Youtube friendships
This is the friendship network of the videosharing site Youtube. Nodes are
users and an undirected edge between two nodes indicates a friendship.
Metadata
Statistics
Size  n =  1,134,890

Volume  m =  2,987,624

Loop count  l =  0

Wedge count  s =  1,474,482,560

Claw count  z =  5,743,242,041,025

Cross count  x =  32,746,672,524,915,828

Triangle count  t =  3,056,386

Square count  q =  468,774,021

4Tour count  T_{4} =  9,654,097,656

Maximum degree  d_{max} =  28,754

Average degree  d =  5.265 05

Fill  p =  4.639 26 × 10^{−6}

Size of LCC  N =  1,134,890

Diameter  δ =  24

50Percentile effective diameter  δ_{0.5} =  4.860 22

90Percentile effective diameter  δ_{0.9} =  6.934 78

Median distance  δ_{M} =  5

Mean distance  δ_{m} =  5.548 06

Gini coefficient  G =  0.714 126

Balanced inequality ratio  P =  0.213 532

Relative edge distribution entropy  H_{er} =  0.877 112

Power law exponent  γ =  2.429 00

Tail power law exponent  γ_{t} =  2.141 00

Degree assortativity  ρ =  −0.036 909 9

Degree assortativity pvalue  p_{ρ} =  0.000 00

Clustering coefficient  c =  0.006 218 56

Spectral norm  α =  210.395

Spectral separation  λ_{1}[A] / λ_{2}[A] =  1.191 91

Nonbipartivity  b_{A} =  0.161 013

Normalized nonbipartivity  b_{N} =  0.002 045 96

Algebraic nonbipartivity  χ =  0.004 266 35

Spectral bipartite frustration  b_{K} =  0.000 202 579

Controllability  C =  588,233

Relative controllability  C_{r} =  0.518 317

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]

Jaewon Yang and Jure Leskovec.
Defining and evaluating network communities based on groundtruth.
In Proc. ACM SIGKDD Workshop on Min. Data Semant., page 3,
2012.
