Benchmark Graphs Research Articles

An Experimental Evaluation of Similarity-Based and Embedding-Based Link Prediction Methods on Graphs

The task of inferring missing links or predicting future ones in a graph based on its current structure is referred to as link prediction. Link prediction methods that are based on pairwise node similarity are well-established approaches in the literature and show good prediction performance in many realworld graphs though they are heuristic. On the other hand, graph embedding approaches learn lowdimensional representation of nodes in graph and are capable of capturing inherent graph features, and thus support the subsequent link prediction task in graph. This paper studies a selection of methods from both categories on several benchmark (homogeneous) graphs with different properties from various domains. Beyond the intra and inter category comparison of the performances of the methods, our aim is also to uncover interesting connections between Graph Neural Network(GNN)- based methods and heuristic ones as a means to alleviate the black-box well-known limitation.

An Experimental Evaluation of Similarity-Based and Embedding-Based Link Prediction Methods on Graphs

The task of inferring missing links or predicting future ones in a graph based on its current structure is referred to as link prediction. Link prediction methods that are based on pairwise node similarity are well-established approaches in the literature and show good prediction performance in many realworld graphs though they are heuristic. On the other hand, graph embedding approaches learn lowdimensional representation of nodes in graph and are capable of capturing inherent graph features, and thus support the subsequent link prediction task in graph. This paper studies a selection of methods from both categories on several benchmark (homogeneous) graphs with different properties from various domains. Beyond the intra and inter category comparison of the performances of the methods, our aim is also to uncover interesting connections between Graph Neural Network(GNN)- based methods and heuristic ones as a means to alleviate the black-box well-known limitation.

Finding Maximum k-Cliques Faster Using Lazy Global Domination

A clique in a graph is a set of vertices, each of which is adjacent to every other vertex in this set. A k-clique relaxes this requirement, requiring vertices to be within a distance k of each other, rather than directly adjacent. In theory, a maximum clique algorithm can easily be adapted to solve the maximum k-clique problem, although large sparse k-clique graphs reduce to large dense clique graphs, which can be computationally challenging. We adapt a state of the art maximum clique algorithm to show that this reduction is in fact useful in practice, and introduce a lazy global domination rule which sometimes vastly reduces the search space. We include experimental results for a range of real-world and benchmark graphs, and a detailed look at random graphs. We also use thread-parallel search to solve some harder instances.

A local core number based algorithm for the maximum clique problem

‎The maximum clique problem (MCP) is to determine a complete subgraph of maximum cardinality in a graph‎. ‎MCP is a fundamental problem in combinatorial optimization and is noticeable for its wide range of applications‎. ‎In this paper‎, ‎we present two branch-and-bound exact algorithms for finding a maximum clique in an undirected graph‎. ‎Many efficient exact branch and bound maximum clique algorithms use approximate coloring to compute an upper bound on the clique number but‎, ‎as a new pruning strategy‎, ‎we show that local core number is more efficient‎. ‎Moreover‎, ‎instead of neighbors set of a vertex‎, ‎our search area is restricted to a subset of the set in each subproblem which speeds up clique finding process‎. ‎This subset is based on the core of the vertices of a given graph‎. ‎We improved the MCQ and MaxCliqueDyn algorithms with respect to the new pruning strategy and search area restriction‎. ‎Experimental results demonstrate that the improved algorithms outperform the previous well-known algorithms for many instances when applied to DIMACS benchmark and random graphs‎.

