On the number of non-zero elements of joint degree vectors

Czabarka, É ; Sadeghi, Kayvan ; Rauh, J ; Short, T ; Székely, L (2017-03-31)


Joint degree vectors give the number of edges between vertices of degree i and degree j for 1 ≤ i ≤ j ≤ 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.