Gnutella (25)
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 25, 2002.
Metadata
Statistics
Size  n =  22,687

Volume  m =  54,705

Loop count  l =  0

Wedge count  s =  533,121

Claw count  z =  2,358,958

Cross count  x =  10,118,599

Triangle count  t =  806

Square count  q =  13,517

4Tour count  T_{4} =  2,350,030

Maximum degree  d_{max} =  66

Maximum outdegree  d^{+}_{max} =  64

Maximum indegree  d^{−}_{max} =  36

Average degree  d =  4.822 59

Fill  p =  0.000 106 290

Size of LCC  N =  22,663

Size of LSCC  N_{s} =  5,153

Relative size of LSCC  N^{r}_{s} =  0.227 134

Diameter  δ =  11

50Percentile effective diameter  δ_{0.5} =  5.140 93

90Percentile effective diameter  δ_{0.9} =  6.548 47

Median distance  δ_{M} =  6

Mean distance  δ_{m} =  5.615 42

Gini coefficient  G =  0.541 804

Balanced inequality ratio  P =  0.270 259

Outdegree balanced inequality ratio  P_{+} =  0.458 496

Indegree balanced inequality ratio  P_{−} =  0.338 086

Relative edge distribution entropy  H_{er} =  0.948 837

Power law exponent  γ =  1.993 94

Tail power law exponent  γ_{t} =  7.121 00

Tail power law exponent with p  γ_{3} =  7.121 00

pvalue  p =  0.133 000

Outdegree tail power law exponent with p  γ_{3,o} =  2.851 00

Outdegree pvalue  p_{o} =  0.704 000

Indegree tail power law exponent with p  γ_{3,i} =  5.221 00

Indegree pvalue  p_{i} =  0.622 000

Degree assortativity  ρ =  −0.172 839

Degree assortativity pvalue  p_{ρ} =  0.000 00

In/outdegree correlation  ρ^{±} =  +0.255 514

Clustering coefficient  c =  0.004 535 56

Directed clustering coefficient  c^{±} =  0.004 200 65

Spectral norm  α =  10.920 0

Operator 2norm  ν =  8.542 71

Cyclic eigenvalue  π =  3.402 93

Algebraic connectivity  a =  0.054 799 7

Reciprocity  y =  0.000 00

Nonbipartivity  b_{A} =  0.148 457

Normalized nonbipartivity  b_{N} =  0.028 354 6

Spectral bipartite frustration  b_{K} =  0.002 835 27

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.
