Synwalk: community detection via random walk modelling

Complex systems, abstractly represented as networks, are ubiquitous in everyday life. Analyzing and understanding these systems requires, among others, tools for community detection. As no single best community detection algorithm can exist, robustness across a wide variety of problem settings is desirable. In this work, we present Synwalk, a random walk-based community detection method. Synwalk builds upon a solid theoretical basis and detects communities by synthesizing the random walk induced by the given network from a class of candidate random walks. We thoroughly validate the effectiveness of our approach on synthetic and empirical networks, respectively, and compare Synwalk’s performance with the performance of Infomap and Walktrap (also random walk-based), Louvain (based on modularity maximization) and stochastic block model inference. Our results indicate that Synwalk performs robustly on networks with varying mixing parameters and degree distributions. We outperform Infomap on networks with high mixing parameter, and Infomap and Walktrap on networks with many small communities and low average degree. Our work has a potential to inspire further development of community detection via synthesis of random walks and we provide concrete ideas for future research.

Optimizing modularity with nonnegative matrix factorization

Community structure detection is one of the fundamental problems in complex network analysis towards understanding the topology structure and function of the network. Modularity is a criterion to evaluate the quality of community structures, and optimization of this quality function over the possible divisions of a network is a sensitive detection method for community structure. However, the direct application of this method is computationally costly. Nonnegative matrix factorization (NMF) is a widely used method for community detection. In this paper, we show that modularity maximization can be approximately reformulated under the framework of NMF with Frobenius norm, especially when [Formula: see text] is large. A new algorithm for detecting community structure is proposed based on the above finding. The new method is compared with four state-of-the-art methods on both synthetic and real-world networks, showing its higher clustering quality over the existing methods.

Incremental Community Detection on Large Complex Attributed Network

Community detection on network data is a fundamental task, and has many applications in industry. Network data in industry can be very large, with incomplete and complex attributes, and more importantly, growing. This calls for a community detection technique that is able to handle both attribute and topological information on large scale networks, and also is incremental. In this article, we propose inc-AGGMMR, an incremental community detection framework that is able to effectively address the challenges that come from scalability, mixed attributes, incomplete values, and evolving of the network. Through construction of augmented graph, we map attributes into the network by introducing attribute centers and belongingness edges. The communities are then detected by modularity maximization. During this process, we adjust the weights of belongingness edges to balance the contribution between attribute and topological information to the detection of communities. The weight adjustment mechanism enables incremental updates of community membership of all vertices. We evaluate inc-AGGMMR on five benchmark datasets against eight strong baselines. We also provide a case study to incrementally detect communities on a PayPal payment network which contains users with transactions. The results demonstrate inc-AGGMMR’s effectiveness and practicability.

Reduction of the molecular hamiltonian matrix using quantum community detection

Quantum chemistry is interested in calculating ground and excited states of molecular systems by solving the electronic Schrödinger equation. The exact numerical solution of this equation, frequently represented as an eigenvalue problem, remains unfeasible for most molecules and requires approximate methods. In this paper we introduce the use of Quantum Community Detection performed using the D-Wave quantum annealer to reduce the molecular Hamiltonian matrix in Slater determinant basis without chemical knowledge. Given a molecule represented by a matrix of Slater determinants, the connectivity between Slater determinants (as off-diagonal elements) is viewed as a graph adjacency matrix for determining multiple communities based on modularity maximization. A gauge metric based on perturbation theory is used to determine the lowest energy cluster. This cluster or sub-matrix of Slater determinants is used to calculate approximate ground state and excited state energies within chemical accuracy. The details of this method are described along with demonstrating its performance across multiple molecules of interest and bond dissociation cases. These examples provide proof-of-principle results for approximate solution of the electronic structure problem using quantum computing. This approach is general and shows potential to reduce the computational complexity of post-Hartree–Fock methods as future advances in quantum hardware become available.