Introduction: Schizophrenia is increasingly conceived as a disorder of brain network connectivity and organization. However, reports of network abnormalities during the early illness stage of psychosis are mixed. This study adopted a data-driven whole-brain approach to investigate functional connectivity and network architecture in a first-episode psychosis cohort relative to healthy controls and whether functional network properties changed abnormally over a 12-month period in first-episode psychosis. Methods: Resting-state functional connectivity was performed at two time points. At baseline, 29 first-episode psychosis individuals and 30 healthy controls were assessed, and at 12 months, 14 first-episode psychosis individuals and 20 healthy controls completed follow-up. Whole-brain resting-state functional connectivity networks were mapped for each individual and analyzed using graph theory to investigate whether network abnormalities associated with first-episode psychosis were evident and whether functional network properties changed abnormally over 12 months relative to controls. Results: This study found no evidence of abnormal resting-state functional connectivity or topology in first-episode psychosis individuals relative to healthy controls at baseline or at 12-months follow-up. Furthermore, longitudinal changes in network properties over a 12-month period did not significantly differ between first-episode psychosis individuals and healthy control. Network measures did not significantly correlate with symptomatology, duration of illness or antipsychotic medication. Conclusions: This is the first study to show unaffected resting-state functional connectivity and topology in the early psychosis stage of illness. In light of previous literature, this suggests that a subgroup of first-episode psychosis individuals who have a neurotypical resting-state functional connectivity and topology may exist. Our preliminary longitudinal analyses indicate that there also does not appear to be deterioration in these network properties over a 12-month period. Future research in a larger sample is necessary to confirm our longitudinal findings.