Gnutella (30)
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 30, 2002.
Metadata
Statistics
Size  n =  36,682

Volume  m =  88,328

Loop count  l =  0

Wedge count  s =  923,756

Claw count  z =  4,477,812

Cross count  x =  19,735,194

Triangle count  t =  1,590

Square count  q =  46,363

4Tour count  T_{4} =  4,242,584

Maximum degree  d_{max} =  55

Maximum outdegree  d^{+}_{max} =  54

Maximum indegree  d^{−}_{max} =  54

Average degree  d =  4.815 88

Fill  p =  6.564 54 × 10^{−5}

Size of LCC  N =  36,646

Size of LSCC  N_{s} =  8,490

Relative size of LSCC  N^{r}_{s} =  0.231 449

Diameter  δ =  11

50Percentile effective diameter  δ_{0.5} =  5.456 36

90Percentile effective diameter  δ_{0.9} =  6.691 63

Median distance  δ_{M} =  6

Mean distance  δ_{m} =  5.898 38

Gini coefficient  G =  0.558 875

Balanced inequality ratio  P =  0.264 050

Outdegree balanced inequality ratio  P_{+} =  0.462 571

Indegree balanced inequality ratio  P_{−} =  0.331 129

Relative edge distribution entropy  H_{er} =  0.947 124

Power law exponent  γ =  2.035 68

Tail power law exponent  γ_{t} =  4.901 00

Tail power law exponent with p  γ_{3} =  4.901 00

pvalue  p =  0.000 00

Outdegree tail power law exponent with p  γ_{3,o} =  4.331 00

Outdegree pvalue  p_{o} =  0.012 000 0

Indegree tail power law exponent with p  γ_{3,i} =  6.551 00

Indegree pvalue  p_{i} =  0.323 000

Degree assortativity  ρ =  −0.103 375

Degree assortativity pvalue  p_{ρ} =  0.000 00

In/outdegree correlation  ρ^{±} =  +0.303 441

Clustering coefficient  c =  0.005 163 70

Directed clustering coefficient  c^{±} =  0.004 631 62

Spectral norm  α =  12.928 7

Operator 2norm  ν =  9.985 77

Cyclic eigenvalue  π =  3.874 98

Algebraic connectivity  a =  0.114 640

Spectral separation  λ_{1}[A] / λ_{2}[A] =  1.199 09

Reciprocity  y =  0.000 00

Nonbipartivity  b_{A} =  0.166 035

Normalized nonbipartivity  b_{N} =  0.061 233 1

Algebraic nonbipartivity  χ =  0.114 605

Spectral bipartite frustration  b_{K} =  0.005 945 19

Controllability  C =  26,966

Relative controllability  C_{r} =  0.735 129

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.
