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


Joint degree vectors give the number of edges between vertices of degree $i$ and degree $j$ for $1\le i\le j\le n-1$ 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.

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