Human trade and movements are central to biological invasions worldwide. Human activities not only transport species across biogeographical barriers, but also accelerate their post‐introduction spread in the landscape. Thus, by constraining human movements, the spatial structure of road networks might greatly affect the regional spread of invasive species. However, few invasion models have accounted for the topology of road networks so far, and its importance for explaining the regional distribution of invasive species remains mostly unexplored. To address this issue, we developed a spatially explicit and mechanistic human‐mediated dispersal model that accounts and tests for the influence of transport networks on the regional spread of invasive species. Using as a model the spread of the invasive ant Lasius neglectus in the middle Rhône valley (France), we show that accounting for the topology of road networks improves our ability to explain the current distribution of the invasive ant. In contrast, we found that using human population density as a proxy for the frequency of transport events decreases models' performance and might thus not be as appropriate as previously thought. Finally, by differentiating road networks into sub‐networks, we show that national and regional roads are more important than smaller roads for explaining spread patterns. Overall, our results demonstrate that the topology of transport networks can strongly bias regional invasion patterns and highlight the importance of better incorporating it into future invasion models. The mechanistic modelling approach developed in this study should help invasion scientists explore how human‐mediated dispersal and topography shape invasion dynamics in landscapes. Ultimately, our approach could be combined with demographic, natural dispersal and environmental suitability models to refine spread scenarios and improve invasive species monitoring and management at regional to national scales. Keywords: biological invasions, human‐mediated dispersal, road network, secondary spread, spatially explicit model, stochastic jump model