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I am a beginner in network topology topics and while I was reading an article about simplicial complexes where the authors had used random simplicial complexes, I came across a formula using "average degree of a d-simplex". I have been looking at other articles online but I couldn't get a simple definition. I was wondering if anyone could help me understand what is the average degree of a d-simplex? Does it exist for all simplicial complexes (both random and not random)? How do we calculate it?

Any help on finding the answer to these questions is very appreciated!

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  • $\begingroup$ Every vertex of a $d$-simplex has degree $d$ (e.g., tetrahedron vertices in $\mathbb{R}^3$ have degree $3$), so there must be a different notion of "average degree," different from the straightforward meaning of the term. Maybe it means the average degree of a simplex that is part of a random complex. $\endgroup$
    – Joseph O'Rourke
    Commented Apr 15, 2022 at 14:00
  • $\begingroup$ Maybe it means the average number of incident d-simplexes to a random d-simplex selected from the complex. $\endgroup$
    – Eric Peterson
    Commented Apr 15, 2022 at 14:11

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