I was just wondering why it is that there are so many overlapping and seemingly random terms in mathematics. For example, I'm learning graph theory and according to different notes or books, two edges are only called incident if they converge on one vertex, but in another book they may be called adjacent. Then in the same book, two vertices are connected by an edge they are called adjacent as well. It seems to be unnecessarily confusing. I'm wondering if that's just because of the lack of communication between mathematicians as they discovered properties or was it because of something else?

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    $\begingroup$ I don’t know the actual history, but I suspect that the diversity of terminology is largely the result of two circumstances. First, graph theory has applications in a variety of fields both within and without mathematics, so graph theoretical results have been discovered by people with a variety of terminological backgrounds; this naturally results in a diversity of terms for the same thing. Secondly, it’s still a relatively young field. \\ The multiple usages of adjacent aren’t really a problem, since context generally makes clear which is intended. $\endgroup$ Jun 26, 2016 at 23:28
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    $\begingroup$ @Darpan Ganatra: If you consider the line graph of a graph (where all edges are the new vertices), then you can still talk abount adjacency of edges. "Incidence" (seems to me) is more widely used nowadays between elements of different type (e.g., vertices and edges). $\endgroup$
    – Moritz
    Jun 27, 2016 at 7:42

1 Answer 1


Obviously the definition of two edges being adjacent would be different from the definition of two vertices being adjacent. The only example you've given is that two adjacent edges are also said to be incident. Incident and adjacent are almost synonymous and I don't think you've really pointed out enough examples of overlapping or seemingly random terms. I'm sure that in other areas of mathematics also (take abstract algebra) you'll again find that different notes or books use different terminology or notation.

In general the basic terminology in graph theory is by now quite standard. Bollobas' Modern Graph Theory is a standard text.


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