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Polytopes from subgraph statistics
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2011 (English)In: FPSAC - Int. Conf. Form. Power Ser. Algebraic Comb., 2011, 305-316 p.Conference paper (Refereed)
Abstract [en]

We study polytopes that are convex hulls of vectors of subgraph densities. Many graph theoretical questions can be expressed in terms of these polytopes, and statisticians use them to understand exponential random graph models. Relations among their Ehrhart polynomials are described, their duals are applied to certify that polynomials are nonnegative, and we find some of their faces. For the general picture we inscribe cyclic polytopes in them and calculate volumes. From the volume calculations we conjecture that a variation of the Selberg integral indexed by Schur polynomials has a combinatorial formula. We inscribe polynomially parametrized sets, called curvy zonotopes, in the polytopes and show that they approximate the polytopes arbitrarily close. © 2011 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France.

Place, publisher, year, edition, pages
2011. 305-316 p.
, FPSAC'11 - 23rd International Conference on Formal Power Series and Algebraic Combinatorics
Keyword [en]
Curvy zonotopes, Exponential random graph models, Graph limits, Polytopes, Subgraph statistics, Exponential random graph model, Subgraphs, Zonotopes, Polynomials, Graph theory
National Category
URN: urn:nbn:se:kth:diva-150625ScopusID: 2-s2.0-84860472450OAI: diva2:744432
23rd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'11, 13 June 2011 through 17 June 2011, Reykjavik

QC 20140908

Available from: 2014-09-08 Created: 2014-09-08 Last updated: 2014-09-08Bibliographically approved

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