A recurrent theme of both cognitive and network neuroscience is that the brain has a consistent subnetwork structure that maps onto functional specialization for different cognitive tasks, such as vision, motor skills, and attention. Understanding how regions in these subnetworks relate is thus crucial to understanding the emergence of cognitive processes. However, the organizing principles that guide how regions within subnetworks communicate, and whether there is a common set of principles across subnetworks, remains unclear. This is partly due to available tools not being suited to precisely quantify the role that different organizational principles play in the organization of a subnetwork. Here, we apply a joint modeling technique – the correlation generalized exponential random graph model (cGERGM) – to more completely quantify subnetwork structure. The cGERGM models a correlation network, such as those given in functional connectivity, as a function of activation motifs – consistent patterns of coactivation (i.e., connectivity) between collections of nodes that describe how the regions within a network are organized (e.g., clustering) – and anatomical properties – relationships between the regions that are dictated by anatomy (e.g., Euclidean distance). By jointly modeling all features simultaneously, the cGERGM models the unique variance accounted for by each feature, as well as a point estimate and standard error for each, allowing for significance tests against a random graph and between graphs. Across eight functional subnetworks, we find remarkably consistent organizational properties guiding subnetwork architecture, suggesting a fundamental organizational basis for subnetwork communication. Specifically, all subnetworks displayed greater clustering than would be expected by chance, but lower preferential attachment (i.e., hub use). These findings suggest that human functional subnetworks follow a segregated highway structure, in which tightly clustered subcommunities develop their own channels of communication rather than relying on hubs.