy t-iFolksonomy Folksonomy 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
Entity metadata:  Nodes are annotated with metadata
2
1,176,793
2,555,080
4.90021 × 10–2 (ε = 1.25201 × 100)
PL Prosper loansInteraction Interaction 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
89,269
3,394,979
1.14084 × 10–1 (ε = 2.77921 × 100)
Cti CiteULike t-iFolksonomy Folksonomy 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
1,038,323
2,411,819
1.35116 × 10–1 (ε = 1.69413 × 100)
CS CiteSeerCitation Citation 2Directed: Edges are directed 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
1
384,413
1,751,463
GC Google.com internalHyperlink Hyperlink 2Directed: Edges are directed 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
Entity metadata:  Nodes are annotated with metadata
2
15,763
171,206
nen Wikinews (en)Authorship Authorship 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
184,536
901,416
1.80022 × 10–1 (ε = 1.74212 × 100)
nfr Wikinews (fr)Authorship Authorship 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
27,954
193,618
3.69423 × 10–1 (ε = 3.42547 × 100)
bfr Wikibooks (fr)Authorship Authorship 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
33,881
201,727
5.38978 × 10–1 (ε = 2.73999 × 100)
mde Wiktionary (de)Authorship Authorship 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
157,806
1,229,501
5.50364 × 10–1 (ε = 3.66671 × 100)
ben Wikibooks (en)Authorship Authorship 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
200,108
1,164,576
5.61451 × 10–1 (ε = 2.98704 × 100)
YT YouTubeSocial Social 1Undirected: Edges are undirected 1Unweighted: Simple edges
Timestamps:  Edges are annotated with a timestamps
1
3,223,589
9,375,374
5.65382 × 10–1 (ε = 2.61153 × 100)
LY Youtube linksSocial Social 2Directed: Edges are directed 1Unweighted: Simple edges
Incomplete:   not all edges or nodes from the original dataset are included
1
1,138,499
4,942,297
YG YouTubeAffiliation Affiliation 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
0
218,563
293,360
Tfr Wikipedia talk, FrenchCommunication Communication 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
Loops:  An edge may connect a node with itself
Timestamps:  Edges are annotated with a timestamps
2
1,420,367
4,641,928
4.10606 × 10–1 (ε = 1.66958 × 100)
Tit Wikipedia talk, ItalianCommunication Communication 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
Loops:  An edge may connect a node with itself
Timestamps:  Edges are annotated with a timestamps
2
863,846
3,067,680
4.68929 × 10–1 (ε = 1.57189 × 100)
Ten Wikipedia talk, EnglishCommunication Communication 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
Loops:  An edge may connect a node with itself
Timestamps:  Edges are annotated with a timestamps
2
2,987,535
24,981,163
5.70522 × 10–1 (ε = 2.07098 × 100)
Tde Wikipedia talk, GermanCommunication Communication 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
Loops:  An edge may connect a node with itself
Timestamps:  Edges are annotated with a timestamps
2
519,403
6,729,794
6.04064 × 10–1 (ε = 2.39662 × 100)
But BibSonomy u-tFolksonomy Folksonomy 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
Entity metadata:  Nodes are annotated with metadata
2
216,261
2,555,080
6.09356 × 10–1 (ε = 2.52773 × 100)
YS Yahoo songsRating Rating 3Bipartite: Edges connect two types of nodes 6Ratings: Edges are ratings
Timestamps:  Edges are annotated with a timestamps
1
2,626,941
256,804,235
7.38143 × 10–1 (ε = 3.77882 × 100)
WO WordNetLexical Lexical 1Undirected: Edges are undirected 1Unweighted: Simple edges
0
146,005
656,999
PW Prosper.comInteraction Interaction 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
0
25,697
35,377
PS Prosper.comAffiliation Affiliation 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
0
14,177
21,017
Vut vi.sualize.us u-tFolksonomy Folksonomy 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
0
116,279
2,298,816
Vui vi.sualize.us u-iFolksonomy Folksonomy 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
0
529,646
2,298,816
Vti vi.sualize.us t-iFolksonomy Folksonomy 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
0
659,472
2,298,816
Sh Hamsterster fullSocial Social 1Undirected: Edges are undirected 1Unweighted: Simple edges
0
2,426
16,631
Shf Hamsterster friendshipsSocial Social 1Undirected: Edges are undirected 1Unweighted: Simple edges
0
1,858
12,534
Sd DogsterSocial Social 1Undirected: Edges are undirected 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
1
426,820
8,546,581
Sc CatsterSocial Social 1Undirected: Edges are undirected 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
1
149,700
5,449,275
Scd Catster/DogsterSocial Social 1Undirected: Edges are undirected 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
1
623,766
15,699,276
PC US patentsCitation Citation 2Directed: Edges are directed 1Unweighted: Simple edges
Acyclic:  No directed cycles are present
1
3,774,768
16,518,947
GN GnutellaComputer Computer 2Directed: Edges are directed 1Unweighted: Simple edges
0
62,586
147,892
