From Classical to Dangling Centrality: Enhancing Quantum-Inspired Fuzzy Social Network Optimization for Distributed Control Systems

The proposed methodology models the distributed control system as a directed complex network, where nodes represent sensors, actuators, and controllers, and edges capture physical flow, control signals, and information exchange. This work builds upon our previously proposed dangling centrality framework for quantum graph representations, extending it toward control-oriented optimization using a quantum-inspired fuzzy approach.

Initially, the system network is encoded into a representation analogous to a quantum state space, where each node's structural influence is mapped to a probability amplitude. A quantum-inspired superposition mechanism is employed to evaluate multiple influence propagation paths simultaneously, enabling efficient exploration of complex network interactions. Dangling centrality, introduced in our prior work, is incorporated through a link-removal strategy to capture network sensitivity and identify structurally critical nodes that significantly impact control stability.

To address uncertainty and incomplete information in real-world control environments, a fuzzy inference layer is integrated into the framework. Classical centrality measures, including degree, betweenness, and eigenvector centrality, along with dangling centrality, are transformed into fuzzy variables and combined using rule-based reasoning. This enables adaptive weighting of multiple structural indicators under varying operating conditions.

Finally, results are extracted through comparative ranking and sensitivity analysis across classical and quantum-inspired evaluations. The methodology highlights nodes that consistently exhibit high structural influence and dynamic sensitivity, supporting improved decision-making for control optimization, fault detection, and system resilience. The proposed framework is compatible with hybrid quantum-classical implementations and provides a pathway toward future realization on near-term quantum computing platforms.

The practical demonstration of the proposed quantum-inspired fuzzy centrality framework is carried out through a simulation-based implementation, supported by a conceptual mapping to quantum computational principles. The distributed control system is modeled as a network derived from a three-tank cyber-physical system, where nodes represent system components and edges represent physical and informational interactions.

The methodology is implemented in a classical simulation environment (e.g., Python/Matlab), where the network is first encoded into a structure analogous to a quantum state representation. The quantum-inspired superposition mechanism is simulated by evaluating multiple influence propagation paths in parallel through matrix-based computations, mimicking the probabilistic exploration of quantum systems. Dangling centrality is computed using a link-removal strategy to analyze structural sensitivity, and its behavior is compared with classical centrality measures across different network configurations.

To further align with quantum computational frameworks, a conceptual quantum circuit model is formulated, where nodes correspond to qubit states and centrality values are interpreted as amplitude distributions. The preparation stage corresponds to initializing the system state, while transformation steps reflect influence propagation and structural perturbation. Measurement is represented by extracting node rankings based on amplitude-like values.

The results demonstrate consistent identification of critical nodes across simulation scenarios, validating the correctness and robustness of the approach. This hybrid simulation-based validation provides a practical and scalable pathway for future implementation on near-term quantum platforms.

The proposed quantum-inspired fuzzy centrality framework demonstrates strong potential for scaling to realistic problem sizes through a hybrid quantum–classical architecture. In this approach, classical computing is utilized for network construction, preprocessing, and fuzzy inference, while quantum-inspired components guide the exploration of complex influence patterns and structural sensitivities. This division enables efficient handling of large-scale distributed control systems, such as smart grids, industrial automation networks, and IoT-enabled cyber-physical infrastructures.

A credible hybridization strategy involves encoding sub-graphs or critical regions of the network into quantum-compatible representations, where influence propagation and node importance evaluation can be treated as amplitude evolution processes. Classical routines manage adjacency structures and rule-based fuzzy aggregation, while quantum-inspired or future quantum modules focus on parallel evaluation of multiple structural configurations. This layered design ensures scalability while remaining compatible with near-term quantum computing paradigms.

From a computational perspective, classical centrality measures particularly those based on shortest paths such as betweenness-exhibit high computational cost for large networks. The proposed framework reduces repeated global recomputation by incorporating dangling centrality, which evaluates structural sensitivity through localized link-removal operations. Combined with parallel exploration inspired by quantum superposition, this leads to more efficient identification of critical nodes in large and dynamic systems.

While full quantum advantage is not yet realized, the methodology provides a scalable pathway toward quantum acceleration as hardware matures. It is especially suited for complex, uncertain environments where hybrid processing can significantly enhance decision-making, robustness, and control performance in next-generation distributed systems.