The onset of positive symptoms in schizophrenia is often preceded by a prodromal phase characterized by neurocognitive abnormalities as well as changes in brain structure and function. Increasing efforts have been made to identify individuals at elevated risk of developing schizophrenia, as early intervention may help prevent progression towards psychosis. The present study uses functional MRI and graph theoretical analysis to characterize the organization of a functional brain network in at-risk mental state patients with varying symptoms assessed with the PANSS and healthy volunteers during performance of a verbal fluency task known to recruit frontal lobe networks and to be impaired in psychosis. We first examined between-groups differences in total network connectivity and global network compactness/efficiency. We then addressed the role of specific brain regions in the network organization by calculating the node-specific "betweeness centrality", "degree centrality" and "local average path length" metrics; different ways of assessing a region's importance in a network. We focused our analysis on the anterior cingulate cortex (ACC); a region known to support executive function that is structurally and functionally impaired in at-risk mental state patients. Although global network connectivity and efficiency were maintained in at-risk patients relative to the controls, we report a significant decrease in the contribution of the ACC to task-relevant network organization in at risk subjects with elevated symptoms (PANSS ≥ 45) relative to both the controls and the less symptomatic at-risk subjects, as reflected by a reduction in the topological centrality of the ACC. These findings provide evidence of network abnormalities and anterior cingulate cortex dysfunction in people with prodromal signs of schizophrenia.