Quantum k-community detection: algorithm proposals and cross-architectural evaluation

Emerging quantum technologies represent a promising alternative for solving hard combinatorial problems in the post-Moore’s law era. For practical purposes, however, the current number of qubits limits the direct applicability to larger real-world instances in the near-term future. Therefore, a promising strategy to overcome this issue is represented by hybrid quantum classical algorithms which leverage classical as well as quantum devices. One prominent example of a hard computational problem is the community detection problem: a partition of a graph into distinct communities such that the ratio between intra-community and inter-community connectivity is maximized. In this paper, we explore the current potential of quantum annealing and gate-based quantum technologies to solve the community detection problem for an arbitrary number of communities. For this purpose, existing algorithms are (re-)implemented and new hybrid algorithms, that can be run on gate-model devices, are proposed. Their performance on standardized benchmark graphs has been evaluated and compared to the one of a state-of-the-art classical heuristic algorithm. Although no quantum speed-up has been achieved, the existing quantum annealing-based methods as well as the novel hybrid algorithms for gate-based quantum computers yield modularity values, which are similar to those of the classical heuristic. However, the modular architecture of the used algorithms allows for fast utilization of more powerful quantum technologies once they become available. Reproducibility: Our code and data are publicly available (Github in Quantum Modularization. https://github.com/jku-win se/quantum_modularization 2021).

A Graph Mining Approach for Ranking and Discovering the Interesting Frequent Subgraph Patterns

Graph mining is a well-established research field, and lately it has drawn in considerable research communities. It allows to process, analyze, and discover significant knowledge from graph data. In graph mining, one of the most challenging tasks is frequent subgraph mining (FSM). FSM consists of applying the data mining algorithms to extract interesting, unexpected, and useful graph patterns from the graphs. FSM has been applied to many domains, such as graphical data management and knowledge discovery, social network analysis, bioinformatics, and security. In this context, a large number of techniques have been suggested to deal with the graph data. These techniques can be classed into two primary categories: (i) a priori-based FSM approaches and (ii) pattern growth-based FSM approaches. In both of these categories, an extensive research work is available. However, FSM approaches are facing some challenges, including enormous numbers of frequent subgraph patterns (FSPs); no suitable mechanism for applying ranking at the appropriate level during the discovery process of the FSPs; extraction of repetitive and duplicate FSPs; user involvement in supplying the support threshold value; large number of subgraph candidate generation. Thus, the aim of this research is to make do with the challenges of enormous FSPs, avoid duplicate discovery of FSPs, and use the ranking for such patterns. Therefore, to address these challenges a new FSM framework A RAnked Frequent pattern-growth Framework (A-RAFF) is suggested. Consequently, A-RAFF provides an efficacious answer to these challenges through the initiation of a new ranking measure called FSP-Rank. The proposed ranking measure FSP-Rank effectively reduced the duplicate and enormous frequent patterns. The effectiveness of the techniques proposed in this study is validated by extensive experimental analysis using different benchmark and synthetic graph datasets. Our experiments have consistently demonstrated the promising empirical results, thus confirming the superiority and practical feasibility of the proposed FSM framework.

Clique Finder

The Maximum Clique Problem (MCP) is a classical NP-hard problem that has gained considerable attention due to its numerous real-world applications and theoretical complexity. It is inherently computationally complex, and so exact methods may require prohibitive computing time. Nature-inspired meta-heuristics have proven their utility in solving many NP-hard problems. In this research, we propose a simulated annealing-based algorithm that we call Clique Finder algorithm to solve the MCP. Our algorithm uses a logarithmic cooling schedule and two moves that are selected in an adaptive manner. The objective (error) function is the total number of missing links in the clique, which is to be minimized. The proposed algorithm was evaluated using benchmark graphs from the open-source library DIMACS, and results show that the proposed algorithm had a high success rate.

PEAVC: An improved minimum vertex cover solver for massive sparse graphs

Several important applications related to complex network analysis require finding small vertex covers in massive sparse graphs. To fulfill this task, this paper proposes a general algorithm framework named PEAF, which includes preprocessing stage, solving stage, and inverse-processing stage. Based on PEAF, a minimum vertex cover (MinVC) solver PEAVC is developed, which uses PreP to reduce the graph, BGVC to obtain a vertex cover of bipartite-graph components, FastVC2 to solve the connected components left, and Inv_PreP to get a vertex cover of the original problem. Computational experiments on 90 massive REAL-WORLD benchmark graphs indicate that PreP can reduce the vertex number by 83.25% on average, which is superior to other graph reduction methods. PEAVC performs remarkably well by discovering 5 best-known results (new upper bounds) never reported in the literature, match the best known results for 63 other instances and obtain exact MinVCs for 55 instances. Experiments also show that PEAVC has an extremely high performance.

