An edge in math is basically a corner more or less. Since a cylinder does not have a single corner, we can conclude that a cylinder does not have any edges.
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none.
http://wiki.answers.com/Q/How_many_straight_edges_...

A cylinder has 3 faces and it has 2 edges and no vertices (corners)
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Two, one at each end connecting the circle part and hte long parts together. As there are no corners, it counds as one edge.
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