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.


Internal namepajek-erdos
Data source
AvailabilityDataset is available for download
Consistency checkDataset passed all tests
Co-authorship network
Dataset timestamp 2002
Node meaningAuthor
Edge meaningCo-authorship
Network formatUnipartite, undirected
Edge typeUnweighted, no multiple edges
LoopsDoes not contain loops
Snapshot Is a snapshot and likely to not contain all data
Join Is the join of an underlying network
Multiplicity Does not have multiple edges, but the underlying data has
Connectedness Only the largest connected component of the original data is included


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 1[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


Fruchterman–Reingold graph drawing

Degree distribution

Cumulative degree distribution

Lorenz curve

Spectral distribution of the adjacency matrix

Spectral distribution of the normalized adjacency matrix

Spectral distribution of the Laplacian

Spectral graph drawing based on the adjacency matrix

Spectral graph drawing based on the Laplacian

Spectral graph drawing based on the normalized adjacency matrix

Degree assortativity

Zipf plot

Hop distribution

Double Laplacian graph drawing

Delaunay graph drawing

Clustering coefficient distribution

Average neighbor degree distribution


Matrix decompositions plots



[1] Jérôme Kunegis. KONECT – The Koblenz Network Collection. In Proc. Int. Conf. on World Wide Web Companion, pages 1343–1350, 2013. [ http ]
[2] Vladimir Batagelj. Pajek datasets., July 2017.