  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.