OR OrkutSocial Social 1Undirected: Edges are undirected 1Unweighted: Simple edges
0
3,072,441
117,184,899
OG OrkutAffiliation Affiliation 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
0
14,297,249
327,037,487
AF US airportsInfrastructure Infrastructure 2Directed: Edges are directed 3Positive weights: Positively weighted edges
0
1,574
28,236
UC UC Irvine messagesCommunication Communication 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
1,899
59,835
8.72694 × 10–1 (ε = 5.86284 × 100)
UF UC Irvine forumInteraction Interaction 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
2,320
33,720
1.30513 × 100 (ε = 6.05656 × 100)
SW Southern women 1Interaction Interaction 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
0
50
89
UG US power gridInfrastructure Infrastructure 1Undirected: Edges are undirected 1Unweighted: Simple edges
0
4,941
6,594
OF OpenFlightsInfrastructure Infrastructure 2Directed: Edges are directed 1Unweighted: Simple edges
0
2,939
30,501
AC arXiv cond-matAuthorship Authorship 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
0
55,467
58,595
OF OpenFlightsInfrastructure Infrastructure 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
Loops:  An edge may connect a node with itself
1
3,425
67,663
Tar Wikipedia talk, ArabicCommunication Communication 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
Loops:  An edge may connect a node with itself
Timestamps:  Edges are annotated with a timestamps
2
1,095,799
1,913,103
1.83031 × 10–1 (ε = 1.86856 × 100)
Tnl Wikipedia talk, DutchCommunication Communication 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
Loops:  An edge may connect a node with itself
Timestamps:  Edges are annotated with a timestamps
2
225,749
1,554,699
5.30214 × 10–1 (ε = 1.97699 × 100)
WK Wikipedia, EnglishCommunication Communication 2Directed: Edges are directed 1Unweighted: Simple edges
0
2,394,385
5,021,410
W2 WikiSignedOnlineContact OnlineContact 2Directed: Edges are directed 4Signed: Positive and negative edges
Loops:  An edge may connect a node with itself
1
138,592
740,397
Wru Wikipedia links, ruHyperlink Hyperlink 2Directed: Edges are directed 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
1
2,853,118
82,056,101
Wpt Wikipedia links, ptHyperlink Hyperlink 2Directed: Edges are directed 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
1
1,603,222
49,021,409
Wpl Wikipedia links, plHyperlink Hyperlink 2Directed: Edges are directed 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
1
1,529,135
57,489,447
Wja Wikipedia links, jaHyperlink Hyperlink 2Directed: Edges are directed 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
1
1,610,638
71,055,717
Wit Wikipedia links, itHyperlink Hyperlink 2Directed: Edges are directed 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
1
1,865,965
91,555,008
Wfr Wikipedia links, frHyperlink Hyperlink 2Directed: Edges are directed 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
1
3,023,165
102,382,410
Wen Wikipedia links, enHyperlink Hyperlink 2Directed: Edges are directed 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
1
12,150,976
378,142,420
Wde Wikipedia links, deHyperlink Hyperlink 2Directed: Edges are directed 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
1
3,225,565
81,626,917
qen Wikiquote (en)Authorship Authorship 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
137,970
549,210
8.18022 × 10–1 (ε = 2.61096 × 100)
men Wiktionary (en)Authorship Authorship 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
2,163,240
8,998,641
8.83404 × 10–1 (ε = 3.45231 × 100)
CH ChessInteraction Interaction 2Directed: Edges are directed 5Multiple signed: Multiple, signed edges are possible
Zero weights:  Edges may have a weight of zero
Timestamps:  Edges are annotated with a timestamps
2
7,301
65,053
9.32937 × 10–1 (ε = 4.53583 × 100)
WP Wikipedia, EnglishHyperlink Hyperlink 2Directed: Edges are directed 1Unweighted: Simple edges
Timestamps:  Edges are annotated with a timestamps
1
1,870,709
39,953,145
1.01057 × 100 (ε = 4.08479 × 100)
WD Wikipedia Threads (de)Communication Communication 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
Loops:  An edge may connect a node with itself
1
91,340
2,435,731
WC Wikipedia (en)Feature Feature 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
0
3,889,933
3,795,796
CO Wikipedia conflictOnlineContact OnlineContact 1Undirected: Edges are undirected 5Multiple signed: Multiple, signed edges are possible
Zero weights:  Edges may have a weight of zero
Timestamps:  Edges are annotated with a timestamps
2
118,100
2,917,785
4.65020 × 10–1 (ε = 4.18165 × 100)
WU WebUni MagdeburgText Text 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
212,552
3,869,707
6.42062 × 10–1 (ε = 2.05982 × 100)
SF StanfordHyperlink Hyperlink 2Directed: Edges are directed 1Unweighted: Simple edges
0
281,903
2,312,497
ND Notre DameHyperlink Hyperlink 2Directed: Edges are directed 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
1
325,729
1,497,134
GO GoogleHyperlink Hyperlink 2Directed: Edges are directed 1Unweighted: Simple edges
