Functional disconnection is thought to underlie schizophrenia and is often studied by characterizing the small-worldness of networks derived from electroencephalogram (EEG) recordings. Decreased small-worldness in schizophrenia has been regularly observed during active tasks, while the results are varied for non-response or resting tasks. We obtained EEG networks in three non-response tasks from 42 (Mage = 42.07 years, SD = 6.38) individuals with schizophrenia and 42 matched controls and found that the schizophrenia group displayed reduced variation in small-worldness across tasks, measured using small-world propensity. We speculate that this observation can be attributed to aberrant functioning of the default mode network. Further, using ordinal regression, we showed that small-world propensity and its variation across tasks are associated with PANSS symptom scores.