On 04/09/07, S. N.C. Dalton <[log in to unmask]> wrote:
> Watts amd Strpgatz used clustering coefficient of a graph to
> determine if a
> graph is small world or not.
Their definition is almost (already) 10 years old and it is
restrictive. It is common now in the literature to check squares
(cycles of 4 steps) instead of triangles. The important is the idea
that elements are clustered (either in triangles, squares or even
trees!) at local level but still have 'shortcuts' that connect them to
the rest of the system in few steps.
Local streets are definitively clustered, or at least this is the way
I see it. Do not get emotionally attached to these 'definitions' of
things by 'might scholars'.
Challenge them! Contradict them! Innovate!
Best Regards,
Lucas Figueiredo
>
> The only time you get a clustering coefficient bigger than zero is
> when 3 or more axial lines
> intersect at a junction. Even then your very dependant on the axial
> lines all being slightly long and precisely how they intersect to
> form lots of mini triangles.
>
> Believe me I programmed in clustering coefficient into webmap@home
> and didn't get anything exciting out of it. Basically clustering
> coefficient works on the basis that If A knows B and B knows C then
> it is likely that C knows A. This is how all the social networking
> stuff works.
>
> For an axial map If street A connects to Street B and Street B
> connects to Street C then it is highly unlikely that street C
> connects to Street A (in fact the reverse is more true).
>
> Same for convex spaces but not for isovist grids.
>
> If you could go out to radius 3 or 4 the case would be different but
> this is not how Watts and Storogatz defined it just degree/connectivity.
>
> Notice we are in an interesting twilight world where axial maps are
> largely 'scale free' (some highly connected hubs, most are low
> connections) but not small world. This is a shame as if they were we
> could use the Derek J. de Solla Price generative mechanism and be
> able to run the growth of cities into the future.
>
> so short of redefining what you mean by small world axial maps are
> not small world and so moderately unique and so abnormal.
>
> sheep
>
--
Lucas Figueiredo
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