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The correct term is line graph -google for it. It's a classical problem in graph theory to find it: http://en.wikipedia.org/wiki/Line_graph Mike's notation may have been unfortunate, but it did for space syntax what no other core space syntax paper it: physicists started reading about it. What Mike points out, basically, is that space syntax can indeed be reduced to this idea. And my point is he is 100% correct in that!!! Now, Alan, I'm afraid that physicists look for social science theories is social science, not in architecture -so my challenge is still on!!! Where are the papers that quote the SLoS for anything but this almost trivial idea (which, by the way, no one knows whether it works or not!) Rui ___________________________________________ Dr. Rui Carvalho School of Mathematical Sciences Queen Mary, University of London Mile End Road, London E1 4NS, UK http://www.ruicarvalho.org/ RuiOn Sat, 25 Oct 2008 23:04:31 +0100, Alan Penn <[log in to unmask]> wrote: >Rui wrote: > >> I will be very pleased if anyone can show that there is more to >> space syntax than the "dual graph" (which, incidentaly, is not dual). > >Thanks to Rui for pointing out - quite correctly by the way - that >whilst the edge vertex dual of the axial graph gives the node graph, >the dual of the node graph is not the axial graph. The reverse >transform requires something like a clique reduction (with all the >difficulties that this involves). It is for this reason that in order >to keep things simple one needs to think of the axial graph as primal >and the node graph as the dual. It is a pity that a number of papers >have been published with misleading terminology in this regard. > >Oh, and of course there is more to space syntax than the graph - there >is a theory of society. Start by reading the Social Logic of Space to >find out more. > >Alan