Gnutella (05)
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 05, 2002.
Metadata
Statistics
Size  n =  8,846

Volume  m =  31,839

Loop count  l =  0

Wedge count  s =  439,066

Claw count  z =  4,075,019

Cross count  x =  52,261,084

Triangle count  t =  1,112

Square count  q =  64,998

4Tour count  T_{4} =  2,339,926

Maximum degree  d_{max} =  88

Maximum outdegree  d^{+}_{max} =  65

Maximum indegree  d^{−}_{max} =  79

Average degree  d =  7.198 51

Fill  p =  0.000 406 925

Size of LCC  N =  8,842

Size of LSCC  N_{s} =  3,234

Relative size of LSCC  N^{r}_{s} =  0.365 589

Diameter  δ =  9

50Percentile effective diameter  δ_{0.5} =  4.268 01

90Percentile effective diameter  δ_{0.9} =  5.467 91

Median distance  δ_{M} =  5

Mean distance  δ_{m} =  4.720 30

Gini coefficient  G =  0.479 385

Balanced inequality ratio  P =  0.318 776

Outdegree balanced inequality ratio  P_{+} =  0.439 116

Indegree balanced inequality ratio  P_{−} =  0.320 079

Relative edge distribution entropy  H_{er} =  0.955 072

Power law exponent  γ =  1.673 51

Tail power law exponent  γ_{t} =  4.641 00

Tail power law exponent with p  γ_{3} =  4.641 00

pvalue  p =  0.000 00

Outdegree tail power law exponent with p  γ_{3,o} =  4.241 00

Outdegree pvalue  p_{o} =  0.600 000

Indegree tail power law exponent with p  γ_{3,i} =  3.291 00

Indegree pvalue  p_{i} =  0.008 000 00

Degree assortativity  ρ =  +0.014 622 6

Degree assortativity pvalue  p_{ρ} =  0.000 224 194

In/outdegree correlation  ρ^{±} =  +0.091 741 3

Clustering coefficient  c =  0.007 597 95

Directed clustering coefficient  c^{±} =  0.007 888 77

Spectral norm  α =  23.549 9

Operator 2norm  ν =  21.420 5

Cyclic eigenvalue  π =  4.356 91

Algebraic connectivity  a =  0.200 163

Reciprocity  y =  0.000 00

Nonbipartivity  b_{A} =  0.122 850

Normalized nonbipartivity  b_{N} =  0.109 553

Algebraic nonbipartivity  χ =  0.199 937

Spectral bipartite frustration  b_{K} =  0.006 940 99

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.