Special Issue on Programming Models and Applications for Multicores and Manycores 2020

This special issue focuses on all aspects of parallel programming on multicore and manycore architectures such as programming models and systems, applications algorithms, performance analysis, and debugging and performance tools. It includes selected articles from the 2020 International Workshop on Programming Models and Applications for Multicores and Manycores (PMAM 2020), which was colocated with the PPoPP 2020 conference, in San Diego, California, February 22–26, 2020. From high-end servers to mobile phones, multicore and manycore systems are steadily entering every aspect of the information technology landscape. While this advanced technology enables new opportunities for scientific discovery, it also opens new challenges. In particular, although program developers have been trained in parallel programming, most existing parallel programs are still prone to errors such as data race and deadlock and suffer from suboptimal performance. In order to fully explore the computing power of multicore and manycore hardware architectures, innovations in parallel programming models as well as the associated development and execution eco-systems are urgently needed to enable delivery of error-free and high-performance parallel programs. The PMAM 2020 workshop provided a discussion forum for people interested in programming environments, models, tools, and applications specifically designed for parallel multicore and manycore hardware environments. The four outstanding contributions for this special issue were selected from eight workshop presentations. The accepted publications cover several emerging research directions, specifically focusing on programming models and runtime techniques on manycore and heterogeneous computing systems for graph and streaming applications, as summarized below. In “A Self-Adjusting Task Granularity Mechanism for the Java Lifeline-Based Global Load Balancer Library,” Finnerty et al. present a tuning mechanism that dynamically adjusts the sensitive task granularity in the load balancing scheme of X10 for Java parallel programs and demonstrate the improved performance of four applications on two manycore supercomputers. In “A Performance Predictor for Implementation Selection of Parallelized Static and Temporal Graph Algorithms,” Rehman et al. analyze the performance of graph workload with different algorithm and hardware conditions. They propose an inter-implementation predictor to choose the best performing parallel implementation for static and temporal graph benchmarks and inputs when executing on a CPU or a GPU architecture by leveraging analytical and neural network models. In “Sharing Non-Cache-Coherent Memory with Bounded Incoherence,” Ren et al. introduce a memory consistency approach, called bounded incoherence, that enables cached access to shared data-structures in non-cache-coherent memory. The proposed model ensures that updates to memory on one node are visible within at most a bounded amount of time on all other nodes. Test results show 30% performance improvement of the PowerGraph graph processing framework over state-of-the-art distributed approaches. In “Code Generation for Energy-Efficient Execution of Dynamic Streaming Task Graphs on Parallel and Heterogeneous Platforms,” Litzinger et al. enhance the programming model of streaming applications by introducing dynamic elements into the task graphs so that the runtime system can remap tasks and adapt the change of streaming-in task structures at runtime. The authors provide a prototype implementation of the toolchain and demonstrate low overhead and low energy consumption of the proposed remapping technique. We hope that the readers of the PMAM 2020 special issue will find the articles insightful in the field of parallel programming for multicore and manycore systems. The guest editors would like to thank all the reviewers and the Concurrency and Computation Practice and Experience Wiley office staff who worked hard to make this high-quality journal issue happen, while facing challenges from the COVID-19 pandemic. Data sharing is not applicable to this article as no new data were created or analyzed in this study.

