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Sleep exerts modulatory effects on the cerebral cortex. Whether sleep modulates local connectivity in the cortex or only individual neural activity, however, is poorly understood. Here we investigated functional connectivity, that is, covarying activity between neurons, during spontaneous sleep–wake states and during and after sleep deprivation using calcium imaging of identified excitatory/inhibitory neurons in the motor cortex. Functional connectivity was estimated with a statistical learning approach glasso and quantified by “the probability of establishing connectivity (sparse/dense)” and “the strength of the established connectivity (weak/strong).” Local cortical connectivity was sparse in non-rapid eye movement (NREM) sleep and dense in REM sleep, which was similar in both excitatory and inhibitory neurons. The overall mean strength of the connectivity did not differ largely across spontaneous sleep–wake states. Sleep deprivation induced strong excitatory/inhibitory and dense inhibitory, but not excitatory, connectivity. Subsequent NREM sleep after sleep deprivation exhibited weak excitatory/inhibitory, sparse excitatory, and dense inhibitory connectivity. These findings indicate that sleep–wake states modulate local cortical connectivity, and the modulation is large and compensatory for stability of local circuits during the homeostatic control of sleep, which contributes to plastic changes in neural information flow.