Cis-regulatory networks (CRNs) play a central role in cellular decision making. Like every other biological system, CRNs undergo evolution, which shapes their properties by a combination of adaptive and nonadaptive evolutionary forces. Teasing apart these forces is an important step toward functional analyses of the different components of CRNs, designing regulatory perturbation experiments, and constructing synthetic networks. Although tests of neutrality and selection based on molecular sequence data exist, no such tests are currently available based on CRNs. In this work, we present a unique genotype model of CRNs that is grounded in a genomic context and demonstrate its use in identifying portions of the CRN with properties explainable by neutral evolutionary forces at the system, subsystem, and operon levels. We leverage our model against experimentally derived data from Escherichia coli. The results of this analysis show statistically significant and substantial neutral trends in properties previously identified as adaptive in origin--degree distribution, clustering coefficient, and motifs--within the E. coli CRN. Our model captures the tightly coupled genome-interactome of an organism and enables analyses of how evolutionary events acting at the genome level, such as mutation, and at the population level, such as genetic drift, give rise to neutral patterns that we can quantify in CRNs.