Truth and distortion in complex networks: a global consistency approach

Abstract: Understanding how reliable information emerges in interconnected populations is a challenge in social science, network theory and data analysis. Many existing approaches model treat truth as an external reference or a property of individual statements, rather than a global consistency feature of the network itself. We introduce a network-based approach in which truth arises from global relational coherence in a multiplex system of interacting individuals. Nodes are individuals with internal states, while edges capture different types of interactions, including declared relations, observed behavior, influence asymmetries and information exchange. We evaluate how well node states align with cooperative or antagonistic interactions, incorporating coercion, variability and mismatches between what individuals say and what they do. Simulations on synthetic networks of one thousand nodes show that the minimum global inconsistency does not coincide with majority opinion or simple averaging. Nodes contributing most to inconsistency create conflicting constraints across interaction layers, defining a measurable distortion field. For example, in online social media during an election, a small number of accounts spreading inconsistent or manipulative information across groups can disrupt overall coherence, even when most users appear to agree. These results suggest possible applications in assessing relational coherence, identifying irreducible inconsistencies and analyzing constraints on collective states. Therefore, truth can be seen as the state of maximal relational coherence, rather than simple agreement or correctness of individual statements.