Complex biological systems are often represented by network graphs. However, their structural features are not adequately captured by existing computational graph models, perhaps because the datasets used to assemble them are incomplete and contain elements that lack shared functions. Here, we analyze three large, near-complete networks that produce specific cellular or behavioral outputs: a molecular yeast mitochondrial regulatory protein network, and two anatomical networks of very different scale, the mouse brain mesoscale connectivity network, and the C. elegans neuronal network. Surprisingly, these networks share similar characteristics. All consist of large communities composed of modules with general functions, and topologically distinct subnetworks spanning modular boundaries responsible for their more specific phenotypical outputs. We created a new model, SBM-PS, which generates networks by combining communities, followed by adjustment of connections by a path selection mechanism. This model captures fundamental architectural features that are common to the three networks.