Amazon (TWEB, 0601)
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 =  403,394

Volume  m =  3,387,388

Loop count  l =  0

Wedge count  s =  72,209,687

Claw count  z =  12,017,835,784

Cross count  x =  5,733,485,265,257

Triangle count  t =  3,986,507

Square count  q =  35,661,461

4Tour count  T_{4} =  579,017,252

Maximum degree  d_{max} =  2,761

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

Maximum indegree  d^{−}_{max} =  2,751

Average degree  d =  16.794 4

Fill  p =  2.081 65 × 10^{−5}

Size of LCC  N =  403,364

Size of LSCC  N_{s} =  395,234

Relative size of LSCC  N^{r}_{s} =  0.979 772

Diameter  δ =  25

50Percentile effective diameter  δ_{0.5} =  5.827 57

90Percentile effective diameter  δ_{0.9} =  7.432 42

Mean distance  δ_{m} =  6.364 93

Gini coefficient  G =  0.331 309

Balanced inequality ratio  P =  0.385 962

Outdegree balanced inequality ratio  P_{+} =  0.453 496

Indegree balanced inequality ratio  P_{−} =  0.307 625

Relative edge distribution entropy  H_{er} =  0.982 804

Power law exponent  γ =  1.447 39

Tail power law exponent  γ_{t} =  3.151 00

Degree assortativity  ρ =  −0.017 647 3

Degree assortativity pvalue  p_{ρ} =  0.000 00

In/outdegree correlation  ρ^{±} =  +0.527 578

Clustering coefficient  c =  0.165 622

Spectral norm  α =  58.957 8

Operator 2norm  ν =  55.621 4

Cyclic eigenvalue  π =  10.000 0

Algebraic connectivity  a =  0.005 446 60

Spectral separation  λ_{1}[A] / λ_{2}[A] =  1.089 28

Reciprocity  y =  0.557 350

Nonbipartivity  b_{A} =  0.081 961 5

Normalized nonbipartivity  b_{N} =  0.035 629 1

Spectral bipartite frustration  b_{K} =  0.001 310 62

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.
