Gnutella (24)
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 24, 2002.
Metadata
Statistics
Size  n =  26,518

Volume  m =  65,369

Loop count  l =  0

Wedge count  s =  721,206

Claw count  z =  10,489,472

Cross count  x =  665,822,688

Triangle count  t =  986

Square count  q =  8,794

4Tour count  T_{4} =  3,085,914

Maximum degree  d_{max} =  355

Maximum outdegree  d^{+}_{max} =  79

Maximum indegree  d^{−}_{max} =  355

Average degree  d =  4.930 16

Fill  p =  9.296 23 × 10^{−5}

Size of LCC  N =  26,498

Size of LSCC  N_{s} =  6,352

Relative size of LSCC  N^{r}_{s} =  0.239 535

Diameter  δ =  11

50Percentile effective diameter  δ_{0.5} =  5.094 74

90Percentile effective diameter  δ_{0.9} =  6.320 12

Median distance  δ_{M} =  6

Mean distance  δ_{m} =  5.531 11

Gini coefficient  G =  0.546 890

Balanced inequality ratio  P =  0.272 759

Outdegree balanced inequality ratio  P_{+} =  0.449 326

Indegree balanced inequality ratio  P_{−} =  0.333 384

Relative edge distribution entropy  H_{er} =  0.948 052

Power law exponent  γ =  1.985 92

Tail power law exponent  γ_{t} =  6.271 00

Tail power law exponent with p  γ_{3} =  6.271 00

pvalue  p =  0.000 00

Outdegree tail power law exponent with p  γ_{3,o} =  2.571 00

Outdegree pvalue  p_{o} =  0.065 000 0

Indegree tail power law exponent with p  γ_{3,i} =  5.121 00

Indegree pvalue  p_{i} =  0.150 000

Degree assortativity  ρ =  −0.007 728 27

Degree assortativity pvalue  p_{ρ} =  0.005 199 95

In/outdegree correlation  ρ^{±} =  +0.292 007

Clustering coefficient  c =  0.004 101 46

Directed clustering coefficient  c^{±} =  0.004 049 56

Spectral norm  α =  19.585 1

Operator 2norm  ν =  19.116 0

Cyclic eigenvalue  π =  3.545 78

Algebraic connectivity  a =  0.122 096

Reciprocity  y =  0.000 00

Nonbipartivity  b_{A} =  0.026 316 2

Normalized nonbipartivity  b_{N} =  0.065 985 4

Spectral bipartite frustration  b_{K} =  0.006 184 77

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.
