Community recognition continues to be a significant difficulty in the analysis of complex networks, especially in dynamic and stochastic contexts where communities change over time. Conventional spectral clustering and Markovian models either include structural regularities or temporal dependencies, although frequently lack the ability to amalgamate both within a cohesive theoretical framework. This study presents a Fourier operator framework inspired by quantum walks that integrates spectral graph theory, Markov processes, and quantum brain dynamics for the discovery of modular structures. We specifically build Fourier-Markov operators based on quantum walk principles to encapsulate both global frequency components and local transition dynamics of evolving networks. Our system utilizes superposition and interference effects by mapping random walks into a quantum-inspired Hilbert space, therefore uncovering latent modular structures with enhanced resolution. The resultant operator family facilitates interpretable community partitions, scalable computation using hybrid classicalquantum methodologies, and resilient detection across temporal snapshots. Experimental assessments on benchmark dynamic networks—encompassing social, biological, and financial graphs—indicate that our approach attains enhanced modularity optimization, temporal stability, and uncertainty calibration relative to leading community detection benchmarks. This study emphasizes the promise of quantum-spectral operators as a novel basis for examining Markovian community dynamics in intricate systems.
Community recognition continues to be a significant difficulty in the analysis of complex networks, especially in dynamic and stochastic contexts where communities change over time. Conventional spectral clustering and Markovian models either include structural regularities or temporal dependencies, although frequently lack the ability to amalgamate both within a cohesive theoretical framework. This study presents a Fourier operator framework inspired by quantum walks that integrates spectral graph theory, Markov processes, and quantum brain dynamics for the discovery of modular structures. We specifically build Fourier-Markov operators based on quantum walk principles to encapsulate both global frequency components and local transition dynamics of evolving networks. Our system utilizes superposition and interference effects by mapping random walks into a quantum-inspired Hilbert space, therefore uncovering latent modular structures with enhanced resolution. The resultant operator family facilitates interpretable community partitions, scalable computation using hybrid classicalquantum methodologies, and resilient detection across temporal snapshots. Experimental assessments on benchmark dynamic networks—encompassing social, biological, and financial graphs—indicate that our approach attains enhanced modularity optimization, temporal stability, and uncertainty calibration relative to leading community detection benchmarks. This study emphasizes the promise of quantum-spectral operators as a novel basis for examining Markovian community dynamics in intricate systems.
In this research, the computational efficiency of large-scale social network analysis is enhanced by the use of quantum random walk algorithms. The goal of this project is to address the need for high-efficiency centralized analysis of large-scale, heterogeneous social networks, community discovery, and dynamic effect mapping. In a theoretically sound framework of quantum random walks, amplitude superposition and unitary evolution principles have been used to improve both the sensitivity to local and global aspects. The solution uses real social network data with up to 5,000 nodes and more than 60,000 edges, and the testing results demonstrate its excellent scalability and fast convergence. Quantum algorithms have discovered community divisions and cut the mixing time by roughly 2.3 times after multiple optimizations. The performance indicators demonstrate that the above method has greatly improved key node detection accuracy and computation time as compared to the conventional baseline model in noisy situations. According to the aforementioned research, quantum-inspired algorithms have been used to expedite the analysis of large-scale data and reveal hidden structures that are challenging to identify using conventional techniques, such as bridge nodes and core-periphery distributions. The research assist data-driven choices in digital social ecosystems and lay the groundwork for in-depth network analysis.
Graph Representation Learning (GRL) has emerged as a cornerstone technique for analysing complex, networked data across diverse domains, including biological systems, social networks, and data analysis. Traditional GRL methods often struggle to capture intricate relationships within complex graphs, particularly those exhibiting non-trivial structural properties such as power-law distributions or hierarchical structures. This paper introduces a novel quantum-inspired algorithm for GRL, utilizing hybrid Quantum-Classical Walks to overcome these limitations. Our approach combines the benefits of both quantum and classical dynamics, allowing the walker to simultaneously explore both highly local and far-reaching connections within the graph. Preliminary results for a case study in network community detection shows that this hybrid dynamic enables the algorithm to adapt effectively to complex graph topologies, offering a robust and versatile solution for GRL tasks.