0
875,713
5,105,039
BS Berkeley/StanfordHyperlink Hyperlink 2Directed: Edges are directed 1Unweighted: Simple edges
0
685,230
7,600,595
UL Unicode languagesFeature Feature 3Bipartite: Edges connect two types of nodes 3Positive weights: Positively weighted edges
Zero weights:  Edges may have a weight of zero
Entity metadata:  Nodes are annotated with metadata
2
1,122
1,255
ZA Zachary karate clubHumanSocial HumanSocial 1Undirected: Edges are undirected 1Unweighted: Simple edges
0
34
78
HT Highland tribesHumanSocial HumanSocial 1Undirected: Edges are undirected 4Signed: Positive and negative edges
0
16
58
TF Twitter (MPI)Social Social 2Directed: Edges are directed 1Unweighted: Simple edges
0
52,579,682
1,963,263,821
TW Twitter (WWW)Social Social 2Directed: Edges are directed 1Unweighted: Simple edges
0
41,652,230
1,468,365,182
WT TREC WT10gHyperlink Hyperlink 2Directed: Edges are directed 1Unweighted: Simple edges
0
1,601,787
8,063,026
WT Web trackersHyperlink Hyperlink 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
0
68,087,704
140,613,762
TO Internet topologyComputer Computer 1Undirected: Edges are undirected 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
Missing orientation:  The dataset was originally directed, but edge directions were discarded and this version is undirected
2
34,761
171,403
1.27898 × 100 (ε = 3.37529 × 100)
CR ChicagoInfrastructure Infrastructure 1Undirected: Edges are undirected 1Unweighted: Simple edges
0
1,467
1,298
Dj JUNG dependencySoftware Software 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
Entity metadata:  Nodes are annotated with metadata
1
6,120
138,706
DJ JDK dependencySoftware Software 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
Entity metadata:  Nodes are annotated with metadata
1
6,434
150,985
ET EuroroadInfrastructure Infrastructure 1Undirected: Edges are undirected 1Unweighted: Simple edges
Entity metadata:  Nodes are annotated with metadata
1
1,174
1,417
CC Cora citationCitation Citation 2Directed: Edges are directed 1Unweighted: Simple edges
Entity metadata:  Nodes are annotated with metadata
1
23,166
91,500
SO Stack OverflowRating Rating 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
Timestamps:  Edges are annotated with a timestamps
1
1,187,072
1,301,942
7.10220 × 10–1 (ε = 4.25938 × 100)
PL PokecSocial Social 2Directed: Edges are directed 1Unweighted: Simple edges
0
1,632,803
30,622,564
LJ LiveJournalSocial Social 2Directed: Edges are directed 1Unweighted: Simple edges
0
4,847,571
68,475,391
If InfectiousHumanContact HumanContact 1Undirected: Edges are undirected 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
410
17,298
9.20776 × 10–2 (ε = 7.21049 × 100)
HY Hypertext 2009HumanContact HumanContact 1Undirected: Edges are undirected 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
113
20,818
1.28539 × 100 (ε = 9.54577 × 100)
ES EpinionsSocial Social 2Directed: Edges are directed 1Unweighted: Simple edges
0
75,879
508,837
SZ Slashdot ZooSocial Social 2Directed: Edges are directed 4Signed: Positive and negative edges
0
79,120
515,397
SD SlashdotCommunication Communication 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
Loops:  An edge may connect a node with itself
Timestamps:  Edges are annotated with a timestamps
2
51,083
140,778
4.45834 × 10–1 (ε = 2.35086 × 100)
R1 TexasInfrastructure Infrastructure 1Undirected: Edges are undirected 1Unweighted: Simple edges
0
1,379,917
1,921,660
RD PennsylvaniaInfrastructure Infrastructure 1Undirected: Edges are undirected 1Unweighted: Simple edges
0
1,088,092
1,541,898
RO CaliforniaInfrastructure Infrastructure 1Undirected: Edges are undirected 1Unweighted: Simple edges
0
1,965,206
2,766,607
RE ReutersText Text 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Entity metadata:  Nodes are annotated with metadata
1
1,846,441
96,903,520
RC ReactomeMetabolic Metabolic 1Undirected: Edges are undirected 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
1
6,327
147,547
Tzh Wikipedia talk, ChineseCommunication Communication 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
Loops:  An edge may connect a node with itself
Timestamps:  Edges are annotated with a timestamps
2
1,219,241
2,284,546
4.50239 × 10–1 (ε = 1.87417 × 100)
Tes Wikipedia talk, SpanishCommunication Communication 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
Loops:  An edge may connect a node with itself
Timestamps:  Edges are annotated with a timestamps
2
497,446
2,702,879
4.51376 × 10–1 (ε = 1.95522 × 100)
Tpt Wikipedia talk, PortugueseCommunication Communication 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
Loops:  An edge may connect a node with itself
Timestamps:  Edges are annotated with a timestamps
2
541,355
2,424,962
Wti Twitter t-iFolksonomy Folksonomy 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
Incomplete:   not all edges or nodes from the original dataset are included
2
1,773,193
2,635,885
1.41236 × 10–1 (ε = 1.34047 × 100)
Wui Twitter u-iFolksonomy Folksonomy 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
