Erdős
This is the co-authorship 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
|
| 4-Tour count | T4 = | 2,598,828
|
| Maximum degree | dmax = | 507
|
| Average degree | d = | 3.421 39
|
| Fill | p = | 0.000 493 993
|
| Size of LCC | N = | 6,927
|
| Diameter | δ = | 4
|
| 50-Percentile effective diameter | δ0.5 = | 3.382 04
|
| 90-Percentile effective diameter | δ0.9 = | 3.876 41
|
| Median distance | δM = | 4
|
| Mean distance | δm = | 3.791 37
|
| Gini coefficient | G = | 0.646 025
|
| Balanced inequality ratio | P = | 0.239 916
|
| Relative edge distribution entropy | Her = | 0.859 838
|
| Power law exponent | γ = | 3.227 63
|
| Tail power law exponent | γt = | 2.161 00
|
| Tail power law exponent with p | γ3 = | 2.161 00
|
| p-value | p = | 0.000 00
|
| Degree assortativity | ρ = | −0.115 577
|
| Degree assortativity p-value | pρ = | 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 | |λ1[A] / λ2[A]| = | 1.430 62
|
| Non-bipartivity | bA = | 0.301 002
|
| Normalized non-bipartivity | bN = | 0.012 483 3
|
| Algebraic non-bipartivity | χ = | 0.024 521 8
|
| Spectral bipartite frustration | bK = | 0.001 791 80
|
| Controllability | C = | 5,979
|
| Relative controllability | Cr = | 0.863 144
|
Plots
Matrix decompositions plots
Downloads
References
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