GraphMix: Improved Training of GNNs for Semi-Supervised Learning

We present GraphMix, a regularization method for Graph Neural Network based semi-supervised object classification, whereby we propose to train a fully-connected network jointly with the graph neural network via parameter sharing and interpolation-based regularization. Further, we provide a theoretical analysis of how GraphMix improves the generalization bounds of the underlying graph neural network, without making any assumptions about the "aggregation" layer or the depth of the graph neural networks. We experimentally validate this analysis by applying GraphMix to various architectures such as Graph Convolutional Networks, Graph Attention Networks and Graph-U-Net. Despite its simplicity, we demonstrate that GraphMix can consistently improve or closely match state-of-the-art performance using even simpler architectures such as Graph Convolutional Networks, across three established graph benchmarks: Cora, Citeseer and Pubmed citation network datasets, as well as three newly proposed datasets: Cora-Full, Co-author-CS and Co-author-Physics.

An effective branch-and-bound algorithm for the maximum [formula omitted]-bundle problem

An s-bundle (where s is a positive integer) is a connected graph, the vertex connectivity of which is at least n−s, where n is the number of vertices in the graph. As a relaxation of the classical clique model, the s-bundle is relevant for representing cohesive groups with an emphasis on the connectivity of members; thus, it is of great practical importance. In this work, we investigate the fundamental problem of finding the maximum s-bundle from a given graph and present an effective branch-and-bound algorithm for solving this NP-hard problem. The proposed algorithm is distinguished owing to its new multi-branching rules, graph coloring-based bounding technique, and reduction rules using structural information. The experiments indicate that the algorithm outperforms the best-known approaches on a wide range of well-known benchmark graphs for different s values. In particular, compared with the popular Russian Doll Search algorithm, the proposed algorithm almost doubles the success rate of solving large social networks in an hour when s=5.

Pseudoinverse graph convolutional networks

Graph Convolutional Networks (GCNs) have proven to be successful tools for semi-supervised classification on graph-based datasets. We propose a new GCN variant whose three-part filter space is targeted at dense graphs. Our examples include graphs generated from 3D point clouds with an increased focus on non-local information, as well as hypergraphs based on categorical data of real-world problems. These graphs differ from the common sparse benchmark graphs in terms of the spectral properties of their graph Laplacian. Most notably we observe large eigengaps, which are unfavorable for popular existing GCN architectures. Our method overcomes these issues by utilizing the pseudoinverse of the Laplacian. Another key ingredient is a low-rank approximation of the convolutional matrix, ensuring computational efficiency and increasing accuracy at the same time. We outline how the necessary eigeninformation can be computed efficiently in each applications and discuss the appropriate choice of the only metaparameter, the approximation rank. We finally showcase our method’s performance regarding runtime and accuracy in various experiments with real-world datasets.

Deep node clustering based on mutual information maximization

Variational Graph Autoencoders (VGAs) are generative models for unsupervised learning of node representations within graph data. While VGAs have been achieved state-of-the-art results for different predictive tasks on graph-structured data, they are susceptible to the over-pruning problem where only a small subset of the stochastic latent units are active. This can limit their modeling capacity and their ability to learn meaningful representations. In this paper, we present SOLI (Stacked auto-encoder for nOde cLusterIng), an information maximization approach for learning graph representations by leveraging maximal cliques. SOLI relies on aggregating useful representations by assigning clique-based weights to various edges in a neighborhood while maximizing mutual information. The learned representations are mindful of graph patches centered around each node, and can be used for a range of downstream tasks, and thus encouraging more active units. We demonstrate strong performance across three graph benchmark datasets.(Code is available at https://github.com/SoheilaMolaei/SOLI.)

Detecting the number of clusters in a network

Abstract Many clustering algorithms for complex networks depend on the choice for the number of clusters and it is often unclear how to make this choice. The number of eigenvalues located outside a circle in the spectrum of the non-backtracking matrix was conjectured to be an estimator of the number of clusters in a graph. We compare the estimate of the number of clusters obtained from the spectrum of the non-backtracking matrix with three estimators based on the concept of modularity and evaluate the methods on several benchmark graphs. We find that the non-backtracking method detects the number of clusters better than the modularity-based methods for the graphs in our simulation study, especially when the clusters have slightly different sizes. The estimates of the non-backtracking method are narrowly distributed around the true number of clusters for all benchmark graphs considered. Additionally, for graphs without a clustering structure, the non-backtracking method detects exactly one cluster, which is a convenient property of an estimator of the number of clusters. However, the lack of a well-defined concept of a cluster prevents sharp conclusions.