Incomplete:   not all edges or nodes from the original dataset are included
2
9,618,743
12,656,613
2.80744 × 10–1 (ε = 1.29996 × 100)
DG DiggCommunication Communication 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
Loops:  An edge may connect a node with itself
Timestamps:  Edges are annotated with a timestamps
2
30,398
87,627
5.02360 × 10–1 (ε = 3.08696 × 100)
Tru Wikipedia talk, RussianCommunication Communication 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
Loops:  An edge may connect a node with itself
Timestamps:  Edges are annotated with a timestamps
2
457,017
2,282,055
5.77545 × 10–1 (ε = 1.80742 × 100)
M3 MovieLens 10MRating Rating 3Bipartite: Edges connect two types of nodes 6Ratings: Edges are ratings
Timestamps:  Edges are annotated with a timestamps
1
150,433
10,000,054
7.45097 × 10–1 (ε = 3.25646 × 100)
Mut MovieLens u-tFolksonomy Folksonomy 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
24,546
95,580
7.58827 × 10–1 (ε = 2.82191 × 100)
Lk Linux kernel mailing list repliesCommunication Communication 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
Loops:  An edge may connect a node with itself
Timestamps:  Edges are annotated with a timestamps
2
63,399
1,096,440
7.66088 × 10–1 (ε = 3.50603 × 100)
Mui MovieLens u-iFolksonomy Folksonomy 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
15,619
95,580
8.39461 × 10–1 (ε = 4.11304 × 100)
NX NetflixRating Rating 3Bipartite: Edges connect two types of nodes 6Ratings: Edges are ratings
Timestamps:  Edges are annotated with a timestamps
1
978,148
100,480,507
8.73160 × 10–1 (ε = 2.85036 × 100)
M2 MovieLens 1MRating Rating 3Bipartite: Edges connect two types of nodes 6Ratings: Edges are ratings
Timestamps:  Edges are annotated with a timestamps
1
15,786
1,000,209
9.63746 × 10–1 (ε = 2.83098 × 100)
Wa TwitterOnlineContact OnlineContact 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
Loops:  An edge may connect a node with itself
Timestamps:  Edges are annotated with a timestamps
2
2,919,613
12,887,063
1.03792 × 100 (ε = 2.99086 × 100)
Mti MovieLens t-iFolksonomy Folksonomy 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
40,657
95,580
1.09157 × 100 (ε = 4.09860 × 100)
RA Manufacturing emailsCommunication Communication 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
Loops:  An edge may connect a node with itself
Timestamps:  Edges are annotated with a timestamps
2
167
82,927
1.22839 × 100 (ε = 2.49547 × 100)
Ws Twitter (ICWSM)Social Social 2Directed: Edges are directed 1Unweighted: Simple edges
0
465,017
834,797
Wut Twitter u-tFolksonomy Folksonomy 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
Incomplete:   not all edges or nodes from the original dataset are included
2
880,846
4,664,605
8.43049 × 10–1 (ε = 2.47827 × 100)
LM LivemochaSocial Social 1Undirected: Edges are undirected 1Unweighted: Simple edges
0
104,103
2,193,083
Lj LiveJournal linksSocial Social 1Undirected: Edges are undirected 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
1
5,204,176
49,174,464
M1 MovieLens 100kRating Rating 3Bipartite: Edges connect two types of nodes 6Ratings: Edges are ratings
Timestamps:  Edges are annotated with a timestamps
1
3,568
100,000
9.31708 × 10–1 (ε = 3.12379 × 100)
MZ ZebraAnimal Animal 1Undirected: Edges are undirected 1Unweighted: Simple edges
0
27
111
Mv Dutch collegeHumanSocial HumanSocial 2Directed: Edges are directed 5Multiple signed: Multiple, signed edges are possible
Zero weights:  Edges may have a weight of zero
Timestamps:  Edges are annotated with a timestamps
2
32
3,062
6.12189 × 10–1 (ε = 1.11198 × 100)
Mt Train bombingHumanContact HumanContact 1Undirected: Edges are undirected 3Positive weights: Positively weighted edges
0
64
243
MT Taro exchangeHumanSocial HumanSocial 2Directed: Edges are directed 1Unweighted: Simple edges
0
22
78
Mc SheepAnimal Animal 2Directed: Edges are directed 3Positive weights: Positively weighted edges
Entity metadata:  Nodes are annotated with metadata
1
28
250
MX Seventh gradersHumanSocial HumanSocial 2Directed: Edges are directed 3Positive weights: Positively weighted edges
Entity metadata:  Nodes are annotated with metadata
1
29
376
Ms SampsonHumanSocial HumanSocial 2Directed: Edges are directed 4Signed: Positive and negative edges
Zero weights:  Edges may have a weight of zero
1
18
189
MR RhesusAnimal Animal 2Directed: Edges are directed 3Positive weights: Positively weighted edges
0
16
111
Mp ProteinMetabolic Metabolic 1Undirected: Edges are undirected 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
1
1,870
2,277
MO Residence hallHumanSocial HumanSocial 2Directed: Edges are directed 3Positive weights: Positively weighted edges
0
217
2,672
MN BibleLexical Lexical 1Undirected: Edges are undirected 2Multiple unweighted: Multiple edges are possible
0
1,773
16,401
MQ MacaquesAnimal Animal 2Directed: Edges are directed 3Positive weights: Positively weighted edges
0
62
1,187
Ml Les MisérablesMisc Misc 1Undirected: Edges are undirected 3Positive weights: Positively weighted edges
0
77
254
