Is there a difference or is it just terminology?
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1$\begingroup$ Just figured that the authors are French. In french an undirected graph is called "un graphe non orienté". This is a strong - but I'm still unsure. $\endgroup$– LonforceCommented Mar 1, 2013 at 14:31
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2$\begingroup$ mathworld.wolfram.com/OrientedGraph.html explains a difference in use between the two terminologies. I'm not convinced that this is standard, but perhaps a graph theorist can weigh in on the issue. $\endgroup$– Lee MosherCommented Mar 1, 2013 at 15:54
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$\begingroup$ @Lonforce: strictly speaking a negative by itself does not define much, or anything. This is a basic tenet of constructive mathematics. Surprising that you seem to have thought this question defined. $\endgroup$– Peter HeinigCommented Aug 8, 2017 at 15:37
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Many people consider that an "oriented graph" is what you get from a simple undirected graph when you assign a direction to each edge. The difference between that and "directed graph" is that a directed graph can have cycles of length 2 even if it is qualified as "simple", whereas an "oriented graph" cannot. On the other hand, there are zillions of papers that use "oriented graph" with identical meaning to "directed graph".
Applying these meanings pedantically in the negative doesn't seem to be a good idea. I'd be very surprised to see anyone using "non-oriented" of a digraph to imply that it doesn't have 2-cycles. I only recall "non-oriented" meaning that the edges don't have directions, which is the same as "undirected".
answered Mar 2, 2013 at 3:57