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