Signed graphs serve as a primary tool for modelling social networks. They can represent relationships between individuals (i.e., nodes) with the use of signed edges. Finding communities in a signed graph is of great importance in many areas, for example, targeted advertisement. We propose an algorithm to detect multiple communities in a signed graph. Our method reduces the multi-community detection problem to a quadratic binary unconstrained optimization problem and uses state-of-the-art quantum or classical optimizers to find an optimal assignment of each individual to a specific community.
Signed graphs serve as a primary tool for modelling social networks. They can represent relationships between individuals (i.e., nodes) with the use of signed edges. Finding communities in a signed graph is of great importance in many areas, for example, targeted advertisement. We propose an algorithm to detect multiple communities in a signed graph. Our method reduces the multi-community detection problem to a quadratic binary unconstrained optimization problem and uses state-of-the-art quantum or classical optimizers to find an optimal assignment of each individual to a specific community.
A very important problem in combinatorial optimization is the partitioning of a network into communities of densely connected nodes; where the connectivity between nodes inside a particular community is large compared to the connectivity between nodes belonging to different ones. This problem is known as community detection, and has become very important in various fields of science including chemistry, biology and social sciences. The problem of community detection is a twofold problem that consists of determining the number of communities and, at the same time, finding those communities. This drastically increases the solution space for heuristics to work on, compared to traditional graph partitioning problems. In many of the scientific domains in which graphs are used, there is the need to have the ability to partition a graph into communities with the "highest quality" possible since the presence of even small isolated communities can become crucial to explain a particular phenomenon. We have explored community detection using the power of quantum annealers, and in particular the D-Wave 2X and 2000Q machines. It turns out that the problem of detecting at most two communities naturally fits into the architecture of a quantum annealer with almost no need of reformulation. This paper addresses a systematic study of detecting two or more communities in a network using a quantum annealer.
We present a quantum-inspired algorithm that utilizes Quantum Hamiltonian Descent (QHD) for efficient community detection. Our approach reformulates the community detection task as a Quadratic Unconstrained Binary Optimization (QUBO) problem, and QHD is deployed to identify optimal community structures. We implement a multi-level algorithm that iteratively refines community assignments by alternating between QUBO problem setup and QHD-based optimization. Benchmarking shows our method achieves up to 5.49% better modularity scores while requiring less computational time compared to classical optimization approaches. This work demonstrates the potential of hybrid quantum-inspired solutions for advancing community detection in largescale graph data.
In a network, the vertices with similar characteristics construct communities. The vertices in a community are well-connected. Detecting the communities in a network is a challenging and important problem in the theory of complex networks. One approach to solving this problem uses the classical random walks on graphs. In quantum computing, quantum walks are the quantum mechanical counterparts of classical random walks. In this article, we employ a variant of Szegedy's quantum walk to develop a procedure for discovering the communities in networks. The limiting probability distribution of quantum walks assists us in determining the inclusion of a vertex in a community. We apply our community detection procedure to a variety of graphs and social networks, including the relaxed caveman graph, l-partition graph, Karate club graph, and the dolphin's social network, among others.
Fraud detection within transaction data is crucial for maintaining financial security, especially in the era of big data. This paper introduces a novel fraud detection method that utilizes quantum computing to implement community detection in transaction networks. We model transaction data as an undirected graph, where nodes represent accounts and edges indicate transactions between them. A modularity function is defined to measure the community structure of the graph. By optimizing this function through the Quadratic Unconstrained Binary Optimization (QUBO) model, we identify the optimal community structure, which is then used to assess the fraud risk within each community. Using a Coherent Ising Machine (CIM) to solve the QUBO model, we successfully divide 308 nodes into four communities. We find that the CIM computes faster than the classical Louvain and simulated annealing (SA) algorithms. Moreover, the CIM achieves better community structure than Louvain and SA as quantified by the modularity function. The structure also unambiguously identifies a high-risk community, which contains almost 70% of all the fraudulent accounts, demonstrating the practical utility of the method for banks' anti-fraud business.
Abstract The problem of detecting communities in real-world networks has been extensively studied in the past, but most of the existing approaches work on single-domain networks, i.e. they consider only one type of relationship between nodes. Single-domain networks may contain noisy edges and they may lack some important information. Thus, some authors have proposed to consider the multiple relationships that connect the nodes of a network, thus obtaining multi-domain networks. However, most community detection approaches are limited to multi-layer networks, i.e. networks generated from the superposition of several single-domain networks (called layers) that are regarded as independent of each other. In addition to being computationally expensive, multi-layer approaches might yield inaccurate results because they ignore potential dependencies between layers. This paper proposes a multi-domain discrete-time quantum walks (MDQW) model for multi-domain networks. First, the walking space of network nodes in multi-domain network is constructed. Second, the quantum permutation circuit of the coin state is designed based on the coded particle state. Then, using different coin states, the shift operator performs several quantum walks on the particles. Finally, the corresponding update rule is selected to move the node according to the measurement result of the quantum state. With continuous update iteration, the shift operator automatically optimizes the discovered community structure. We experimentally compared our MDQW method with four state-of-the-art competitors on five real datasets. We used the normalized mutual information (NMI) to compare clustering quality, and we report an increase in NMI of up to 3.51 of our MDQW method in comparison with the second-best performing competitor. The MDQW method is much faster than its competitors, allowing us to conclude that MDQW is a useful tool in the analysis of large real-life multi-domain networks. Finally, we illustrate the usefulness of our approach on two real-world case studies.
Determining community structure is a central topic in the study of complex networks, be it technological, social, biological or chemical, static or in interacting systems.In this paper, we extend the concept of community detection from classical to quantum systems-a crucial missing component of a theory of complex networks based on quantum mechanics.We demonstrate that certain quantum mechanical effects cannot be captured using current classical complex network tools and provide new methods that overcome these problems.Our approaches are based on defining closeness measures between nodes, and then maximizing modularity with hierarchical clustering.Our closeness functions are based on quantum transport probability and state fidelity, two important quantities in quantum information theory.To illustrate the effectiveness of our approach in detecting community structure in quantum systems, we provide several examples, including a naturally occurring light-harvesting complex, LHCII.The prediction of our simplest algorithm, semiclassical in nature, mostly agrees with a proposed partitioning for the LHCII found in quantum chemistry literature, whereas our fully quantum treatment of the problem uncovers a new, consistent, and appropriately quantum community structure.