The factors governing invasiveness and invasibility are important for understanding invasions in plant communities, but most previous work does not incorporate network‐level interaction structure. We addressed this gap by simulating perennial plant communities at multiple life stages that varied in species richness and interaction network structures (transitive and intransitive), characteristics associated with species coexistence, using a stochastic lattice model that incorporated local competition, facilitation, and dispersal. Resident communities were invaded with alien species that varied in their fecundity, dispersal, and competitive abilities. We found that community structures that are known to promote coexistence also increased invasibility; communities with intransitive interaction networks on the whole were more invasible than transitive communities. However, the interaction between species richness and network structure was complex, as intransitive communities with few species were relatively resistant and transitive communities with many species were relatively invasible. Thus, simple rules linking intransitivity and diversity may not reflect the complex relationships between community structure and dynamics that occur in more realistic spatial systems. Spatial patterns of clustering and segregation were associated with higher invasibility and successful invaders intensified these patterns in communities, particularly at large spatial scales. Invasiveness and alien species abundance were associated with species‐level characteristics (fecundity and dispersal), but community‐level characteristics were also important, particularly competitive tolerance to the resident community. These results emphasize the importance of a community‐level approach, involving network‐level structure and spatial patterns, in adding nuance to our understanding of invasions in plant communities.