  When re-structuring patient cohorts into so-called population graphs,
initially independent data points can be incorporated into one interconnected
graph structure. This population graph can then be used for medical downstream
tasks using graph neural networks (GNNs). The construction of a suitable graph
structure is a challenging step in the learning pipeline that can have severe
impact on model performance. To this end, different graph assessment metrics
have been introduced to evaluate graph structures. However, these metrics are
limited to classification tasks and discrete adjacency matrices, only covering
a small subset of real-world applications. In this work, we introduce extended
graph assessment metrics (GAMs) for regression tasks and continuous adjacency
matrices. We focus on two GAMs in specific: \textit{homophily} and
\textit{cross-class neighbourhood similarity} (CCNS). We extend the notion of
GAMs to more than one hop, define homophily for regression tasks, as well as
continuous adjacency matrices, and propose a light-weight CCNS distance for
discrete and continuous adjacency matrices. We show the correlation of these
metrics with model performance on different medical population graphs and under
different learning settings.
