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

  • Éva Czabarka
  • Johannes Rauh
  • Kayvan Sadeghi
  • Taylor Short
  • László Székely
Keywords: Degree sequence, Joint degree distribution, Joint degree vector, Joint degree matrix, Exponential random graph model

Abstract

Joint degree vectors give the number of edges between vertices of degree i and degree j for 1ijn1 in an n-vertex graph. We find lower and upper bounds for the maximum number of nonzero elements in a joint degree vector as a function of n. This provides an upper bound on the number of estimable parameters in the exponential random graph model with bidegree-distribution as its sufficient statistics.

Published
2017-03-31
Article Number
P1.55