Re: [Boost-users] graph search algorithm

From: Saul Spatz (spatzs_at_[hidden])
Date: 2006-09-05 00:00:35

This description of the algorithm comes from the documentation for the
computer algebra system magma
http://magma.maths.usyd.edu.au/magma/htmlhelp/text1472.htm#14914

Face(u, v) : GrphVert, GrphVert -> SeqEnum

    Returns the face of the planar graph G bordered by the directed edge [u,
v] as an ordered list of edges of G.

    Note that a directed edge and an orientation determine a face uniquely:
We can assume without loss of generality that the plane is given a clockwise
orientation. Then given a directed edge e = [u_1, v_1], the face defined by
e is the ordered set of edges [u_1, v_1], [u_2, v_2], ..., [u_m, v_m] such
that v_i = u_(i + 1) for all i, 1 <= i < m, v_m = u_1, and for each v_i =
u_(i + 1), the neighbours of v_i, u_i and v_(i + 1), are consecutive
vertices in v_i's adjacency list whose order is anti-clockwise. 

George Kelly wrote:
> 
> I have a undirected graph set on a 2D plane.
> 
> Imagine the graph looking something like the USA where the edges form 
> the borders of the states.
> 
> I would like to automatically recognise all of the enclosed regions (the 
> states) by searching the graph and store each state as a subgraph.
> 
> How can I search the graph returning only the enclosed regions?
> 
> Thanks, any suggestions appreciated.
> 
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> 

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