Joint Trust-Distrust Structure Shapes Belief Propagation and Collective Dynamics

Abstract

Belief propagation in social networks depends on how trust and distrust jointly shape interpersonal influence. We develop a network model that treats trust and distrust as distinct but statistically coupled quantities. Their joint values determine the net trust and uncertainty of each relationship, and a neighbor can influence an agent only when both threshold conditions are satisfied. We show that the correlation between trust and distrust reshapes the transition between consensus and fragmentation by changing the availability of influential neighbors. Network connectivity also affects this transition, whereas degree heterogeneity has a more limited effect when networks have comparable mean degree. Moreover, the availability of influential neighbors alone does not determine the final consensus: correlations between relational properties and network degree can select agents with different degree compositions, altering the direction and magnitude of collective belief. Finally, we introduce a comfort index that quantifies the expected availability of influential neighbors and analytically links the joint trust-distrust structure to collective dynamics. Our results establish a mechanistic connection between relational structure, effective social influence, and emergent collective belief states.