Variability in higher order structure of noise added to weighted networks

The complex behavior of many real-world systems depends on a network of both strong and weak edges. Distinguishing between true weak edges and low-weight edges caused by noise is a common problem in data analysis, and solutions tend to either remove noise or study noise in the absence of data. In this work, we instead study how noise and data coexist, by examining the structure of noisy, weak edges that have been synthetically added to model networks. We find that the structure of low-weight, noisy edges varies according to the topology of the model network to which it is added, that at least three qualitative classes of noise structure emerge, and that these noisy edges can be used to classify the model networks. Our results demonstrate that noise does not present as a monolithic nuisance, but rather as a nuanced, topology-dependent, and even useful entity in characterizing higher-order network interactions.