Amazon (TWEB, 0505)
This is the network of items on Amazon that have been mentioned by Amazon's
"People who bought X also bought Y" function. Nodes in the network are
products, and a directed edge from A to B denotes that product A is frequently
copurchased with product B
Metadata
Statistics
Size  n =  410,236

Volume  m =  3,356,824

Wedge count  s =  73,010,387

Claw count  z =  13,066,960,840

Cross count  x =  6,535,362,358,695

Triangle count  t =  3,951,063

Square count  q =  35,492,004

4Tour count  T_{4} =  580,856,454

Maximum degree  d_{max} =  2,770

Maximum outdegree  d^{+}_{max} =  10

Maximum indegree  d^{−}_{max} =  2,760

Average degree  d =  16.365 3

Fill  p =  1.994 63 × 10^{−5}

Size of LCC  N =  410,236

Diameter  δ =  22

50Percentile effective diameter  δ_{0.5} =  5.873 77

90Percentile effective diameter  δ_{0.9} =  7.598 41

Median distance  δ_{M} =  6

Mean distance  δ_{m} =  6.445 36

Gini coefficient  G =  0.345 933

Balanced inequality ratio  P =  0.381 900

Outdegree balanced inequality ratio  P_{+} =  0.456 242

Indegree balanced inequality ratio  P_{−} =  0.300 735

Relative edge distribution entropy  H_{er} =  0.981 321

Power law exponent  γ =  1.456 63

Tail power law exponent  γ_{t} =  3.131 00

Tail power law exponent with p  γ_{3} =  3.131 00

pvalue  p =  0.344 000

Outdegree tail power law exponent with p  γ_{3,o} =  1.601 00

Outdegree pvalue  p_{o} =  0.000 00

Indegree tail power law exponent with p  γ_{3,i} =  3.041 00

Indegree pvalue  p_{i} =  0.260 000

Degree assortativity  ρ =  −0.016 877 6

Degree assortativity pvalue  p_{ρ} =  0.000 00

In/outdegree correlation  ρ^{±} =  +0.516 865

Clustering coefficient  c =  0.162 349

Directed clustering coefficient  c^{±} =  0.376 872

Spectral norm  α =  60.055 2

Operator 2norm  ν =  56.511 3

Cyclic eigenvalue  π =  10.000 0

Algebraic connectivity  a =  0.011 075 2

Spectral separation  λ_{1}[A] / λ_{2}[A] =  1.095 27

Reciprocity  y =  0.546 580

Nonbipartivity  b_{A} =  0.086 984 5

Normalized nonbipartivity  b_{N} =  0.030 406 0

Algebraic nonbipartivity  χ =  0.055 096 0

Spectral bipartite frustration  b_{K} =  0.001 158 18

Controllability  C =  28,515

Relative controllability  C_{r} =  0.069 508 8

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]

Jure Leskovec, Lada A. Adamic, and Bernardo A. Huberman.
The dynamics of viral marketing.
ACM Trans. on the Web, 1(1), 2007.
