Saul Spatz wrote:

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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If you read the boost graph library book, there is a section where it describes how to detect cycles. I think that may help. Alejandro Aragon