Amazon (TWEB, 0302)
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 =  262,111

Volume  m =  1,234,877

Wedge count  s =  9,120,350

Claw count  z =  179,870,447

Cross count  x =  7,684,700,994

Triangle count  t =  717,719

4Tour count  T_{4} =  58,097,680

Maximum degree  d_{max} =  425

Maximum outdegree  d^{+}_{max} =  5

Maximum indegree  d^{−}_{max} =  420

Average degree  d =  9.422 55

Size of LCC  N =  262,111

Size of LSCC  N_{s} =  241,761

Relative size of LSCC  N^{r}_{s} =  0.922 361

Diameter  δ =  38

50Percentile effective diameter  δ_{0.5} =  8.062 96

90Percentile effective diameter  δ_{0.9} =  10.312 3

Median distance  δ_{M} =  9

Mean distance  δ_{m} =  8.607 23

Gini coefficient  G =  0.244 370

Balanced inequality ratio  P =  0.412 963

Outdegree balanced inequality ratio  P_{+} =  0.488 977

Indegree balanced inequality ratio  P_{−} =  0.338 093

Relative edge distribution entropy  H_{er} =  0.990 128

Power law exponent  γ =  1.558 15

Tail power law exponent  γ_{t} =  3.681 00

Tail power law exponent with p  γ_{3} =  3.681 00

pvalue  p =  0.000 00

Outdegree tail power law exponent with p  γ_{3,o} =  4.061 00

Outdegree pvalue  p_{o} =  0.000 00

Indegree tail power law exponent with p  γ_{3,i} =  3.381 00

Indegree pvalue  p_{i} =  0.971 000

Degree assortativity  ρ =  −0.002 479 34

Degree assortativity pvalue  p_{ρ} =  0.000 881 004

In/outdegree correlation  ρ^{±} =  +0.246 615

Clustering coefficient  c =  0.236 083

Spectral norm  α =  24.642 3

Operator 2norm  ν =  21.218 1

Cyclic eigenvalue  π =  5.000 00

Algebraic connectivity  a =  0.002 533 67

Reciprocity  y =  0.542 702

Nonbipartivity  b_{A} =  0.185 757

Normalized nonbipartivity  b_{N} =  0.038 117 4

Spectral bipartite frustration  b_{K} =  0.002 439 56

Controllability  C =  19,530

Relative controllability  C_{r} =  0.074 510 4

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.
