MovieLens user–item
This bipartite network consists of 72,000 users who applied tags to 10,000
movies from http://movielens.umn.edu/. Left nodes represent users and right
nodes represent movies. An edge connects a user with a movie he has assigned a
tag to.
Metadata
Statistics
Size  n =  11,610

Left size  n_{1} =  4,009

Right size  n_{2} =  7,601

Volume  m =  95,580

Unique edge count  m̿ =  55,484

Wedge count  s =  10,527,036

Claw count  z =  3,111,884,288

Cross count  x =  940,679,536,237

Square count  q =  7,490,391

4Tour count  T_{4} =  102,152,360

Maximum degree  d_{max} =  6,012

Maximum left degree  d_{1max} =  6,012

Maximum right degree  d_{2max} =  308

Average degree  d =  16.465 1

Average left degree  d_{1} =  23.841 4

Average right degree  d_{2} =  12.574 7

Fill  p =  0.001 820 79

Average edge multiplicity  m̃ =  1.722 66

Size of LCC  N =  11,557

Diameter  δ =  9

50Percentile effective diameter  δ_{0.5} =  3.304 04

90Percentile effective diameter  δ_{0.9} =  4.618 16

Median distance  δ_{M} =  4

Mean distance  δ_{m} =  3.768 25

Gini coefficient  G =  0.746 738

Balanced inequality ratio  P =  0.209 128

Left balanced inequality ratio  P_{1} =  0.125 811

Right balanced inequality ratio  P_{2} =  0.250 983

Relative edge distribution entropy  H_{er} =  0.849 226

Power law exponent  γ =  1.817 63

Tail power law exponent  γ_{t} =  2.401 00

Tail power law exponent with p  γ_{3} =  2.401 00

pvalue  p =  0.929 000

Left tail power law exponent with p  γ_{3,1} =  1.651 00

Left pvalue  p_{1} =  0.000 00

Right tail power law exponent with p  γ_{3,2} =  3.321 00

Right pvalue  p_{2} =  0.002 000 00

Degree assortativity  ρ =  −0.221 845

Degree assortativity pvalue  p_{ρ} =  0.000 00

Spectral norm  α =  307.003

Algebraic connectivity  a =  0.176 189

Spectral separation  λ_{1}[A] / λ_{2}[A] =  1.279 70

Controllability  C =  5,981

Relative controllability  C_{r} =  0.515 159

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 ]

[2]

GroupLens Research.
MovieLens data sets.
http://www.grouplens.org/node/73, October 2006.
