Is there interesting structure in the collaboration graph of Paul Erdös?
I used the "Erdos1" list that resides at the Erdös Number Project home page to populate a nonsymmetrical variant of the "communications matrix" used by sociologists. Here each column represents an Erdös1 author and each row represents either an Erdös2 author or an Erdös1 author who has collaborated with at least one other Erdös1 author. A cell in the matrix is either zero or one. A nonzero cell indicates coauthorship.
I extracted the largest connected component of the graph, which turned out to be most of it, consisting of 441 columns and 4948 rows. I rearranged the rows and columns (by means of a simulated annealing algorithm) to maximize adjacency along the diagonal. The 441x495pixel image below represents the 441x4948 matrix squashed vertically for a more readable display. The dark areas represent clusters of individuals who have tended to collaborate with each other. I have identifed the more prolific Erdös1 (column) authors in the most prominent clusters  see notes 2 through 5.
< Erdos1 authors (441) > 

^     Note 2 >          Note 3 > Erdos2 authors (4948  see Note 1)   Note 4 >    Note 5 >         v 
1. Row authors include both Erdös2 authors and those Erdös1 authors who collaborated with other Erdös1 authors.
2. This cluster includes RC Mullin, DR Stinson, CJ Colbourn
3. Includes MK Saks, N Alon, DJ Kleitman, RL Graham, FRK Chung, L Lovasz
4. Includes F Harary, G Chartrand
5. Includes S Shelah
Charles Packer mailbox@cpacker.org