Probabilistic inequalities for evaluating structural network measures

Proving interrelations between structural graph measures analytically has been intricate. Generally, relations between structural graph measures describe the interplay between measures which turned out to be useful for better understanding the properties of such quantities. The results which have been achieved so far are restricted to simple measures or special graph classes such as trees. In this paper, we introduce a probabilistic approach for establishing inequalities between quantitative network measures on random networks. Those inequalities between different graph measures lead to a deeper understanding of the mathematical apparatus and, in particular, to a discussion of quality aspects of structural graph measures, which is a major contribution of this paper.