Aphasia is a common consequence of a stroke which affects language processing. In search of an objective biomarker for aphasia, we used EEG to investigate how functional network patterns in the cortex are affected in persons with post-stroke chronic aphasia (PWA) compared to healthy controls (HC) while they are listening to a story. EEG was recorded from 22 HC and 27 PWA while they listened to a 25-min-long story. Functional connectivity between scalp regions was measured with the weighted phase lag index. The Network-Based Statistics toolbox was used to detect altered network patterns and to investigate correlations with behavioural tests within the aphasia group. Differences in network geometry were assessed by means of graph theory and a targeted node-attack approach. Group-classification accuracy was obtained with a support vector machine classifier. PWA showed stronger inter-hemispheric connectivity compared to HC in the theta-band (4.5-7 Hz), whilst a weaker subnetwork emerged in the low-gamma band (30.5-49 Hz). Two subnetworks correlated with semantic fluency in PWA respectively in delta- (1-4 Hz) and low-gamma-bands. In the theta-band network, graph alterations in PWA emerged at both local and global level, whilst only local changes were found in the low-gamma-band network. As assessed with the targeted node-attack, PWA exhibit a more scale-free network compared to HC. Network metrics effectively discriminated PWA and HC (AUC = 83%). Overall, we showed for that EEG-network metrics are effective biomarkers to assess natural speech processing in chronic aphasia. We hypothesize that the detected alterations reflect compensatory mechanisms associated with recovery.