scholarly journals A Sparse Completely Positive Relaxation of the Modularity Maximization for Community Detection

2018 ◽  
Vol 40 (5) ◽  
pp. A3091-A3120 ◽  
Author(s):  
Junyu Zhang ◽  
Haoyang Liu ◽  
Zaiwen Wen ◽  
Shuzhong Zhang
Keyword(s):  
Community Detection ◽  
Completely Positive ◽  
Modularity Maximization

scholarly journals Reduction of the molecular hamiltonian matrix using quantum community detection

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Susan M. Mniszewski ◽  
Pavel A. Dub ◽  
Sergei Tretiak ◽  
Petr M. Anisimov ◽  
Yu Zhang ◽  
...  
Keyword(s):  
Community Detection ◽  
Slater Determinant ◽  
Hamiltonian Matrix ◽  
Approximate Methods ◽  
Molecular Systems ◽  
Hartree Fock ◽  
Molecular Hamiltonian ◽  
Structure Problem ◽  
Modularity Maximization ◽  
Chemical Knowledge

AbstractQuantum 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.

Incremental Community Detection on Large Complex Attributed Network

2021 ◽  
Vol 15 (6) ◽  
pp. 1-20
Author(s):  
Zhe Chen ◽  
Aixin Sun ◽  
Xiaokui Xiao
Keyword(s):  
Community Detection ◽  
Large Scale ◽  
Network Data ◽  
Topological Information ◽  
Community Membership ◽  
Attributed Network ◽  
Benchmark Datasets ◽  
Modularity Maximization ◽  
Large Scale Networks

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.

scholarly journals The Eminence of Co-Expressed Ties in Schizophrenia Network Communities

Data ◽  
2019 ◽  
Vol 4 (4) ◽  
pp. 149
Author(s):  
Amulyashree Sridhar ◽  
Sharvani GS ◽  
AH Manjunatha Reddy ◽  
Biplab Bhattacharjee ◽  
Kalyan Nagaraj
Keyword(s):  
Community Detection ◽  
Biological Networks ◽  
Gene Networks ◽  
Biological Interactions ◽  
K Nearest Neighbors ◽  
Nonlinear Network ◽  
Detection Algorithms ◽  
Network Communities ◽  
Disease Condition ◽  
Modularity Maximization

Exploring gene networks is crucial for identifying significant biological interactions occurring in a disease condition. These interactions can be acknowledged by modeling the tie structure of networks. Such tie orientations are often detected within embedded community structures. However, most of the prevailing community detection modules are intended to capture information from nodes and its attributes, usually ignoring the ties. In this study, a modularity maximization algorithm is proposed based on nonlinear representation of local tangent space alignment (LTSA). Initially, the tangent coordinates are computed locally to identify k-nearest neighbors across the genes. These local neighbors are further optimized by generating a nonlinear network embedding function for detecting gene communities based on eigenvector decomposition. Experimental results suggest that this algorithm detects gene modules with a better modularity index of 0.9256, compared to other traditional community detection algorithms. Furthermore, co-expressed genes across these communities are identified by discovering the characteristic tie structures. These detected ties are known to have substantial biological influence in the progression of schizophrenia, thereby signifying the influence of tie patterns in biological networks. This technique can be extended logically on other diseases networks for detecting substantial gene “hotspots”.

scholarly journals Community Detection in Airline Networks: An Empirical Analysis of American vs. Southwest Airlines

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Weiwei Wu ◽  
Haoyu Zhang ◽  
Shengrun Zhang ◽  
Frank Witlox
Keyword(s):  
Case Studies ◽  
Empirical Analysis ◽  
Community Detection ◽  
Topological Structure ◽  
Community Structures ◽  
Operation Pattern ◽  
Airline Networks ◽  
Modularity Maximization ◽  
Influential Nodes ◽  
Southwest Airlines

In this paper, we develop a route-traffic-based method for detecting community structures in airline networks. Our model is both an application and an extension of the Clauset-Newman-Moore (CNM) modularity maximization algorithm, in that we apply the CNM algorithm to large airline networks, and take both route distance and passenger volumes into account. Therefore, the relationships between airports are defined not only based on the topological structure of the network but also by a traffic-driven indicator. To illustrate our model, two case studies are presented: American Airlines and Southwest Airlines. Results show that the model is effective in exploring the characteristics of the network connections, including the detection of the most influential nodes and communities on the formation of different network structures. This information is important from an airline operation pattern perspective to identify the vulnerability of networks.

scholarly journals Limits of modularity maximization in community detection

2011 ◽  
Vol 84 (6) ◽  
Author(s):  
Andrea Lancichinetti ◽  
Santo Fortunato
Keyword(s):  
Community Detection ◽  
Modularity Maximization
Sign in / Sign up

Export Citation Format

Share Document