MK KangarooAnimal Animal 1Undirected: Edges are undirected 3Positive weights: Positively weighted edges
0
17
91
MI PhysiciansHumanSocial HumanSocial 2Directed: Edges are directed 1Unweighted: Simple edges
0
241
1,098
MH HighschoolHumanSocial HumanSocial 2Directed: Edges are directed 3Positive weights: Positively weighted edges
0
70
366
Mh HensAnimal Animal 2Directed: Edges are directed 1Unweighted: Simple edges
0
32
496
ME Adolescent healthHumanSocial HumanSocial 2Directed: Edges are directed 3Positive weights: Positively weighted edges
0
2,539
12,969
MC CrimeInteraction Interaction 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
Entity metadata:  Nodes are annotated with metadata
1
2,209
1,476
MA CattleAnimal Animal 2Directed: Edges are directed 3Positive weights: Positively weighted edges
0
28
217
Mg BlogsHyperlink Hyperlink 2Directed: Edges are directed 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
Entity metadata:  Nodes are annotated with metadata
2
1,224
19,025
MB BisonAnimal Animal 2Directed: Edges are directed 3Positive weights: Positively weighted edges
0
26
314
MW WindsurfersHumanContact HumanContact 1Undirected: Edges are undirected 3Positive weights: Positively weighted edges
0
43
336
RM Reality MiningHumanContact HumanContact 1Undirected: Edges are undirected 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
96
1,086,404
1.53150 × 100 (ε = 3.23015 × 101)
MV Human protein (Vidal)Metabolic Metabolic 1Undirected: Edges are undirected 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
1
3,133
6,726
MS Human protein (Stelzl)Metabolic Metabolic 2Directed: Edges are directed 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
1
1,706
6,207
MP PDZBaseMetabolic Metabolic 1Undirected: Edges are undirected 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
1
212
244
ML Little Rock LakeTrophic Trophic 2Directed: Edges are directed 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
1
183
2,494
MF Human protein (Figeys)Metabolic Metabolic 2Directed: Edges are directed 1Unweighted: Simple edges
0
2,239
6,452
TC Air traffic controlInfrastructure Infrastructure 2Directed: Edges are directed 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
1
1,226
2,615
GW GowallaSocial Social 1Undirected: Edges are undirected 1Unweighted: Simple edges
0
196,591
950,327
BK BrightkiteSocial Social 1Undirected: Edges are undirected 1Unweighted: Simple edges
0
58,228
214,078
LG LiveJournalAffiliation Affiliation 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
0
13,891,479
112,307,385
LX LinuxSoftware Software 2Directed: Edges are directed 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
1
30,837
213,954
Ud Wikipedia, nl (dynamic)Hyperlink Hyperlink 2Directed: Edges are directed 8Dynamic: Edges can appear and disappear
Loops:  An edge may connect a node with itself
Timestamps:  Edges are annotated with a timestamps
2
1,039,252
20,070,561
8.71927 × 10–1 (ε = 4.70301 × 100)
Up Wikipedia, pl (dynamic)Hyperlink Hyperlink 2Directed: Edges are directed 8Dynamic: Edges can appear and disappear
Loops:  An edge may connect a node with itself
Timestamps:  Edges are annotated with a timestamps
2
1,033,050
25,026,208
9.63288 × 10–1 (ε = 4.38802 × 100)
Ui Wikipedia, it (dynamic)Hyperlink Hyperlink 2Directed: Edges are directed 8Dynamic: Edges can appear and disappear
Loops:  An edge may connect a node with itself
Timestamps:  Edges are annotated with a timestamps
2
1,204,009
34,826,283
9.98447 × 10–1 (ε = 4.78728 × 100)
Ug Wikipedia, de (dynamic)Hyperlink Hyperlink 2Directed: Edges are directed 8Dynamic: Edges can appear and disappear
Loops:  An edge may connect a node with itself
Timestamps:  Edges are annotated with a timestamps
2
2,166,669
86,337,879
1.00066 × 100 (ε = 4.78850 × 100)
Uf Wikipedia, fr (dynamic)Hyperlink Hyperlink 2Directed: Edges are directed 8Dynamic: Edges can appear and disappear
Loops:  An edge may connect a node with itself
Timestamps:  Edges are annotated with a timestamps
2
2,212,682
59,008,831
1.01639 × 100 (ε = 4.06262 × 100)
Us Wikipedia, simple en (dynamic)Hyperlink Hyperlink 2Directed: Edges are directed 8Dynamic: Edges can appear and disappear
Loops:  An edge may connect a node with itself
Timestamps:  Edges are annotated with a timestamps
2
100,312
1,627,472
1.06373 × 100 (ε = 3.96137 × 100)
LI Libimseti.czSocial Social 2Directed: Edges are directed 6Ratings: Edges are ratings
0
220,970
17,359,346
EL Wikipedia electionsOnlineContact OnlineContact 2Directed: Edges are directed 4Signed: Positive and negative edges
Loops:  An edge may connect a node with itself
Timestamps:  Edges are annotated with a timestamps
Incomplete:   not all edges or nodes from the original dataset are included
3
7,118
103,675
1.01217 × 10–2 (ε = 2.74238 × 100)
Ol Facebook (WOSN)Social Social 1Undirected: Edges are undirected 1Unweighted: Simple edges
Timestamps:  Edges are annotated with a timestamps
Incomplete:   not all edges or nodes from the original dataset are included
2
63,731
817,035
5.16567 × 10–1 (ε = 6.09425 × 100)
