Context Network-theoretic tools contribute to understanding real-world system dynamics, such as species survival or spread. Network visualization helps illustrate structural heterogeneity, but details about heterogeneity are lost when summarizing networks with a single mean-style measure. Researchers have indicated that a system composed of multiple metrics may be a more useful determinant of structure, but a formal method for grouping metrics is still lacking. Objectives Our objective is to present a tool that can account for multiple properties of network structure, which can be related to model outcomes. Methods We develop an approach using the statistical concept of moments and systematically test the hypothesis that this system of metrics is sufficient to explain variation in processes that take place on networks, using an ecological system as an example. Results Our results indicate that the moments approach outperforms single summary metrics by adjusted-R2 and AIC model fit criteria, and accounts for a majority of the variation in process outcomes. Conclusions Our scheme is helpful for indicating when additional structural information is needed to describe system process outcomes such as survival or spread.