Hi Sheep,
Axial and continuity maps are 'small-worlds' in the sense that they
average path length is very low and scales with the logarithm of the
graph size (that is why integration can be closeness / log(n)). About
the clustering factor, the original 'small-world' definition looks for
triangles in the local organisation. Obviously, cities are 'grids',
therefore we need to look at 'squares' or cycles of 4 steps. Making
this adaptation, line maps are small-worlds. See details at:
http://eprints.ucl.ac.uk/archive/00002694/
About their degree distribution and radius effects, there are surely
some shadows that still need to be investigated.
Regards,
Lucas
On 04/09/07, S. N.C. Dalton <[log in to unmask]> wrote:
> To come to Lucas's rescue I would say syntactical ( or rather axial/
> convex) graphs are abnormal,
> They are not random
> They are not regular (latice,circle) graphs
> They are not planar graphs (common subset of graphs although building
> J-graphs can be)
>
> most importantly
>
> They are not small world graphs ( these require having a high cluster
> factor that axial/convex maps cannot)
> Urban graphs do have a non even distribution of connectives they tend
> to be closer to a Possion distribution than a exponential
> Urban Connectivity distributions do have a tendency to exhibit a
> double hump.
>
> I don't know if this is specfic to urban axial graphs but the
> correlation between total depth with in a radius R and number of
> items (nodes) within radius R correlates with r-squared of 0.999*
> (typically). Where R is less than the saturation (edge effect) radius.
>
> so yes I would say abnormal describes them.
>
> sheep
>
> On 2 Sep 2007, at 14:44, Lucas Figueiredo wrote:
>
> > Dear Fred,
> >
> > By j-graph I guess you interested in drawing 'normal graphs'. I would
> > recommend you to test these ones:
> >
> > NetDraw: http://www.analytictech.com/downloadnd.htm
> > Pajek: http://vlado.fmf.uni-lj.si/pub/networks/pajek/
> >
> > And my favourite: yEd
> > http://www.yworks.com/en/products_yed_about.htm
> >
> > They do not implement integration. However, you can replace
> > integration by closeness centraly as long you normalise the values
> > using the logarithm or the graph size. In other words:
> >
> > Integration ~ closeness / log(n)
> >
> > See Park 2005 for details:
> > http://www.spacesyntax.tudelft.nl/media/longpapers2/hoontaepark.pdf
> >
> > I am assuming that you do not need local integration as j-graphs are
> > usually explored in small systems.
> >
> > Good luck,
> > Lucas Figueiredo
> >
> > On 02/09/07, Frederico de Holanda <[log in to unmask]> wrote:
> >>
> >>
> >> Dear all:
> >>
> >> I forward the consultation I have made to Jorge:
> >>
> >> What are the software people are currently using to draw and measure
> >> j-graphs? Are they available through the internet? We have had
> >> problems in
> >> trying to download Jass, it has not worked so far. And New wave is
> >> totally
> >> out of date for unfriendliness... We have to have a more automatic
> >> procedure.
> >>
> >> Best and thanks.
> >>
> >> Fred
> >>
> >>
> >> Frederico de Holanda
>
--
Lucas Figueiredo
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