If a graph that includes built forms (illustration attached) is considered,
the distribution of sources and sinks could no longer be even. It is a
complicated graph, although it can be simplified by aggregating all built
form units associated to each public space unit into an attribute to be
loaded to the open space units; such an attribute could, further, be
specified according to source or sink characteristic and parametrized with
appropriate attraction functions.
SEE GRAPH ATTACHED
Fig 1 (attached): on the left, a graph with open space units (white circles)
and built form units, labeled as sink (red ones) and source (black ones); on
the right, a simplified graph in which built form units becomes attributes
loaded to open space units. Numbers (1, 2) refer to the amount of built
form units associated to each open space unit, letters (SI, SO) refer to
parameters associated to sink and source attraction functions.
In addition, if classic Freeman's betweenness centrality is "equipped" with
a gravitational-like structure, in which the LENGHTof shortest paths are
taken into account, so that each node falling in a shortest path is granted
only a proportional fraction of the centrality owed to the pair of nodes
being measured, then the tendency to concentrate BC near the geographic
centre could no longer be a must. The centrality generated by a pair of
nodes not adjacent to each other becomes a tension which value is the
product of both nodes' attributes; this tension can be distributed among all
nodes belonging to the shortest paths, such as in: T(Bae) = (2^SO .
2^SI)/2, in which T(Bae) is the tension in B due to the pair A-E (refering
to the graph attached, once again). The tension distribution could include
the pair that originated it, as well as a decaing function, of course.
Moreover, there is the possibility to consider a directed graph, in which
all pairs of nodes should necessarily be SO > SI, generating a measure of
"organized" centrality, or polarity. In both cases, correlation to flows do
not seem to be trivial. There are interesting spatial dynamics which could
derive from this too.
This is not traditional SS, of course, I'm not sure it is spatial analysis
either, but, anyway, there it is; old stuff, published in E&P B 1994
(Modelling intraurban configurational development), 1997 (Urban convergence:
morphology and attraction) and SSS3 (Urban centrality: a configurational
model of a self-organized process).
----- Original Message -----
From: "Rui Carvalho" <[log in to unmask]>
To: <[log in to unmask]>
Sent: Wednesday, March 18, 2009 8:27 AM
Subject: Re: [SPACESYNTAX] Betweenness centrality correlates trivially with
traffic flows on urban networks
1. Betweenness centrality assumes an equal density of sources and sinks,
independently of spatial aggregation effects.
In layman's words: there are as many different offices as there are
households.
2. The shortest path between north and south greater London would go through
the centre of London, not through the M25. But traffic does not flow along
topological shortest paths -it flows along the routes with the highest
capacity.
Are these obvious points of any relevance to this community?
That's not up to me to decide. But I'm obviously skeptical that this line of
research will have an impact beyond the space syntax symposium series, which
is why my research has shifted to other urban problems.
All the best,
Rui
______________________________________
Recent work on spatial networks, GIS datasets and cities:
1. Robustness of Trans-European Gas Networks: The Hot Backbone
Rui Carvalho, Lubos Buzna, Flavio Bono, Eugenio Gutierrez, Wolfram Just,
David Arrowsmith
http://arxiv.org/abs/0903.0195
2. LivingScience -where Science is Happening:
http://www.livingscience.ethz.ch/
Dr. Rui Carvalho
School of Mathematical Sciences
Queen Mary, University of London
Mile End Road, London E1 4NS, UK
http://www.ruicarvalho.org/
|