The effect of an invasive species on the species richness of its host community can range from catastrophic to negligible to beneficial. Here, we use a network model of plant–pollinator community formation to consider the influence of invader and invasion-related properties (including physical characteristics, assignment and type of interacting partners, and number of independent introductions of the species into the community) and community properties (including connectance and nestedness) on the outcome of an invasion. As expected from empirical work, invaders with properties atypical of the regional species pool drive the strongest changes in species richness. However, we find that an increase in species richness corresponds to an increase in the community's spectral nestedness coupled with a decrease in connectance. While such a response has been observed in real invaded systems, these results differ from previous theoretical studies in which these two measures respond in a similar way outside the context of species invasions.