SX Sexual escortsRating Rating 3Bipartite: Edges connect two types of nodes 7Multiple ratings: Multiple weighted edges are allowed
Timestamps:  Edges are annotated with a timestamps
1
26,836
50,632
7.94200 × 10–1 (ε = 2.83835 × 100)
Ow FacebookCommunication Communication 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
Loops:  An edge may connect a node with itself
Timestamps:  Edges are annotated with a timestamps
2
46,952
876,993
8.72097 × 10–1 (ε = 5.00818 × 100)
Fc FilmtipsetInteraction Interaction 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
104,890
1,266,753
1.00448 × 100 (ε = 3.78276 × 100)
Lb Last.fm bandInteraction Interaction 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
176,061
19,150,868
1.10444 × 100 (ε = 5.17573 × 100)
Ls Last.fm songInteraction Interaction 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
1,086,604
19,150,868
1.15370 × 100 (ε = 3.95966 × 100)
YD Yahoo advertisersLexical Lexical 2Directed: Edges are directed 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
1
653,260
2,931,708
J2 Jester 150Rating Rating 3Bipartite: Edges connect two types of nodes 6Ratings: Edges are ratings
0
101,524
1,728,847
J1 Jester 100Rating Rating 3Bipartite: Edges connect two types of nodes 6Ratings: Edges are ratings
0
146,942
4,136,360
HY HyvesSocial Social 1Undirected: Edges are undirected 1Unweighted: Simple edges
0
1,402,673
2,777,419
TR TREC (disks 4–5)Text Text 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
0
2,285,379
151,632,178
R2 Reuters-21578Text Text 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
0
81,791
1,464,182
EX Wikipedia (en)Text Text 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
0
279,519
7,846,807
GH GithubAuthorship Authorship 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
Entity metadata:  Nodes are annotated with metadata
1
233,905
440,237
FR FriendsterSocial Social 2Directed: Edges are directed 1Unweighted: Simple edges
Incomplete:   not all edges or nodes from the original dataset are included
1
68,349,466
2,586,147,869
FW Florida ecosystem wetTrophic Trophic 2Directed: Edges are directed 3Positive weights: Positively weighted edges
0
128
2,106
FD Florida ecosystem dryTrophic Trophic 2Directed: Edges are directed 3Positive weights: Positively weighted edges
0
128
2,137
FO FOLDOCHyperlink Hyperlink 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
0
13,356
125,207
FX FlixsterSocial Social 1Undirected: Edges are undirected 1Unweighted: Simple edges
0
2,523,386
7,918,801
LF Flickr linksSocial Social 1Undirected: Edges are undirected 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
1
1,715,255
15,551,250
FL FlickrSocial Social 2Directed: Edges are directed 1Unweighted: Simple edges
Timestamps:  Edges are annotated with a timestamps
1
2,302,925
33,140,017
9.60503 × 10–1 (ε = 2.78687 × 100)
FG FlickrAffiliation Affiliation 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
0
895,589
8,545,307
FI FlickrMisc Misc 1Undirected: Edges are undirected 1Unweighted: Simple edges
0
105,938
2,316,948
Fr FilmtipsetRating Rating 3Bipartite: Edges connect two types of nodes 7Multiple ratings: Multiple weighted edges are allowed
Timestamps:  Edges are annotated with a timestamps
1
225,153
19,554,219
9.68650 × 10–1 (ε = 4.12458 × 100)
Ff FilmtipsetSocial Social 1Undirected: Edges are undirected 1Unweighted: Simple edges
0
39,199
87,415
TL Twitter listsSocial Social 2Directed: Edges are directed 1Unweighted: Simple edges
0
23,370
33,101
GP Google+Social Social 2Directed: Edges are directed 1Unweighted: Simple edges
0
23,628
39,242
EF Facebook (NIPS)Social Social 1Undirected: Edges are undirected 1Unweighted: Simple edges
0
2,888
2,981
ER EpinionsRating Rating 3Bipartite: Edges connect two types of nodes 6Ratings: Edges are ratings
Timestamps:  Edges are annotated with a timestamps
1
996,744
13,668,320
3.42512 × 10–1 (ε = 2.81777 × 100)
EP EpinionsSocial Social 2Directed: Edges are directed 4Signed: Positive and negative edges
Loops:  An edge may connect a node with itself
Timestamps:  Edges are annotated with a timestamps
2
131,828
841,372
5.91685 × 10–1 (ε = 2.87147 × 100)
EN EnronCommunication Communication 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
Loops:  An edge may connect a node with itself
Timestamps:  Edges are annotated with a timestamps
2
87,273
1,148,072
7.85895 × 10–1 (ε = 3.81678 × 100)
EU EU institutionCommunication Communication 2Directed: Edges are directed 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
Incomplete:   not all edges or nodes from the original dataset are included
2
265,214
420,045
it Wikipedia (it)Authorship Authorship 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
2,531,261
26,241,217
1.08684 × 100 (ε = 3.51966 × 100)
en Wikipedia (en)Authorship Authorship 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
29,143,573
266,769,613
1.10598 × 100 (ε = 3.36988 × 100)
fr Wikipedia (fr)Authorship Authorship 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
4,598,826
46,168,355
1.11031 × 100 (ε = 3.38954 × 100)
es Wikipedia (es)Authorship Authorship 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
