Background: Apathy, a common neuropsychiatric (NPS) in patients with mild cognitive impairment (MCI) and Alzheimer's disease (AD), is associated with structural and metabolic brain changes. However, functional connectivity changes across the brain in association with apathy remain unclear. In this study, graph theoretical measures of integration and segregation from resting state functional connectivity in MCI and AD patients with low depression scores, and healthy controls. Methods: In MCI and AD patients with low depression scores, graph theoretical measures of integration and segregation were derived from resting state functional connectivity in patients, which were compared between those with apathy (NPS_A, n = 21) to those without NPS (NPS_None, n = 28) and those with NPS other than apathy (NPS_NA, n = 38). Additionally, the same measures were compared between AD patients and healthy controls (amyloid uptake below threshold levels). Results: Altered whole brain global efficiency and reduced local efficiency were found in NPS_A compared to NPS_None and NPS_NA. In similar contrasts, apathy was associated with increased participation coefficient in the frontoparietal and cingulo-opercular template-based networks. A study-specific network definition also showed similar results. In comparison, AD patients showed higher modularity compared to controls at the whole brain level and higher participation coefficient in the ventral attention network. Limitations: The severity and dimensions of apathy were not assessed. Conclusions: Loss of segregation in the frontoparietal and cingulo-opercular network, which are involved in the control of goal-directed behavior, was associated with apathy in MCI/AD. The results also suggest that network-level changes in AD patients may underlie specific NPS.