28th Cumberland Conference on Combinatorics, Graph Theory & Computing
Kayvan Sadeghi
Carnegie Mellon University http://www.stat.cmu.edu/people/faculty/kayvans 

Abstract 
On the maximum number of nonzeros in graphical joint degree matrices
Graphical joint degree matrices (JDMs) are n1 by n1 matrices whose (i,j) element represents the number of edges between vertices of degree i and vertices of degree j in a graph with n nodes. Finding the maximum possible number of nonzero elements of a graphical JDM for a fixed number of nodes seems quite challenging. In this talk, we discuss and motivate this problem based on statistical random graph analysis. We provide reasonable lower and upper bounds for this maximum number as well as a conjecture for the asymptotic maximum number of nonzero elements of a graphical JDM and graphs that attain it. 