Gnutella (31)
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 31, 2002.
Metadata
Statistics
Size  n =  62,586

Volume  m =  147,892

Loop count  l =  0

Wedge count  s =  1,568,174

Claw count  z =  8,171,989

Cross count  x =  43,841,182

Triangle count  t =  2,024

Square count  q =  42,466

4Tour count  T_{4} =  6,908,208

Maximum degree  d_{max} =  95

Maximum outdegree  d^{+}_{max} =  78

Maximum indegree  d^{−}_{max} =  68

Average degree  d =  4.726 04

Fill  p =  3.775 70 × 10^{−5}

Size of LCC  N =  62,561

Size of LSCC  N_{s} =  14,149

Relative size of LSCC  N^{r}_{s} =  0.226 073

Diameter  δ =  11

50Percentile effective diameter  δ_{0.5} =  5.479 36

90Percentile effective diameter  δ_{0.9} =  6.751 31

Median distance  δ_{M} =  6

Mean distance  δ_{m} =  5.956 53

Gini coefficient  G =  0.562 578

Balanced inequality ratio  P =  0.263 936

Outdegree balanced inequality ratio  P_{+} =  0.455 637

Indegree balanced inequality ratio  P_{−} =  0.330 897

Relative edge distribution entropy  H_{er} =  0.948 442

Power law exponent  γ =  2.062 94

Tail power law exponent  γ_{t} =  4.831 00

Tail power law exponent with p  γ_{3} =  4.831 00

pvalue  p =  0.000 00

Outdegree tail power law exponent with p  γ_{3,o} =  6.051 00

Outdegree pvalue  p_{o} =  0.713 000

Indegree tail power law exponent with p  γ_{3,i} =  5.561 00

Indegree pvalue  p_{i} =  0.210 000

Degree assortativity  ρ =  −0.092 557 8

Degree assortativity pvalue  p_{ρ} =  0.000 00

In/outdegree correlation  ρ^{±} =  +0.288 763

Clustering coefficient  c =  0.003 872 02

Directed clustering coefficient  c^{±} =  0.003 653 97

Spectral norm  α =  13.181 2

Operator 2norm  ν =  10.896 2

Cyclic eigenvalue  π =  3.659 28

Algebraic connectivity  a =  0.113 127

Spectral separation  λ_{1}[A] / λ_{2}[A] =  1.137 32

Reciprocity  y =  0.000 00

Nonbipartivity  b_{A} =  0.120 738

Normalized nonbipartivity  b_{N} =  0.059 887 0

Algebraic nonbipartivity  χ =  0.113 103

Spectral bipartite frustration  b_{K} =  0.005 981 14

Controllability  C =  46,227

Relative controllability  C_{r} =  0.738 616

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.
