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 co-purchased with product B

Metadata

CodeAm
Internal nameamazon0505
NameAmazon (TWEB, 0505)
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 =410,236
Volume m =3,356,824
Loop count l =0
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
4-Tour count T4 =580,856,454
Maximum degree dmax =2,770
Maximum outdegree d+max =10
Maximum indegree dmax =2,760
Average degree d =16.365 3
Fill p =1.994 63 × 10−5
Size of LCC N =410,236
Size of LSCC Ns =390,304
Relative size of LSCC Nrs =0.951 413
Diameter δ =22
50-Percentile effective diameter δ0.5 =5.873 77
90-Percentile effective diameter δ0.9 =7.598 41
Median distance δM =6
Mean distance δm =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 Her =0.981 321
Power law exponent γ =1.456 63
Tail power law exponent γt =3.131 00
Degree assortativity ρ =−0.016 877 6
Degree assortativity p-value pρ =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 2-norm ν =56.511 3
Cyclic eigenvalue π =10.000 0
Algebraic connectivity a =0.011 075 2
Reciprocity y =0.546 580
Non-bipartivity bA =0.086 984 5
Normalized non-bipartivity bN =0.030 406 0
Algebraic non-bipartivity χ =0.055 096 0
Spectral bipartite frustration bK =0.001 158 18

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.