A Comprehensive Analysis of Multilayer Community Detection Algorithms for Application to EEG-Based Brain Networks.

Modular organization is an emergent property of brain networks, responsible for shaping communication processes and underpinning brain functioning. Moreover, brain networks are intrinsically multilayer since their attributes can vary across time, subjects, frequency, or other domains. Identifying the modular structure in multilayer brain networks represents a gateway toward a deeper understanding of neural processes underlying cognition. Electroencephalographic (EEG) signals, thanks to their high temporal resolution, can give rise to multilayer networks able to follow the dynamics of brain activity. Despite this potential, the community organization has not yet been thoroughly investigated in brain networks estimated from EEG. Furthermore, at the state of the art, there is still no agreement about which algorithm is the most suitable to detect communities in multilayer brain networks, and a way to test and compare them all under a variety of conditions is lacking. In this work, we perform a comprehensive analysis of three algorithms at the state of the art for multilayer community detection (namely, genLouvain, DynMoga, and FacetNet) as compared with an approach based on the application of a single-layer clustering algorithm to each slice of the multilayer network. We test their ability to identify both steady and dynamic modular structures. We statistically evaluate their performances by means of ad hoc benchmark graphs characterized by properties covering a broad range of conditions in terms of graph density, number of clusters, noise level, and number of layers. The results of this simulation study aim to provide guidelines about the choice of the more appropriate algorithm according to the different properties of the brain network under examination. Finally, as a proof of concept, we show an application of the algorithms to real functional brain networks derived from EEG signals collected at rest with closed and open eyes. The test on real data provided results in agreement with the conclusions of the simulation study and confirmed the feasibility of multilayer analysis of EEG-based brain networks in both steady and dynamic conditions.

Community detection in networks using graph embeddings.

Graph embedding methods are becoming increasingly popular in the machine learning community, where they are widely used for tasks such as node classification and link prediction. Embedding graphs in geometric spaces should aid the identification of network communities as well because nodes in the same community should be projected close to each other in the geometric space, where they can be detected via standard data clustering algorithms. In this paper, we test the ability of several graph embedding techniques to detect communities on benchmark graphs. We compare their performance against that of traditional community detection algorithms. We find that the performance is comparable, if the parameters of the embedding techniques are suitably chosen. However, the optimal parameter set varies with the specific features of the benchmark graphs, like their size, whereas popular community detection algorithms do not require any parameter. So, it is not possible to indicate beforehand good parameter sets for the analysis of real networks. This finding, along with the high computational cost of embedding a network and grouping the points, suggests that, for community detection, current embedding techniques do not represent an improvement over network clustering algorithms.

A solution-driven multilevel approach for graph coloring

Graph coloring is one of the most studied NP-hard problems with a wide range of applications. In this work, the first solution-driven multilevel algorithm for this computationally challenging problem is investigated. Following the general idea of multilevel optimization, the proposed algorithm combines an original solution-driven coarsening procedure with an uncoarsening procedure as well as an effective refinement procedure. The algorithm is assessed on 47 popular DIMACS and COLOR benchmark graphs, and compared with 13 state-of-the-art coloring methods in the literature. We close one large graph (wap01a.col) by providing its chromatic number for the first time. Impacts of the key ingredients of the algorithm are also investigated.

