spaf@gatech.UUCP (Gene Spafford) (10/05/84)
I just recompiled our uucp mail database and ran a short awk script
over it for the heck of it. The information I got was:
Number of paths with 1 hop is 38
Number of paths with 2 hops is 1277
Number of paths with 3 hops is 1070
Number of paths with 4 hops is 498
Number of paths with 5 hops is 81
Number of paths with 6 hops is 18
Number of paths with 7 hops is 1
Number of paths with > 7 hops is 0
Average path length is 2.786193 hops.
I passed this along to our system administrator who made the following,
rather interesting conjecture:
The Johnson Theorem
-------------------
The average number of sites in the uucp paths from a well-connected
site to all reachable sites tends towards "e" as the number of sites
tends towards infinity.
Anybody have any further input?
--
Off the Wall of Gene Spafford
The Clouds Project, School of ICS, Georgia Tech, Atlanta GA 30332
CSNet: Spaf @ GATech ARPA: Spaf%GATech.CSNet @ CSNet-Relay.ARPA
uucp: ...!{akgua,allegra,amd,hplabs,ihnp4,seismo,ut-sally}!gatech!spaf