Bundesliga (2016/2017)

These are results of football games in Germany from the Bundesliga in the season 2016/2017, in form of a directed, signed graph. Nodes are teams, and each directed edge from A to B denotes that team A played at home against team B. The edge weights are the goal difference, and thus positive if the home team wins, negative when the away team wins, and zero for a draw. The exact game results are not represented; only the goal differences are. The data was copied by hand from Wikipedia.


Internal nameleague-de1-2016
NameBundesliga (2016/2017)
AvailabilityDataset is available for download
Consistency checkDataset passed all tests
Interaction network
Dataset timestamp 2016 ⋯ 2017
Node meaningTeam
Edge meaningGame
Network formatUnipartite, directed
Edge typeSigned, possibly weighted, multiple edges
ReciprocalContains reciprocal edges
Directed cyclesContains directed cycles
LoopsDoes not contain loops
Skew-symmetry Inverted edges can be interpreted as negated edges
Complete Edges exist between all possible nodes
Zero weights Edges may have weight zero


Size n =18
Volume m =306
Unique edge count m̿ =232
Loop count l =0
Wedge count s =2,448
Claw count z =47,061
Cross count x =277,047
Triangle count t =816
Square count q =7,605
4-Tour count T4 =70,048
Maximum degree dmax =34
Maximum outdegree d+max =17
Maximum indegree dmax =17
Average degree d =34.000 0
Fill p =0.758 170
Average edge multiplicity m̃ =1.318 97
Size of LCC N =18
Size of LSCC Ns =18
Relative size of LSCC Nrs =1.000 00
Diameter δ =1
50-Percentile effective diameter δ0.5 =0.471 246
90-Percentile effective diameter δ0.9 =0.894 249
Median distance δM =1
Mean distance δm =0.945 619
Gini coefficient G =0.056 034 5
Balanced inequality ratio P =0.461 207
Outdegree balanced inequality ratio P+ =0.443 966
Indegree balanced inequality ratio P =0.448 276
Relative edge distribution entropy Her =0.998 181
Power law exponent γ =7.854 65
Tail power law exponent γt =8.991 00
Tail power law exponent with p γ3 =8.991 00
p-value p =0.002 000 00
Outdegree tail power law exponent with p γ3,o =8.991 00
Outdegree p-value po =0.545 000
Indegree tail power law exponent with p γ3,i =8.991 00
Indegree p-value pi =0.538 000
Degree assortativity ρ =−0.113 517
Degree assortativity p-value pρ =0.052 656 1
In/outdegree correlation ρ± =+0.155 646
Clustering coefficient c =1.000 00
Directed clustering coefficient c± =0.755 752
Spectral norm α =19.599 8
Operator 2-norm ν =18.513 2
Cyclic eigenvalue π =3.242 63
Algebraic connectivity a =30.008 7
Spectral separation 1[A] / λ2[A]| =1.048 79
Reciprocity y =0.741 379
Non-bipartivity bA =0.771 061
Normalized non-bipartivity bN =0.825 038
Algebraic non-bipartivity χ =12.256 3
Spectral bipartite frustration bK =0.188 882
Negativity ζ =0.353 448
Algebraic conflict ξ =14.823 2
Triadic conflict τ =0.459 959
Spectral signed frustration φ =0.326 982
Controllability C =0
Relative controllability Cr =0.000 00


Fruchterman–Reingold graph drawing

Degree distribution

Cumulative degree distribution

Lorenz curve

Spectral distribution of the adjacency matrix

Spectral distribution of the normalized adjacency matrix

Spectral distribution of the Laplacian

Spectral graph drawing based on the adjacency matrix

Spectral graph drawing based on the Laplacian

Spectral graph drawing based on the normalized adjacency matrix

Degree assortativity

Zipf plot

Hop distribution

Double Laplacian graph drawing

Delaunay graph drawing

In/outdegree scatter plot

Item rating evolution

Edge weight/multiplicity distribution

Clustering coefficient distribution

Average neighbor degree distribution


Matrix decompositions plots



[1] Jérôme Kunegis. KONECT – The Koblenz Network Collection. In Proc. Int. Conf. on World Wide Web Companion, pages 1343–1350, 2013. [ http ]
[2] Michaël Fanuel and Johan A. K. Suykens. Deformed Laplacians and spectral ranking in directed networks. Applied and Computational Harmonic Analysis, 2017. In press.