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Is a line considered a face in graph theory?

For example just a straight line point to point.

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    Please try to make your titles more descriptive. Almost all your questions are titled " Question".2012-02-20

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No, that is an edge. There is one face in your graph though: the unbounded or infinite face, sometimes denoted $f_\infty$.

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    The degree of $f_\infty$ in this case is 2, since your walk uses the edge twice to return to the starting vertex. Note that the sum of all the degrees of the faces in a planar graph is always twice the number of edges.2012-02-20