Pro League (2016/2017)

These are results of football games in Belgium from the Pro League 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-be1-2016
NamePro League (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
Zero weights Edges may have weight zero


Size n =16
Volume m =239
Unique edge count m̿ =179
Loop count l =0
Wedge count s =1,680
Claw count z =26,932
Cross count x =135,430
Triangle count t =560
Square count q =4,755
4-Tour count T4 =44,548
Maximum degree dmax =30
Maximum outdegree d+max =15
Maximum indegree dmax =15
Average degree d =29.875 0
Fill p =0.745 833
Average edge multiplicity m̃ =1.335 20
Size of LCC N =16
Size of LSCC Ns =16
Relative size of LSCC Nrs =1.000 00
Diameter δ =1
50-Percentile effective diameter δ0.5 =0.468 872
90-Percentile effective diameter δ0.9 =0.893 774
Median distance δM =1
Mean distance δm =0.941 392
Gini coefficient G =0.058 310 1
Balanced inequality ratio P =0.458 101
Outdegree balanced inequality ratio P+ =0.441 341
Indegree balanced inequality ratio P =0.424 581
Relative edge distribution entropy Her =0.997 941
Power law exponent γ =10.234 9
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 =8.621 00
Outdegree p-value po =0.424 000
Indegree tail power law exponent with p γ3,i =8.991 00
Indegree p-value pi =0.305 000
Degree assortativity ρ =−0.121 119
Degree assortativity p-value pρ =0.065 527 0
In/outdegree correlation ρ± =−0.196 684
Clustering coefficient c =1.000 00
Directed clustering coefficient c± =0.754 960
Spectral norm α =17.370 6
Operator 2-norm ν =16.497 7
Cyclic eigenvalue π =2.398 84
Algebraic connectivity a =23.683 3
Spectral separation 1[A] / λ2[A]| =1.047 16
Reciprocity y =0.703 911
Non-bipartivity bA =0.777 520
Normalized non-bipartivity bN =0.832 478
Algebraic non-bipartivity χ =11.269 5
Spectral bipartite frustration bK =0.194 302
Negativity ζ =0.335 196
Algebraic conflict ξ =12.789 0
Triadic conflict τ =0.476 923
Spectral signed frustration φ =0.304 500
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.