Neural Network Topology Construction and Classroom Interaction Benchmark Graph Based on Big Data Analysis

With the rapid development of artificial intelligence and deep learning in recent years, many universities have put forward the goal of achieving digitalization, intelligent, and education informatization on campus. Throughout the lecture and learning process, the classroom status is an important reference factor to assess students’ acceptance of the course and the quality of lectures. However, at present, classroom status analysis is mainly conducted manually, which can distract teachers’ attention, so it is of great research significance to find a method that can improve the efficiency of classroom status analysis. In this paper, we choose an offline method to analyze the status of a classroom video recording in terms of students’ behavior and attendance in terms of frames, in which student behavior is identified by an improved target detection algorithm and attendance is analyzed by face recognition. By analyzing the structure of the neural network model, an improved neural network model is proposed for its characteristics of a large number of parameters and poor detection of small targets in the basic network. The backbone network is replaced by the improved neural network, and the depth‐separable convolutional network is used to reduce the network parameters and increase the computation speed. The information in the deeper feature map is fused upward into the shallow layer to improve the accuracy of small target recognition. Finally, the optimization algorithm is incorporated into the network to optimize the network model and accelerate the model convergence speed. In addition, this paper incorporates the improved behavior recognition method and face recognition method into the system to realize the analysis of the offline classroom status. The system is divided into a teacher side and a management side, where the teacher side is responsible for uploading course recordings and the management side is responsible for randomly analyzing students’ status and attendance at any time, and the combination of the two forms a convenient and comprehensive classroom status analysis system platform. Users can upload classroom videos through the instructor interface and can view the classroom status analysis results of a course at any time by searching randomly in the administration. In this paper, the classroom status is mainly judged by the recognition of students’ behaviors.

Adaptive Hypergraph Auto-Encoder for Relational Data Clustering

The embedded representation and clustering tasks both play important roles in relational data analysis and mining. Traditional methods mainly employ graph structure to describe relational data, but intuitive pairwise connections among nodes are insufficient to model high-order data in the real-world, such as the relations between proteins and polypeptide chains. Hypergraphs are a generalization of graphs, and hypergraphs can well model high-order data. When modeling relational data in the real world, hypergraphs are often accompanied by node attributes, i.e. attributed hypergraphs. Besides this, how to integrate the structural information and attribute information appropriately is another important task, while has not been investigated systematically. In this paper, we propose Adaptive Hypergraph Auto-Encoder(AHGAE) to learn node embeddings in low-dimensional space. Our method can utilize the high-order relation to generate embedding for clustering. It is composed of two procedures, i.e. the adaptive hypergraph Laplacian smoothing filter and the relational reconstruction auto-encoder. It has the advantage of integrating more complex data relations compared with graph-based methods, which leads to better modeling and clustering performance. The proposed method has been evaluated on hypergraph datasets and benchmark graph datasets. Experimental results and comparison with the state-of-the-art methods have demonstrated the effectiveness of our proposed method.

Graphs, Entities, and Step Mixture for Enriching Graph Representation

Graph neural networks have shown promising results on representing and analyzing diverse graph-structured data, such as social networks, traffic flow, drug discovery, and recommendation systems. Existing approaches for graph neural networks typically suffer from the oversmoothing issue that results in indistinguishable node representation, as recursive and simultaneous neighborhood aggregation deepens. Also, most methods focus on transductive scenarios that are limited to fixed graphs, which do not generalize properly to unseen graphs. To address these issues, we propose a novel graph neural network that considers both edge-based neighborhood relationships and node-based entity features with multiple steps, i.e. G raph E ntities with S tep M ixture via random walk (GESM). GESM employs a mixture of various steps through random walk to alleviate the oversmoothing problem, an attention mechanism to dynamically reflect interrelations depending on node information, and structure-based regularization to enhance embedding representation. With intensive experiments, we show that our proposed GESM achieves state-of-the-art or comparable performances on eight benchmark graph datasets in both transductive and inductive learning tasks. Furthermore, we empirically demonstrate the superiority of our method on the oversmoothing issue with rich graph representations. Our source code is available at https://github.com/ShinKyuY/GESM .