I prefer the Caldarelli and colleagues's definition:
Caldarelli, G., R. Pastor-Satorras, et al. (2004). "Structure of
cycles and local ordering in complex networks." Eur. Phys. J. B 38:
183-186.
It extracts specifically cycles of k steps. 'K-clustering' mixes all
cycles and probably is ill-defined as the original clustering
coefficient, which is degree biased.
Of course, there is the original one: 'axial ringness' (Hillier and
Hanson, 1984).
Best Regards,
Lucas Figueiredo
On 04/09/07, Alasdair Turner <[log in to unmask]> wrote:
> Of course, there's always Bin Jiang.
>
> Here's the paper where he and Christophe Claramunt introduce the
> k-clustering coefficient.
>
> Jiang B, Claramunt C, 2004, "Topological analysis of urban street
> networks" Environment and Planning B: Planning and Design 31(1) 151 – 162
>
>
> Lucas Figueiredo wrote:
> > 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
> >>
> >
> >
>
> --
> Course Director
> MSc Adaptive Architecture & Computation
> UCL Bartlett School of Graduate Studies
>
> http://www.vr.ucl.ac.uk/people/alasdair
>
--
Lucas Figueiredo
|