Information networks: principles, axioms, and higher-order structures

This paper establishes fundamental principles and precise definitions for information networks, distinguishing them from classical material networks. Material networks obey conservation laws (mass, energy, momentum) that necessitate the division of flow at junctions. Information networks, by contrast, operate under fundamentally different rules: information can be copied rather than divided, and its transmission does not deplete the source. These observations are formalized into a set of axioms defining information networks, including the non-conservation of information quantity, replicability without degradation, and non-rivalrous consumption. Mathematical consequences are derived, including scaling laws, entropy dynamics, and network capacity bounds. The framework is then extended to higher-order interactions using hypergraphs and simplicial complexes, which naturally capture the simultaneous broadcast and hierarchical sharing properties of information flow. A concrete example of coupled oscillator networks with two distinct coupling schemes (commodity versus informational) illustrates the applicability of the framework. The proposed definitions provide a foundation for analyzing information networks across physics, computer science, economics, and biology.