Facebook
The is the directed network of a small subset of posts to other user's wall on
Facebook. The nodes of the network are Facebook users, and each directed edge
represents one post, linking the users writing a post to the users whose wall
the post is written on. Since users may write multiple posts on a wall, the
network allows multiple edges connecting a single node pair. Since users may
write on their own wall, the network contains loops.
Metadata
Statistics
Size  n =  46,952

Volume  m =  876,993

Unique edge count  m̿ =  274,086

Loop count  l =  21,451

Wedge count  s =  4,331,017

Claw count  z =  221,524,187

Cross count  x =  6,265,197,027

Triangle count  t =  122,852

Square count  q =  1,265,222

4Tour count  T_{4} =  27,812,668

Maximum degree  d_{max} =  2,696

Maximum outdegree  d^{+}_{max} =  1,430

Maximum indegree  d^{−}_{max} =  1,428

Average degree  d =  37.357 0

Fill  p =  0.000 124 331

Average edge multiplicity  m̃ =  3.199 70

Size of LCC  N =  43,953

Size of LSCC  N_{s} =  30,793

Relative size of LSCC  N^{r}_{s} =  0.655 840

Diameter  δ =  18

50Percentile effective diameter  δ_{0.5} =  5.192 22

90Percentile effective diameter  δ_{0.9} =  6.835 71

Median distance  δ_{M} =  6

Mean distance  δ_{m} =  5.711 18

Gini coefficient  G =  0.734 791

Balanced inequality ratio  P =  0.207 820

Outdegree balanced inequality ratio  P_{+} =  0.219 194

Indegree balanced inequality ratio  P_{−} =  0.213 269

Relative edge distribution entropy  H_{er} =  0.938 798

Power law exponent  γ =  1.704 87

Tail power law exponent  γ_{t} =  4.431 00

Tail power law exponent with p  γ_{3} =  4.431 00

pvalue  p =  0.010 000 0

Outdegree tail power law exponent with p  γ_{3,o} =  4.751 00

Outdegree pvalue  p_{o} =  0.000 00

Indegree tail power law exponent with p  γ_{3,i} =  3.691 00

Indegree pvalue  p_{i} =  0.000 00

Degree assortativity  ρ =  +0.219 968

Degree assortativity pvalue  p_{ρ} =  0.000 00

In/outdegree correlation  ρ^{±} =  +0.737 949

Clustering coefficient  c =  0.085 096 9

Directed clustering coefficient  c^{±} =  0.082 923 0

Spectral norm  α =  1,717.63

Operator 2norm  ν =  904.598

Cyclic eigenvalue  π =  856.606

Algebraic connectivity  a =  0.037 776 7

Spectral separation  λ_{1}[A] / λ_{2}[A] =  1.011 73

Reciprocity  y =  0.624 862

Nonbipartivity  b_{A} =  0.011 597 7

Normalized nonbipartivity  b_{N} =  0.029 854 5

Spectral bipartite frustration  b_{K} =  0.001 767 33

Controllability  C =  9,391

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]

Bimal Viswanath, Alan Mislove, Meeyoung Cha, and Krishna P. Gummadi.
On the evolution of user interaction in Facebook.
In Proc. Workshop on Online Soc. Netw., pages 37–42, 2009.
