A Mathematical Framework for Misinformation Propagation in Complex Networks: Topology-Dependent Distortion and Control
Misinformation is pervasive in natural, biological, social, and engineered systems, yet its quantitative characterization remains challenging. We develop a general mathematical framework for quantifying information distortion in distributed systems by modeling how local transmission errors accumulate along network geodesics and reshape each agent's perceived global state. Through a drift-fluctuation decomposition of pathwise binomial noise, we derive closed-form expressions for node-level perception distributions and show that directional bias induces only a uniform shift in the mean, preserving the fluctuation structure. Applying the framework to canonical graph ensembles, we uncover strong topological signatures of misinformation: Erdős-Rényi random graphs exhibit a double-peaked distortion profile driven by connectivity transitions and geodesic-length fluctuations, scale-free networks suppress misinformation through hub-mediated integration, and optimally rewired small-world networks achieve comparable suppression by balancing clustering with short paths. A direct comparison across regular lattices, Erdős-Rényi random graphs, Watts-Strogatz small-world networks, and Barabási-Albert scale-free networks reveals a connectivity-dependent crossover. In the extremely sparse regime, scale-free and Erdős-Rényi networks behave similarly. At intermediate sparsity, Watts-Strogatz small-world networks exhibit the lowest misinformation. In contrast, Barabás-Albert scale-free networks maintain low misinformation in sparse and dense regimes, while regular lattices produce the highest distortion across connectivities. We additionally show how sparsity constraints, structural organization, and connection costs delineate regimes of minimal misinformation.