Purpose The structure of relationships in a social network affects the suicide risk of the people embedded within it. Although current interventions often modify the social perceptions (e.g., perceived support and sense of belonging) for people at elevated risk, few seek to directly modify the structure of their surrounding social networks. We show social network structure is a worthwhile intervention target in its own right. Methods A simple model illustrates the potential of interventions to modify social structure. The effect of these basic structural interventions on suicide risk is simulated and evaluated. Its results are briefly compared to emerging empirical findings for real network interventions. Results Even an intentionally simplified intervention on social network structure (i.e., random addition of social connections) is likely to be both effective and safe. Specifically, this illustrative intervention had a high probability of reducing the overall suicide risk, without increasing the risk of those who were healthy at baseline. It also frequently resolved stable, high-risk clusters of people at elevated risk. These illustrative results are generally consistent with emerging evidence from real social network interventions for suicide. Conclusion Social network structure is a neglected, but valuable intervention target for suicide prevention.