Given a finite simple connected graph G, one can define a reflexive lattice polytope called the symmetric edge polytope of G. Symmetric edge polytopes have attracted a significant amount of interest from researchers in geometric and algebraic combinatorics, with regard to both their geometric structure and their algebraic and combinatorial invariants. I will discuss recent work, joint with Kaitlin Bruegge and Matthew Kahle, regarding the number of facets of symmetric edge polytopes. Results and conjectures will be discussed regarding graph clustering metrics, degree sequences, and empirical sampling from various random graph models.
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