Many systems such as social networks and biological networks take the form of complex networks, which have a community structure.Community detection in complex networks is of great interest to many researchers in statistical physics and mathematical physics.There have been studies on community detection that use the classical random walk.The present study utilizes the discrete-time quantum walk instead.The quantum walk plays an important role in various fields, especially in research on quantum computers, and attracts much attention from mathematical physics too.The discrete-time quantum walk has two properties: it linearly spreads on a flat space, and it localizes in some cases because of quantum coherence.We demonstrate that these properties of the quantum walk are useful for community detection on complex networks.We define the discrete-time quantum walk on complex networks and utilize it for community detection.We numerically show that the quantum walk with a Fourier coin is localized in a community to which the initial node belongs.Meanwhile, the quantum walk with a Grover coin tends to be localized around the initial node, not over a community.The probability of a classical random walk on the same network converges to a uniform distribution with a relaxation time generally unknown a priori.We thus claim that the time average of the probability of a Fourier-coin quantum walk on complex networks reveals the community structure more explicitly than that of a Grover-coin quantum walk and a snapshot of the classical random walk.We first demonstrate our method of community detection for a prototypical three-community network, producing the correct grouping.We then apply our method to two real-world networks, namely, Zachary's karate club and the U.S. Airport network.We successfully reveal the community structure, the two communities of the instructor and the administrator in the former and major airline companies in the latter.
This paper presents a novel approach to graph traversal and feature extraction leveraging the principles of quantum walks. Classical graph algorithms often suffer from performance limitations when dealing with large, complex graphs, primarily due to their sequential nature and the exponential growth of possible paths. Quantum walks, utilizing superposition and interference, provide a fundamentally different paradigm for graph exploration, offering the potential for significant speedups. We detail the theoretical framework for applying quantum walks to graph traversal, focusing on the efficient extraction of features from nodes and edges. The core concept involves mapping the graph's nodes and edges onto a quantum Hilbert space, allowing the quantum walk to explore the graph's connectivity in a probabilistic manner. We demonstrate how interference effects can be strategically utilized to guide the walk towards regions of interest, thereby enhancing feature extraction. The methodology outlined here provides a robust foundation for developing quantum algorithms for graph analysis across various domains, including social network analysis, knowledge graph reasoning, and anomaly detection. This work establishes a new direction for graph processing, shifting from classical sequential algorithms to quantum probabilistic exploration, ultimately leading to improved efficiency and scalability.
Complex networks are structurally disordered systems that often display clustering behavior. The emergent clusters, also known as communities, consist of nodes that are more connected among themselves than they are connected with the rest of the network. Analyzing community structure is an important problem in network theory, with numerous applications in different fields. In this work I investigate the evolution of a continuoustime quantum random walk on a social network with benchmark community structure and show that it can be used to perform community detection.
Link prediction is a fundamental task in network science that involves estimating the likelihood of missing or future connections between nodes based on the structural patterns of a graph. While Graph Neural Networks (GNNs) have become a dominant approach, Random Walk (RW)-based methods remain highly relevant due to their lower computational demands in large-scale networks. Although recent hybrid quantum-classical walks have shown promise in exploring graph structures, existing continuous-time models are computationally expensive as they require solving high-dimensional systems of differential equations. In this paper, we propose a discrete version of a recent hybrid quantum-classical random walk algorithm that significantly improves computational efficiency by utilizing state vector representations instead of density matrices. Our method, inspired by the Quantum Jumps approach, alternates between coherent evolution and measurement-driven state collapse to generate trajectories for node embeddings. We integrate this algorithm into a link prediction pipeline and evaluate its performance across various synthetic topologies, including Grid, Power-Law, Erdös-Rényi, Barabási-Albert, and Community graphs. The experimental results demonstrate that the proposed discrete hybrid walks consistently outperform classical random walk approaches in Community and Grid topologies, showing that quantum-inspired dynamics can capture complex structural information more effectively than classical dynamics for specific topologies.