The architecture whereby activity across many brain regions integrates to encode individual appetitive social behavior remains unknown. Here we measure electrical activity from eight brain regions as mice engage in a social preference assay. We then use machine learning to discover a network that encodes the extent to which individual mice engage another mouse. This network is organized by theta oscillations leading from prelimbic cortex and amygdala that converge on the ventral tegmental area. Network activity is synchronized with cellular firing, and frequency-specific activation of a circuit within this network increases social behavior. Finally, the network generalizes, on a mouse-by-mouse basis, to encode individual differences in social behavior in healthy animals but fails to encode individual behavior in a 'high confidence' genetic model of autism. Thus, our findings reveal the architecture whereby the brain integrates distributed activity across timescales to encode an appetitive brain state underlying individual differences in social behavior.