CAIDA
This is the undirected network of autonomous systems of the Internet connected
with each other from the CAIDA project, collected in 2007. Nodes are autonomous
systems (AS), and edges denote communication.
Metadata
Statistics
Size  n =  26,475

Volume  m =  53,381

Loop count  l =  0

Wedge count  s =  14,906,270

Claw count  z =  7,839,606,991

Cross count  x =  3,916,793,044,776

Triangle count  t =  36,365

Square count  q =  2,287,349

4Tour count  T_{4} =  78,030,634

Maximum degree  d_{max} =  2,628

Average degree  d =  4.032 56

Fill  p =  0.000 152 321

Size of LCC  N =  26,475

Diameter  δ =  17

50Percentile effective diameter  δ_{0.5} =  3.407 07

90Percentile effective diameter  δ_{0.9} =  4.636 96

Median distance  δ_{M} =  4

Mean distance  δ_{m} =  3.912 47

Gini coefficient  G =  0.628 058

Balanced inequality ratio  P =  0.268 963

Relative edge distribution entropy  H_{er} =  0.838 051

Power law exponent  γ =  2.508 65

Tail power law exponent  γ_{t} =  2.091 00

Tail power law exponent with p  γ_{3} =  2.091 00

pvalue  p =  0.733 000

Degree assortativity  ρ =  −0.194 646

Degree assortativity pvalue  p_{ρ} =  0.000 00

Clustering coefficient  c =  0.007 318 73

Spectral norm  α =  69.643 4

Algebraic connectivity  a =  0.020 436 8

Spectral separation  λ_{1}[A] / λ_{2}[A] =  1.235 74

Nonbipartivity  b_{A} =  0.190 767

Normalized nonbipartivity  b_{N} =  0.011 209 8

Algebraic nonbipartivity  χ =  0.020 451 8

Spectral bipartite frustration  b_{K} =  0.001 267 92

Controllability  C =  19,127

Relative controllability  C_{r} =  0.722 455

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, Jon Kleinberg, and Christos Faloutsos.
Graph evolution: Densification and shrinking diameters.
ACM Trans. Knowl. Discov. from Data, 1(1):1–40, 2007.
