I'm working on a Graph Theory research project, and one of the key components is talking about the indegrees and the outdegrees of a few particular vertices. I need to define a term for the value of indegree-outdegree for a particular vertex. Or for vertex $v$ does the value $\deg^{-}(v) - \deg^{+}(v)$ have a name?

Some possible terms have been "netdegree" or "flow value," which would suffice for my needs, but I would like to make sure I use the existing terminology if possible.

  • $\begingroup$ I don't know of any standard terminology. I like "net income." $\endgroup$
    – saulspatz
    Nov 13 '20 at 0:29
  • $\begingroup$ I believe the word "excess" can also be used (especially if your graph relates to flow networks). $\endgroup$
    – paulinho
    Nov 13 '20 at 0:30

I believe this is called the imbalance of a vertex, see for example this paper: https://core.ac.uk/download/pdf/42932978.pdf

Note that this is defined as indegree - outdegree, but clearly this can be easily reversed.


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