  A useful property of a network that can be used to characterize many systems
is the degree distribution. However, many complex networks exhibit
higher--order degree correlations that must be studied through other means,
such as clustering coefficients, the Newman r factor, and the average nearest
neighbour degree (ANND). In this paper we develop an expansion of the
conditional probability that can be used to parameterize such degree
correlations. The measures of degree correlations associated with this
expansion can be used to signal the presence of non--linear correlations.
