English

On the Number of Non-zero Elements of Joint Degree Vectors

Combinatorics 2017-02-23 v4

Abstract

Joint degree vectors give the number of edges between vertices of degree ii and degree jj for 1ijn11\le i\le j\le n-1 in an nn-vertex graph. We find lower and upper bounds for the maximum number of nonzero elements in a joint degree vector as a function of nn. This provides an upper bound on the number of estimable parameters in the exponential random graph model with bidegree-distribution as its sufficient statistics.

Keywords

Cite

@article{arxiv.1511.01035,
  title  = {On the Number of Non-zero Elements of Joint Degree Vectors},
  author = {Eva Czabarka and Johannes Rauh and Kayvan Sadeghi and Taylor Short and Laszlo A Szekely},
  journal= {arXiv preprint arXiv:1511.01035},
  year   = {2017}
}