erdos_collaboration — Erdős collaboration graph (1997-2002)

Description

Networks of the mathematicians with Erdős number 1 or 2, i.e. the co-authors of Paul Erdős, and the co-authors of these, from the data of the Erdős Number Project of J. W. Grossman, as converted to Pajek networks by V. Batagelj and A. Mrvar, in four versions of the data: erdos97, erdos98, erdos99 (from 1997, 1998 and 1999) and erdos02 (from 2002). Each node is a mathematician, and an undirected edge connects two of them if they wrote a paper together. The data list the co-authors of the people with Erdős number 1 only, so that the edges join people with Erdős number 1, or people with Erdős numbers 1 and 2; there are no edges between people with Erdős number 2. Paul Erdős himself (and his edges to his co-authors) is included only in erdos02.

Batagelj and Mrvar also distribute the networks of the people with Erdős number 1 for 1997 to 1999 (e.g. ERDOS971.NET); they are not included as separate networks, since they are the subgraphs of the full networks induced by these people.

The networks have the following properties:

name: the name of the mathematician (in upper case, except in erdos97 and for a few names of erdos02).
erdos_number: the Erdős number of the mathematician (0 for Paul Erdős, 1 or 2 otherwise). For erdos97 to erdos99 they are given by the partitions distributed with the networks; for erdos02 they follow from the network.

Tags

Social Collaboration Unweighted Metadata

Citation

V. Batagelj, A. Mrvar, "Some analyses of Erdős collaboration graph." Social Networks 22(2), 173-186 (2000) 10.1016/S0378-8733(00)00023-X Sci-Hub
J. W. Grossman, P. D. F. Ion, "On a portion of the well-known collaboration graph." Congressus Numerantium 108, 129-131 (1995) oakland.edu

Upstream URL OK

https://web.archive.org/web/20041128004146/http://vlado.fmf.uni-lj.si/pub/networks/data/default.htm
https://oakland.edu/enp/

Networks

Tip: click on a column header to sort the list, or hover over it for a description.

Column legend

$\left<k\right>$: Mean degree
$\sigma_k$: Standard deviation of the degrees
$\lambda_h$: Largest eigenvalue of the Hashimoto (non-backtracking) matrix
$\tau$: Random walk mixing time
$r$: Degree assortativity
$c$: Global clustering coefficient
$\oslash$: (Pseudo-) diameter
$S$: Relative size of the largest component
NPs: Node properties
EPs: Edge properties

Name	Nodes	Edges	$\left<k\right>$	$\sigma_k$	$\lambda_h$	$\tau$	$r$	$c$	$\oslash$	$S$	Kind	Mode	NPs	gt	GraphML	GML	csv
erdos97	5,488	8,972	3.27	9.04	19.01	92.78	-0.23	0.04	12	0.99	Undirected	Unipartite	name erdos_number	145 KiB	193 KiB	190 KiB	163 KiB
erdos98	5,822	9,505	3.27	9.20	19.36	238.42	-0.23	0.04	12	0.99	Undirected	Unipartite	name erdos_number	152 KiB	202 KiB	199 KiB	174 KiB
erdos99	6,100	9,939	3.26	9.28	19.58	238.38	-0.24	0.04	12	0.99	Undirected	Unipartite	name erdos_number	160 KiB	213 KiB	211 KiB	181 KiB
erdos02	6,927	11,850	3.42	11.69	25.03	79.21	-0.12	0.04	4	1.00	Undirected	Unipartite	name erdos_number	181 KiB	242 KiB	238 KiB	205 KiB

Ridiculograms^*

^* These are automatically generated force-directed visualizations, and can be quite meaningless for networks both big and small. They should not be taken seriously as sources of scientific insight. See here for a discussion.