Hello,
Just a quick note on the topic of small worlds and planar graphs. It is
probably an overstatement to suggest that planar graphs cannot be small world.
One contra-example is the power-grid, which has been shown to be a small
world and is largely planar -remember: not all spatial networks are street
networks!
Also, some care is due when talking about street networks as planar:
strictly speaking, the presence of bridges and tunnels means that these
networks are not planar by definition. They could be called quasi-planar,
though and this is the sort of thing physicists like to investigate :)
All the best,
Rui
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Dr. Rui Carvalho
School of Mathematical Sciences
Queen Mary, University of London
Mile End Road, London E1 4NS, UK
http://www.ruicarvalho.org/
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