Regimes of Influence in Trust-Uncertainty Gated Networks

Abstract: In many social communities, individuals can simultaneously trust and distrust the same source, a feature standard opinion-dynamics models often ignore. We formalize this ambivalence with Gated Network Credence, in which each directed relationship encodes distinct trust and distrust assessments. These jointly determine "net trust" - the willingness to rely on a source - and "uncertainty" - the conflict between trust and distrust within the same relationship. Agents update beliefs only when net trust exceeds a threshold and uncertainty falls below another, yielding an effective influence graph whose topology drives long-run belief states. Sweeping both thresholds uncovers four regimes - Pluralistic, Selective, Concordant, and Fortified - that differ in openness to trust and conflict. We find a consistent hub-periphery reversal: in the Selective regime, high-degree agents dominate influence, whereas in the Concordant regime, stringent uncertainty filtering disproportionately removes active influence channels associated with high-degree agents, enabling peripheral lower-degree agents to exert greater leverage over the collective equilibrium. This reversal holds across synthetic and empirical networks. Our results show that belief dynamics depend not only on network structure but also on how relational ambivalence between trust and distrust gates interpersonal influence.