Erdős
This is the coauthorship graph around Paul Erdős. The network is as of 2002,
and contains people who have, directly and indirectly, written papers with Paul
Erdős. This network is used to define the "Erdős number", i.e., the distance
between any node and Paul Erdős. This dataset was assembled by the Pajek
project; we do not know the extent of data that is included.
Metadata
Statistics
Size  n =  6,927

Volume  m =  11,850

Loop count  l =  0

Wedge count  s =  501,868

Claw count  z =  34,527,952

Cross count  x =  3,284,183,513

Triangle count  t =  5,973

Square count  q =  70,957

4Tour count  T_{4} =  2,598,828

Maximum degree  d_{max} =  507

Average degree  d =  3.421 39

Fill  p =  0.000 493 993

Size of LCC  N =  6,927

Diameter  δ =  4

50Percentile effective diameter  δ_{0.5} =  3.382 04

90Percentile effective diameter  δ_{0.9} =  3.876 41

Median distance  δ_{M} =  4

Mean distance  δ_{m} =  3.791 37

Gini coefficient  G =  0.646 025

Balanced inequality ratio  P =  0.239 916

Relative edge distribution entropy  H_{er} =  0.859 838

Power law exponent  γ =  3.227 63

Tail power law exponent  γ_{t} =  2.161 00

Tail power law exponent with p  γ_{3} =  2.161 00

pvalue  p =  0.000 00

Degree assortativity  ρ =  −0.115 577

Degree assortativity pvalue  p_{ρ} =  2.797 36 × 10^{−71}

Clustering coefficient  c =  0.035 704 6

Spectral norm  α =  30.398 4

Algebraic connectivity  a =  0.024 726 3

Spectral separation  λ_{1}[A] / λ_{2}[A] =  1.430 62

Nonbipartivity  b_{A} =  0.301 002

Normalized nonbipartivity  b_{N} =  0.012 483 3

Algebraic nonbipartivity  χ =  0.024 521 8

Spectral bipartite frustration  b_{K} =  0.001 791 80

Controllability  C =  5,979

Relative controllability  C_{r} =  0.863 144

Plots
Matrix decompositions plots
Downloads
References