Graph Exploration Research Articles

KGScope: Interactive Visual Exploration of Knowledge Graphs With Embedding-Based Guidance.

Knowledge graphs have been commonly used to represent relationships between entities and are utilized in the industry to enhance service qualities. As knowledge graphs integrate data from a variety of sources, they can also be useful references for data analysts. However, there is a lack of effective tools to make the most of the rich information in knowledge graphs. Existing knowledge graph exploration systems are ineffective because they did not consider various user needs and characteristics of knowledge graphs. Exploratory approaches specifically designed to uncover and summarize insights in knowledge graphs have not been well studied yet. In this article, we propose KGScope that supports interactive visual explorations and provides embedding-based guidance to derive insights from knowledge graphs. We demonstrate KGScope with usage scenarios and assess its efficacy in supporting the exploration of knowledge graphs with a user study. The results show that KGScope supports knowledge graph exploration effectively by providing useful information and helping explore the entire network.

Visualising Paths for Exploratory Search in the Health IT Ontology.

Due to a lack of systematisation and unbiased information, finding the optimal combination of software products for health information systems is a challenging endeavour. We present a novel approach to visually explore the domain of application systems and software products for health care along the paths of the Health IT ontology (HITO). We present an algorithm and implementation in a web application that is freely available at the HITO website and licensed under the open source MIT licence. In comparison to other approaches of path-based exploration of knowledge graphs, the novelty of our approach is the use of path finding on the ontology level and combining this both with the instances of the classes along the chosen path as well as search filters to limit the search space. Our approach can be adapted to other domains where users with complex information needs interact with ontologies and knowledge graphs and can be supported by generative artificial intelligence in the future.

AutoGMap: Learning to Map Large-Scale Sparse Graphs on Memristive Crossbars.

The sparse representation of graphs has shown great potential for accelerating the computation of graph applications (e.g., social networks and knowledge graphs) on traditional computing architectures (CPU, GPU, or TPU). But, the exploration of large-scale sparse graph computing on processing-in-memory (PIM) platforms (typically with memristive crossbars) is still in its infancy. To implement the computation or storage of large-scale or batch graphs on memristive crossbars, a natural assumption is that a large-scale crossbar is demanded, but with low utilization. Some recent works question this assumption; to avoid the waste of storage and computational resource, the fixed-size or progressively scheduled "block partition" schemes are proposed. However, these methods are coarse-grained or static and are not effectively sparsity-aware. This work proposes the dynamic sparsity-aware mapping scheme generating method that models the problem with a sequential decision-making model, and optimizes it by reinforcement learning (RL) algorithm (REINFORCE). Our generating model [long short-term memory (LSTM), combined with the dynamic-fill scheme] generates remarkable mapping performance on the small-scale graph/matrix data (complete mapping costs 43% area of the original matrix) and two large-scale matrix data (costing 22.5% area on qh882 and 17.1% area on qh1484). Our method may be extended to sparse graph computing on other PIM architectures, not limited to the memristive device-based platforms.

An improved upper bound for the online graph exploration problem on unicyclic graphs

The online graph exploration problem, which was proposed by Kalyanasundaram and Pruhs (Theor Comput Sci 130(1):125–138, 1994), is defined as follows: Given an edge-weighted undirected connected graph and a specified vertex (called the origin), the task of an algorithm is to compute a path from the origin to the origin which contains all the vertices of the given graph. The goal of the problem is to find such a path of minimum weight. At each time, an online algorithm knows only the weights of edges each of which consists of visited vertices or vertices adjacent to visited vertices. Fritsch (Inform Process Lett 168:1006096, 2021) showed that the competitive ratio of an online algorithm is at most three for any unicyclic graph. On the other hand, Brandt et al. (Theor Comput Sci 839:176–185, 2020) showed a lower bound of two on the competitive ratio for any unicyclic graph. In this paper, we showed the competitive ratio of an online algorithm is at most 5/2 for any unicyclic graph.

An Experimental Evaluation of Summarisation-Based Frequent Subgraph Mining for Subgraph Searching

The subgraph searching is a fundamental operation for the analysis and exploration of graphs. Nowadays, molecular databases are nearing close to one hundred million molecules. Since finding all the data graphs in a graph database that contain the query graph using subgraph isomorphism is an NP-complete problem, indexes are built and processed. Further, to assist the formulation of the query by a user, the visual exploratory subgraph query paradigm proposes a graphical user interface and leverages exploration time to reduce query processing time. However, state-of-the-art approaches need to scale better to dynamic graph databases and suffer from efficiency problems. In addition, the existing Summarisation-based frequent subgraph mining for visual exploratory subgraph searching (SuMExplorer) is lacking implementation and evaluation study for handling visual subgraph similarity search and modify operations. In this paper, we present a novel index structure, which aids the subgraph searching using the summarised-based weighted frequent subgraph mining on data graphs. By the structure-preserving, we exploit the indexes to support similarity and modify operations. We conduct extensive performance studies on both real-world and synthetic datasets to evaluate the overall performance of the extended SuMExplorer to the recent visual exploratory FERRARI and traditional subgraph search algorithms (such as the gIndex and the GRAPES-DD). Our results showed that our indexes can query up to 3 times faster in comparison to the FERRARI while reducing the storage footprint by 2 orders of magnitude.

Parameterized Complexity of Streaming Diameter and Connectivity Problems

We initiate the investigation of the parameterized complexity of Diameter and Connectivity in the streaming paradigm. On the positive end, we show that knowing a vertex cover of size k allows for algorithms in the Adjacency List (AL) streaming model whose number of passes is constant and memory is O(logn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(\\log n)$$\\end{document} for any fixed k. Underlying these algorithms is a method to execute a breadth-first search in O(k)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(k)$$\\end{document} passes and O(klogn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(k \\log n)$$\\end{document} bits of memory. On the negative end, we show that many other parameters lead to lower bounds in the AL model, where Ω(n/p)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega (n/p)$$\\end{document} bits of memory is needed for any p-pass algorithm even for constant parameter values. In particular, this holds for graphs with a known modulator (deletion set) of constant size to a graph that has no induced subgraph isomorphic to a fixed graph H, for most H. For some cases, we can also show one-pass, Ω(nlogn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega (n \\log n)$$\\end{document} bits of memory lower bounds. We also prove a much stronger Ω(n2/p)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega (n^2/p)$$\\end{document} lower bound for Diameter on bipartite graphs. Finally, using the insights we developed into streaming parameterized graph exploration algorithms, we show a new streaming kernelization algorithm for computing a vertex cover of size k. This yields a kernel of 2k vertices (with O(k2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(k^2)$$\\end{document} edges) produced as a stream in poly(k)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {poly}(k)$$\\end{document} passes and only O(klogn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(k \\log n)$$\\end{document} bits of memory.

Efficient parallelism in Breadth-First Search: A comprehensive analysis and implementation

The Breadth-First Search (BFS) entails a systematic traversal of a given graph, G = (V, E), layer by layer, starting from a specific vertex. Recognized as a cornerstone methodology for graph exploration, the importance of BFS has skyrocketed, especially with the increasing demands of graph-based data processing. However, as the vertex count expands, traditional serial implementations reveal their limitations, faltering in terms of time and space efficiency. This paper aims to contrast the efficiencies of standard BFS with its parallelized iteration. Introducing a shared-memory model of level-synchronous parallel BFS, the approach integrates optimizations to navigate the challenges posed by implicit barriers and critical sections. Employing the Graph500 benchmark, this parallel methodology is meticulously evaluated, highlighting the speedup concerning various thread counts. