How to remove "non-closing" edges in CGAL

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I have a CGAL Arrangement graph looking like this:

,_____,  ,_____,   ,_____,
|     |  |     |   |     |
|--   |  |     |---|     |   ---
|_____|  |_____|   |_____|

I want to remove all the edges that doesn't "close" a polygon like the horizontal one inside the square, the one linking the two other squares, and the alone edge.

Is there a way to do this in CGAL? Also, does this kind of edge have a name in topology or in graph theory?

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