3,623,742
27,011,506
1.17118 × 100 (ε = 3.05932 × 100)
de Wikipedia (de)Authorship Authorship 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
4,046,832
57,323,775
1.17251 × 100 (ε = 3.63093 × 100)
mfr Wiktionary (fr)Authorship Authorship 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
1,917,281
7,399,298
1.20956 × 100 (ε = 3.54192 × 100)
EA Edinburgh Associative ThesaurusLexical Lexical 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
Loops:  An edge may connect a node with itself
1
23,132
511,764
DB DoubanSocial Social 1Undirected: Edges are undirected 1Unweighted: Simple edges
0
154,908
327,162
DO DolphinsAnimal Animal 1Undirected: Edges are undirected 1Unweighted: Simple edges
0
62
159
DNc DNC emailsCommunication Communication 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
Loops:  An edge may connect a node with itself
Timestamps:  Edges are annotated with a timestamps
2
2,029
39,264
1.18369 × 100 (ε = 3.12748 × 100)
DN DNC emails co-recipientsOnlineContact OnlineContact 1Undirected: Edges are undirected 2Multiple unweighted: Multiple edges are possible
0
2,029
136,602
Dt Discogs artist–styleFeature Feature 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Entity metadata:  Nodes are annotated with metadata
1
3,236,269
24,085,580
Ds Discogs label–styleFeature Feature 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Entity metadata:  Nodes are annotated with metadata
1
487,911
5,255,950
Dr Discogs label–genreFeature Feature 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Entity metadata:  Nodes are annotated with metadata
1
541,557
4,147,665
Da Discogs artist–genreFeature Feature 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Entity metadata:  Nodes are annotated with metadata
1
3,509,661
19,033,891
Dl DiscogsAffiliation Affiliation 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Entity metadata:  Nodes are annotated with metadata
1
3,780,417
14,414,659
Cui CiteULike u-iFolksonomy Folksonomy 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
777,199
2,411,819
9.00989 × 10–2 (ε = 1.55255 × 100)
DF Digg friendsSocial Social 2Directed: Edges are directed 1Unweighted: Simple edges
Timestamps:  Edges are annotated with a timestamps
Incomplete:   not all edges or nodes from the original dataset are included
2
279,630
1,731,653
6.54108 × 10–1 (ε = 2.49387 × 100)
Dui Delicious uiFolksonomy Folksonomy 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
Entity metadata:  Nodes are annotated with metadata
Incomplete:   not all edges or nodes from the original dataset are included
3
35,444,383
301,186,579
6.87183 × 10–1 (ε = 2.68027 × 100)
Dti Delicious tiFolksonomy Folksonomy 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
Entity metadata:  Nodes are annotated with metadata
Incomplete:   not all edges or nodes from the original dataset are included
3
42,801,712
301,183,605
7.91114 × 10–1 (ε = 2.96128 × 100)
DBT TV TropesFeature Feature 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
0
216,508
3,232,134
WR WritersAuthorship Authorship 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
0
224,925
144,340
TM TeamsAffiliation Affiliation 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
0
1,836,793
1,366,466
ST MoviesFeature Feature 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
0
233,283
281,396
RL Record labelsAffiliation Affiliation 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
0
355,095
233,286
PR ProducersAuthorship Authorship 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
0
236,510
207,268
OC OccupationAffiliation Affiliation 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
0
356,884
250,945
LO LocationFeature Feature 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
0
397,589
293,697
DL Wikipedia, EnglishHyperlink Hyperlink 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
0
18,268,992
172,183,984
GE DBpedia genreFeature Feature 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
0
525,651
463,497
CN CountriesAffiliation Affiliation 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
0
1,182,526
637,134
DB DBpediaMisc Misc 2Directed: Edges are directed 2Multiple unweighted: Multiple edges are possible
0
3,966,924
13,820,853
Pc DBLPCoauthorship Coauthorship 1Undirected: Edges are undirected 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
1,314,050
18,986,618
1.07566 × 100 (ε = 6.26927 × 100)
Pi DBLPCitation Citation 2Directed: Edges are directed 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
1
12,591
49,743
Pa DBLPAuthorship Authorship 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
0
6,851,776
8,649,016
CU Contiguous USAInfrastructure Infrastructure 1Undirected: Edges are undirected 1Unweighted: Simple edges
0
49
107
HA HaggleHumanContact HumanContact 1Undirected: Edges are undirected 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
274
28,244
1.19421 × 100 (ε = 7.83017 × 100)
CY Youtube friendshipSocial Social 1Undirected: Edges are undirected 1Unweighted: Simple edges
0
1,134,890
2,987,624
