Cognition is supported by a network of axonal connections between gray matter regions within and between right and left cerebral cortex. Global organizing principles of this circuitry were examined with network analysis tools applied to monosynaptic association (within one side) and commissural (between sides) connections between all 77 cortical gray matter regions in each hemisphere of the rat brain. The analysis used 32,350 connection reports expertly collated from published pathway tracing experiments, and 5,394 connections of a possible 23,562 were identified, for a connection density of 23%—of which 20% (1,084) were commissural. Network community detection yielded a stable bihemispheric six-module solution, with an identical set in each hemisphere of three modules topographically forming a lateral core and medial shell arrangement of cortical regions. Functional correlations suggest the lateral module deals preferentially with environmental sensory-motor interactions and the ventromedial module deals preferentially with visceral control, affect, and short-term memory, whereas the dorsomedial module resembles the default mode network. Analysis of commissural connections revealed a set of unexpected rules to help generate hypotheses. Most notably, there is an order of magnitude more heterotopic than homotopic projections; all cortical regions send more association than commissural connections, and for each region, the latter are always a subset of the former; the number of association connections from each cortical region strongly correlates with the number of its commissural connections; and the module (dorsomedial) lying closest to the corpus callosum has the most complete set of commissural connections—and apparently the most complex function.