Abstract

Complex systems are frequently organised as networks of interconnected components whose behaviour depends on the stability of relationships between nodes. Examples include communication systems, infrastructure networks, ecological interactions, social networks, and financial systems. This paper interprets network stability within the Paton System framework as an admissibility condition governing the persistence of interconnected systems. Network systems remain stable when interactions between nodes remain compatible with structural and operational constraints. When interaction pressures exceed these limits, instability may propagate through the network, potentially leading to cascading disruption or systemic collapse. Understanding network stability through admissibility boundaries provides a structural interpretation of resilience and instability in complex interconnected systems.