Gnutella (06)
This is a network of Gnutella hosts from 2002. The nodes represent Gnutella
hosts, and the directed edges represent connections between them. The dataset
is from August 06, 2002.
Metadata
Statistics
Size  n =  8,717

Volume  m =  31,525

Loop count  l =  0

Wedge count  s =  422,567

Claw count  z =  3,435,901

Cross count  x =  37,997,204

Triangle count  t =  1,142

Square count  q =  90,764

4Tour count  T_{4} =  2,479,430

Maximum degree  d_{max} =  115

Maximum outdegree  d^{+}_{max} =  113

Maximum indegree  d^{−}_{max} =  64

Average degree  d =  7.232 99

Fill  p =  0.000 414 926

Size of LCC  N =  8,717

Size of LSCC  N_{s} =  3,226

Relative size of LSCC  N^{r}_{s} =  0.370 081

Diameter  δ =  10

50Percentile effective diameter  δ_{0.5} =  4.239 78

90Percentile effective diameter  δ_{0.9} =  5.502 86

Median distance  δ_{M} =  5

Mean distance  δ_{m} =  4.708 66

Gini coefficient  G =  0.479 743

Balanced inequality ratio  P =  0.319 730

Outdegree balanced inequality ratio  P_{+} =  0.447 835

Indegree balanced inequality ratio  P_{−} =  0.316 987

Relative edge distribution entropy  H_{er} =  0.955 378

Power law exponent  γ =  1.673 37

Tail power law exponent  γ_{t} =  4.621 00

Tail power law exponent with p  γ_{3} =  4.621 00

pvalue  p =  0.000 00

Outdegree tail power law exponent with p  γ_{3,o} =  2.621 00

Outdegree pvalue  p_{o} =  0.500 000

Indegree tail power law exponent with p  γ_{3,i} =  3.311 00

Indegree pvalue  p_{i} =  0.018 000 0

Degree assortativity  ρ =  +0.051 569 4

Degree assortativity pvalue  p_{ρ} =  2.135 94 × 10^{−38}

In/outdegree correlation  ρ^{±} =  +0.108 984

Clustering coefficient  c =  0.008 107 59

Directed clustering coefficient  c^{±} =  0.008 110 16

Spectral norm  α =  22.377 9

Operator 2norm  ν =  19.328 0

Cyclic eigenvalue  π =  4.739 55

Algebraic connectivity  a =  0.183 650

Spectral separation  λ_{1}[A] / λ_{2}[A] =  1.166 58

Reciprocity  y =  0.000 00

Nonbipartivity  b_{A} =  0.172 952

Normalized nonbipartivity  b_{N} =  0.120 710

Algebraic nonbipartivity  χ =  0.183 577

Spectral bipartite frustration  b_{K} =  0.006 345 13

Controllability  C =  5,035

Relative controllability  C_{r} =  0.577 607

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]

Matei Ripeanu, Ian Foster, and Adriana Iamnitchi.
Mapping the Gnutella network: Properties of largescale
peertopeer systems and implications for system design.
IEEE Internet Comput. J., 6, 2002.
