Large-scale toxicity intervention in social networks: evaluating integer programming-optimized focal toxic structures

Abstract Social networks face growing threats from focal toxic structures (FTSs) that distort discourse and amplify toxic content. This study evaluates network intervention effectiveness of three FTS sets using a Russia–Ukraine conflict dataset (324,769 users): R1 FTS Set (79 structures from baseline WFSA), R2 FTS Set (78 structures from optimized WFSA called WFSA-IP), and R3 FTS Set (40 structures from hybrid selection $$R1 \oplus R2$$ , comprising best-performing structures from each disjoint set where $$R1 \cap R2 = \emptyset $$ ). We assessed intervention performance across four metrics using Bonferroni correction ( $$\alpha = 0.0125$$ ). The R2 FTS Set demonstrated superior effectiveness relative to R1 across all metrics, with large effect sizes ( $$d = 0.75$$ –1.49, all $$p < 0.0125$$ ). The R3 hybrid FTS Set consistently outperformed R1 but showed mixed performance versus R2 (1/4 metrics). Results establish clear FTSs’ intervention effectiveness hierarchies: optimized algorithm-identified structures (R2) achieve transformative improvements over baseline structures (R1), while hybrid selection approaches (R3) provide value over baseline but approach performance boundaries constrained by the constituent algorithms’ optimization levels. Findings offer actionable insights for large-scale content moderation using FTS-based intervention strategies with algorithmic diversity considerations.