Amazon (TWEB, 0312)

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 nameamazon0312
NameAmazon (TWEB, 0312)
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 =400,727
Volume m =3,200,440
Loop count l =0
Wedge count s =68,910,455
Claw count z =11,384,145,457
Cross count x =5,194,846,371,818
Triangle count t =3,686,467
Square count q =32,229,022
4-Tour count T4 =538,173,734
Maximum degree dmax =2,757
Maximum outdegree d+max =10
Maximum indegree dmax =2,747
Average degree d =15.973 2
Fill p =1.993 03 × 10−5
Size of LCC N =400,727
Size of LSCC Ns =380,167
Relative size of LSCC Nrs =0.948 693
Diameter δ =20
50-Percentile effective diameter δ0.5 =5.923 42
90-Percentile effective diameter δ0.9 =7.694 74
Median distance δM =6
Mean distance δm =6.485 28
Gini coefficient G =0.339 932
Balanced inequality ratio P =0.381 034
Outdegree balanced inequality ratio P+ =0.447 854
Indegree balanced inequality ratio P =0.301 316
Relative edge distribution entropy Her =0.981 791
Power law exponent γ =1.457 51
Tail power law exponent γt =3.141 00
Degree assortativity ρ =−0.020 251 1
Degree assortativity p-value pρ =0.000 00
In/outdegree correlation ρ± =+0.460 073
Clustering coefficient c =0.160 489
Directed clustering coefficient c± =0.387 446
Spectral norm α =57.466 9
Operator 2-norm ν =54.945 9
Cyclic eigenvalue π =10.000 0
Algebraic connectivity a =0.021 646 5
Reciprocity y =0.531 534
Non-bipartivity bA =0.066 845 6
Normalized non-bipartivity bN =0.036 611 5
Algebraic non-bipartivity χ =0.063 564 7
Spectral bipartite frustration bK =0.001 354 97

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

SynGraphy

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.