A mathematical framework for misinformation propagation in complex networks: Topology-dependent distortion and...

Area of Science:

• Complex Systems Science
• Network Science
• Information Theory

Background:

• Misinformation is widespread across diverse systems.
• Quantifying information distortion in networks is difficult due to context and network heterogeneity.
• Existing models struggle with real-world network complexity.

Purpose of the Study:

• To develop a general mathematical framework for quantifying information distortion in distributed systems.
• To analyze how local errors propagate and accumulate along network paths.
• To understand the topological signatures of misinformation in various network structures.

Main Methods:

• Developed a mathematical framework modeling error accumulation along network geodesics.
• Utilized drift-fluctuation decomposition of binomial noise for analysis.
• Derived closed-form expressions for node-level perception distributions.
• Applied the framework to canonical graph ensembles (Erdős-Rényi, scale-free, small-world, regular lattices).

Main Results:

• Discovered a shift-invariance principle for error propagation in networks.
• Identified distinct misinformation profiles for different network topologies.
• Scale-free networks show misinformation suppression via hubs; small-world networks balance clustering and path length.
• Found a connectivity-dependent crossover in misinformation levels across network types.

Conclusions:

• Network topology critically influences information reliability and misinformation spread.
• Sparsity, structural organization, and connection costs define regimes of minimal misinformation.
• The framework provides analytical tools for understanding and controlling information distortion in complex networked systems.