Objective: To identify whether abnormal electroencephalography (EEG) connectivity is present before the onset of epileptic spasms (ES) in infants with tuberous sclerosis complex (TSC). Methods: Scalp EEG recordings were collected prospectively in infants diagnosed with TSC in the first year of life. This study compared the earliest recorded EEG from infants prior to ES onset (n = 16) and from infants who did not develop ES (n = 28). Five minutes of stage II or quiet sleep was clipped and filtered into canonical EEG frequency bands. Mutual information values between each pair of EEG channels were compared directly and used as a weighted graph to calculate graph measures of global efficiency, characteristic path length, average clustering coefficient, and modularity. Results: At the group level, infants who later developed ES had increased EEG connectivity in sleep. They had higher mutual information values between most EEG channels in all frequency bands adjusted for age. Infants who later developed ES had higher global efficiency and average clustering coefficients, shorter characteristic path lengths, and lower modularity across most frequency bands adjusted for age. This suggests that infants who went on to develop ES had increased local and long-range EEG connectivity with less segregation of graph regions into distinct modules. Significance: This study suggests that increased neural connectivity precedes clinical ES onset in a cohort of infants with TSC. Overconnectivity may reflect progressive pathologic network synchronization culminating in generalized ES. Further research is needed before scalp EEG connectivity measures can be used as a potential biomarker of ES risk and treatment response in pre-symptomatic infants with TSC.