Gnutella (08)
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 08, 2002.
Metadata
Statistics
Size  n =  6,301

Volume  m =  20,777

Loop count  l =  0

Wedge count  s =  346,033

Claw count  z =  4,859,306

Cross count  x =  82,247,965

Triangle count  t =  2,383

Square count  q =  87,885

4Tour count  T_{4} =  2,128,766

Maximum degree  d_{max} =  97

Maximum outdegree  d^{+}_{max} =  48

Maximum indegree  d^{−}_{max} =  91

Average degree  d =  6.594 83

Fill  p =  0.000 523 399

Size of LCC  N =  6,299

Size of LSCC  N_{s} =  2,068

Relative size of LSCC  N^{r}_{s} =  0.328 202

Diameter  δ =  9

50Percentile effective diameter  δ_{0.5} =  4.239 68

90Percentile effective diameter  δ_{0.9} =  5.505 27

Median distance  δ_{M} =  5

Mean distance  δ_{m} =  4.698 13

Gini coefficient  G =  0.524 081

Balanced inequality ratio  P =  0.301 800

Outdegree balanced inequality ratio  P_{+} =  0.449 439

Indegree balanced inequality ratio  P_{−} =  0.312 798

Relative edge distribution entropy  H_{er} =  0.940 926

Power law exponent  γ =  1.753 74

Tail power law exponent  γ_{t} =  4.741 00

Tail power law exponent with p  γ_{3} =  4.741 00

pvalue  p =  0.000 00

Outdegree tail power law exponent with p  γ_{3,o} =  3.251 00

Outdegree pvalue  p_{o} =  0.314 000

Indegree tail power law exponent with p  γ_{3,i} =  2.841 00

Indegree pvalue  p_{i} =  0.000 00

Degree assortativity  ρ =  +0.035 550 4

Degree assortativity pvalue  p_{ρ} =  4.200 30 × 10^{−13}

In/outdegree correlation  ρ^{±} =  +0.139 852

Clustering coefficient  c =  0.020 659 9

Directed clustering coefficient  c^{±} =  0.024 736 2

Spectral norm  α =  28.375 5

Operator 2norm  ν =  23.950 8

Cyclic eigenvalue  π =  5.119 29

Algebraic connectivity  a =  0.073 895 5

Spectral separation  λ_{1}[A] / λ_{2}[A] =  1.382 34

Reciprocity  y =  0.000 00

Nonbipartivity  b_{A} =  0.276 591

Normalized nonbipartivity  b_{N} =  0.040 345 9

Algebraic nonbipartivity  χ =  0.073 763 8

Spectral bipartite frustration  b_{K} =  0.002 795 52

Controllability  C =  4,107

Relative controllability  C_{r} =  0.651 801

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.
