Chess
These are results of chess games. Each node is a chess player, and a directed
edge represents a game, with the white player having an outgoing edge and the
black player having an ingoing edge. The weight of the edge represents the
outcome (+1 white won, 0 draw, −1 black won). The dataset is anonymous: the
identity of the players is unknown, and timestamps are approximate. Timestamps
are given to a one month precision, and may have been shifted towards the
future by an unknown amount.
Metadata
Statistics
Size  n =  7,301

Volume  m =  65,053

Unique edge count  m̿ =  34,564

Loop count  l =  0

Wedge count  s =  2,588,788

Claw count  z =  16,498,559

Cross count  x =  272,731,448

Triangle count  t =  108,595

Square count  q =  324,301

4Tour count  T_{4} =  6,216,178

Maximum degree  d_{max} =  280

Maximum outdegree  d^{+}_{max} =  152

Maximum indegree  d^{−}_{max} =  140

Average degree  d =  17.820 3

Fill  p =  0.000 741 048

Average edge multiplicity  m̃ =  1.882 10

Size of LCC  N =  7,115

Size of LSCC  N_{s} =  4,738

Relative size of LSCC  N^{r}_{s} =  0.648 952

Diameter  δ =  13

50Percentile effective diameter  δ_{0.5} =  3.392 21

90Percentile effective diameter  δ_{0.9} =  4.831 00

Median distance  δ_{M} =  4

Mean distance  δ_{m} =  3.949 93

Gini coefficient  G =  0.590 957

Balanced inequality ratio  P =  0.270 918

Outdegree balanced inequality ratio  P_{+} =  0.287 091

Indegree balanced inequality ratio  P_{−} =  0.293 311

Relative edge distribution entropy  H_{er} =  0.928 663

Power law exponent  γ =  1.617 64

Tail power law exponent  γ_{t} =  3.071 00

Tail power law exponent with p  γ_{3} =  3.071 00

pvalue  p =  0.000 00

Outdegree tail power law exponent with p  γ_{3,o} =  3.061 00

Outdegree pvalue  p_{o} =  0.000 00

Indegree tail power law exponent with p  γ_{3,i} =  3.061 00

Indegree pvalue  p_{i} =  0.000 00

Degree assortativity  ρ =  +0.306 204

Degree assortativity pvalue  p_{ρ} =  0.000 00

In/outdegree correlation  ρ^{±} =  +0.805 364

Clustering coefficient  c =  0.125 845

Directed clustering coefficient  c^{±} =  0.040 989 8

Spectral norm  α =  18.856 4

Operator 2norm  ν =  13.746 3

Cyclic eigenvalue  π =  3.192 15

Algebraic connectivity  a =  0.085 875 0

Spectral separation  λ_{1}[A] / λ_{2}[A] =  1.138 15

Reciprocity  y =  0.071 345 9

Nonbipartivity  b_{A} =  0.652 749

Normalized nonbipartivity  b_{N} =  0.051 195 9

Algebraic nonbipartivity  χ =  0.086 281 2

Spectral bipartite frustration  b_{K} =  0.002 148 26

Negativity  ζ =  0.419 222

Algebraic conflict  ξ =  0.076 742 9

Triadic conflict  τ =  0.493 546

Spectral signed frustration  φ =  0.001 957 64

Controllability  C =  1,465

Relative controllability  C_{r} =  0.214 495

Plots
Matrix decompositions plots
Downloads
References
[1]

Jérôme Kunegis.
KONECT – The Koblenz Network Collection.
In Proc. Int. Conf. on World Wide Web Companion, pages
1343–1350, 2013.
[ http ]
