Re: "small world" networks and Grid2d

[Catherine Dibble]

hi Matt,

I've been doing Smallworld simulations since Duncan Watts's 
and Steve Strogatz's _Nature_ paper was first published 
last June.  I'm currently in the process of adding LEDA 
graph tools to Swarm to provide exactly such shortcuts 
to Discrete2D spaces.

I've also done some (non-Swarm) Smallworld simulations on
Berkeley's Cray that show very *different* results when you
add "Smallworld" shortcuts to a 2D "Geographic" landscape.
Duncan agrees that rings are special in this respect. 
The intuition is that 2D geographic landscapes already
allow agents to take "slow diagonal shortcuts" across the
landscape; something that is forbidden by the structure
of a ring.                                              

Graph/Network shortcuts are still fundamentally important
structures to add to Swarm 2D landscapes for other reasons, 
but you should not expect to duplicate the precipitous drop 
in Characteristic Path Length.

Catherine Dibble
Department of Geography, UCSB
address@hidden
http://www.econ.ucsb.edu/~cath 

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