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Persistent developmental stuttering is a speech disorder that primarily affects normal speech fluency but encompasses a complex set of symptoms ranging from reduced sensorimotor integration to socioemotional challenges. Here, we investigated the whole-brain structural connectome and its topological alterations in adults who stutter. Diffusion-weighted imaging data of 33 subjects (13 adults who stutter and 20 fluent speakers) were obtained along with a stuttering severity evaluation. The structural brain network properties were analysed using network-based statistics and graph theoretical measures particularly focussing on community structure, network hubs and controllability. Bayesian power estimation was used to assess the reliability of the structural connectivity differences by examining the effect size. The analysis revealed reliable and wide-spread decreases in connectivity for adults who stutter in regions associated with sensorimotor, cognitive, emotional and memory-related functions. The community detection algorithms revealed different subnetworks for fluent speakers and adults who stutter, indicating considerable network adaptation in adults who stutter. Average and modal controllability differed between groups in a subnetwork encompassing frontal brain regions and parts of the basal ganglia. The results revealed extensive structural network alterations and substantial adaptation in neural architecture in adults who stutter well beyond the sensorimotor network. These findings highlight the impact of the neurodevelopmental effects of persistent stuttering on neural organization and the importance of examining the full structural connectome and the network alterations that underscore the behavioural phenotype.