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 co-purchased with product B

Metadata

CodeAm
Internal nameamazon0302
NameAmazon (TWEB, 0302)
Data sourcehttp://snap.stanford.edu/data/amazonDATE.html
AvailabilityDataset is not available for download
Consistency checkDataset passed all tests
Category
Miscellaneous network
Node meaningProduct
Edge meaningCo-purchase
Network formatUnipartite, directed
Edge typeUnweighted, no multiple edges
ReciprocalContains reciprocal edges
Directed cyclesContains directed cycles
LoopsDoes not contain loops

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
Square count q =2,477,087
4-Tour count T4 =58,097,680
Maximum degree dmax =425
Maximum outdegree d+max =5
Maximum indegree dmax =420
Average degree d =9.422 55
Fill p =1.797 44 × 10−5
Size of LCC N =262,111
Size of LSCC Ns =241,761
Relative size of LSCC Nrs =0.922 361
Diameter δ =38
50-Percentile effective diameter δ0.5 =8.062 96
90-Percentile effective diameter δ0.9 =10.312 3
Mean distance δm =8.607 23
Gini coefficient G =0.244 370
Relative edge distribution entropy Her =0.990 128
Power law exponent γ =1.558 15
Tail power law exponent γt =3.681 00
Tail power law exponent with p γ3 =3.681 00
p-value p =0.000 00
Outdegree tail power law exponent with p γ3,o =4.061 00
Outdegree p-value po =0.000 00
Indegree tail power law exponent with p γ3,i =3.381 00
Indegree p-value pi =0.962 000
Degree assortativity ρ =−0.002 479 34
Degree assortativity p-value pρ =0.000 881 004
In/outdegree correlation ρ± =+0.246 615
Clustering coefficient c =0.236 083
Spectral norm α =24.642 3
Operator 2-norm ν =21.218 1
Cyclic eigenvalue π =5.000 00
Algebraic connectivity a =0.002 533 67
Reciprocity y =0.542 702
Non-bipartivity bA =0.185 757
Normalized non-bipartivity bN =0.038 117 4
Spectral bipartite frustration bK =0.002 439 56

Plots

Degree distribution

Cumulative degree distribution

Lorenz curve

Spectral distribution of the adjacency matrix

Spectral distribution of the normalized adjacency matrix

Spectral distribution of the Laplacian

Spectral graph drawing based on the adjacency matrix

Spectral graph drawing based on the Laplacian

Spectral graph drawing based on the normalized adjacency matrix

Hop distribution

In/outdegree scatter plot

Clustering coefficient distribution

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.