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Abstract Understanding what makes a community vulnerable to invasion is integral to the successful management of invasive species. Our understanding of how characteristics of resident plant interactions, such as the network architecture of interactions, can affect the invasibility of plant communities is limited. Using a simulation model, we tested how successfully a new plant invader established in communities with different network architectures of species interactions. We also investigated whether species interaction networks lead to relationships between invasibility and other community properties also affected by species interaction networks, such as diversity, species dominance, compositional stability and the productivity of the resident community. We found that higher invasibility strongly related with a lower productivity of the resident community. Plant interaction networks influenced diversity and invasibility in ways that led to complex but clear relationships between the two. Heterospecific interactions that increased diversity tended to decrease invasibility. Negative conspecific interactions always increased diversity and invasibility, but increased invasibility more when they increased diversity less. This study provides new theoretical insights into the effects of plant interaction networks on community invasibility and relationships between diversity and invasibility. Combined with increasing empirical evidence, these insights could have useful implications for the management of invasive plant species.