Internet topology
This is the network of connections between autonomous systems of the Internet.
The nodes are autonomous systems (AS), i.e. collections of connected IP routing
prefixes controlled by independent network operators. Edges are connections
between autonomous systems. Multiple edges may connect two nodes, each
representing an individual connection in time. Edges are annotated with the
timepoint of the connection.
Metadata
Statistics
Size  n =  34,761

Volume  m =  171,403

Unique edge count  m̿ =  114,496

Loop count  l =  0

Wedge count  s =  34,304,301

Claw count  z =  20,603,857,222

Cross count  x =  10,997,020,148,941

Triangle count  t =  554,749

Square count  q =  79,912,964

4Tour count  T_{4} =  776,736,356

Maximum degree  d_{max} =  5,305

Average degree  d =  9.861 80

Fill  p =  0.000 189 517

Average edge multiplicity  m̃ =  1.497 02

Size of LCC  N =  34,761

Diameter  δ =  10

50Percentile effective diameter  δ_{0.5} =  3.304 83

90Percentile effective diameter  δ_{0.9} =  4.372 41

Median distance  δ_{M} =  4

Mean distance  δ_{m} =  3.783 62

Gini coefficient  G =  0.808 028

Balanced inequality ratio  P =  0.164 131

Relative edge distribution entropy  H_{er} =  0.807 662

Power law exponent  γ =  2.233 38

Tail power law exponent  γ_{t} =  1.921 00

Tail power law exponent with p  γ_{3} =  1.921 00

pvalue  p =  0.000 00

Degree assortativity  ρ =  −0.214 867

Degree assortativity pvalue  p_{ρ} =  0.000 00

Clustering coefficient  c =  0.048 514 2

Spectral norm  α =  425.817

Algebraic connectivity  a =  0.044 087 6

Spectral separation  λ_{1}[A] / λ_{2}[A] =  2.341 89

Nonbipartivity  b_{A} =  0.586 838

Normalized nonbipartivity  b_{N} =  0.016 724 9

Algebraic nonbipartivity  χ =  0.032 772 5

Spectral bipartite frustration  b_{K} =  0.001 321 95

Controllability  C =  24,439

Relative controllability  C_{r} =  0.703 058

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]

Beichuan Zhang, Raymond Liu, Daniel Massey, and Lixia Zhang.
Collecting the Internet ASlevel topology.
SIGCOMM Comput. Communication Review, 35(1):53–61, 2005.
