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In graph theory, are undirected graphs assumed to be reflexive? I know that in directed graphs vertices do not point to themselves unless explicitly stated, but what about undirected graphs?

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In general, undirected graphs are not assumed to be reflexive. A lot of graph theory concerns "simple graphs", which are undirected and have no "loops", where a loop is an edge joining a vertex to itself. Unless the presence of loops is explicitly stated, I would assume they're not there.

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Thanks for the quick response. That's what I was thinking, but you confirmed it! – Mark Apr 8 '14 at 1:34

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