CD DBLP co-authorshipCoauthorship Coauthorship 1Undirected: Edges are undirected 1Unweighted: Simple edges
0
317,080
1,049,866
CA Amazon (MDS)Misc Misc 1Undirected: Edges are undirected 1Unweighted: Simple edges
0
334,863
925,872
THc arXiv hep-thCitation Citation 2Directed: Edges are directed 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
1
27,770
352,807
PHc arXiv hep-phCitation Citation 2Directed: Edges are directed 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
1
34,546
421,578
Cut CiteULike u-tFolksonomy Folksonomy 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
198,707
2,411,819
8.13852 × 10–1 (ε = 2.85268 × 100)
Dut Delicious utFolksonomy Folksonomy 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
Entity metadata:  Nodes are annotated with metadata
Incomplete:   not all edges or nodes from the original dataset are included
3
6,178,261
301,186,579
1.08441 × 100 (ε = 3.27077 × 100)
DV Digg votesRating Rating 3Bipartite: Edges connect two types of nodes 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
Incomplete:   not all edges or nodes from the original dataset are included
2
282,371
3,018,197
1.23849 × 100 (ε = 5.60307 × 100)
TH arXiv hep-thCoauthorship Coauthorship 1Undirected: Edges are undirected 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
22,908
2,673,133
PH arXiv hep-phCoauthorship Coauthorship 1Undirected: Edges are undirected 2Multiple unweighted: Multiple edges are possible
Timestamps:  Edges are annotated with a timestamps
1
28,093
4,596,803
AP arXiv astro-phCoauthorship Coauthorship 1Undirected: Edges are undirected 1Unweighted: Simple edges
0
18,771
198,050
SC South African CompaniesAffiliation Affiliation 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
0
17
13
Ar American RevolutionAffiliation Affiliation 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
0
277
160
BC Corporate LeadershipAffiliation Affiliation 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
0
64
99
Sw Southern women 2Interaction Interaction 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
0
15
14
BM Club membershipAffiliation Affiliation 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
0
65
95
Bx BookCrossing (ratings)Rating Rating 3Bipartite: Edges connect two types of nodes 6Ratings: Edges are ratings
0
341,559
433,652
BX BookCrossing (implicit)Rating Rating 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
0
551,079
1,149,739
SK SkitterComputer Computer 1Undirected: Edges are undirected 1Unweighted: Simple edges
0
1,696,415
11,095,298
IN CAIDAComputer Computer 1Undirected: Edges are undirected 1Unweighted: Simple edges
Missing orientation:  The dataset was originally directed, but edge directions were discarded and this version is undirected
1
26,475
53,381
AS Route viewsComputer Computer 1Undirected: Edges are undirected 1Unweighted: Simple edges
Loops:  An edge may connect a node with itself
Missing orientation:  The dataset was originally directed, but edge directions were discarded and this version is undirected
2
6,474
13,895
PG Pretty Good PrivacyOnlineContact OnlineContact 1Undirected: Edges are undirected 1Unweighted: Simple edges
Incomplete:   not all edges or nodes from the original dataset are included
1
10,680
24,316
PM Caenorhabditis elegansMetabolic Metabolic 1Undirected: Edges are undirected 2Multiple unweighted: Multiple edges are possible
Loops:  An edge may connect a node with itself
1
453
4,596
JZ Jazz musiciansHumanSocial HumanSocial 1Undirected: Edges are undirected 1Unweighted: Simple edges
Incomplete:   not all edges or nodes from the original dataset are included
1
198
2,742
A@ U. Rovira i VirgiliCommunication Communication 1Undirected: Edges are undirected 1Unweighted: Simple edges
Missing orientation:  The dataset was originally directed, but edge directions were discarded and this version is undirected
1
1,133
5,451
AR Amazon ratingsRating Rating 3Bipartite: Edges connect two types of nodes 7Multiple ratings: Multiple weighted edges are allowed
Timestamps:  Edges are annotated with a timestamps
Incomplete:   not all edges or nodes from the original dataset are included
2
5,523,029
5,838,041
6.04802 × 10–1 (ε = 2.52309 × 100)
Am Amazon (TWEB)Misc Misc 2Directed: Edges are directed 1Unweighted: Simple edges
0
403,394
3,387,388
AD AdvogatoSocial Social 2Directed: Edges are directed 3Positive weights: Positively weighted edges
Loops:  An edge may connect a node with itself
Entity metadata:  Nodes are annotated with metadata
2
6,541
51,127
AN David CopperfieldLexical Lexical 1Undirected: Edges are undirected 1Unweighted: Simple edges
Entity metadata:  Nodes are annotated with metadata
Missing orientation:  The dataset was originally directed, but edge directions were discarded and this version is undirected
2
112
425
AM Actor moviesAffiliation Affiliation 3Bipartite: Edges connect two types of nodes 1Unweighted: Simple edges
0
639,286
1,470,404
CL Actor collaborationsMisc Misc 1Undirected: Edges are undirected 2Multiple unweighted: Multiple edges are possible
0
382,219
33,115,812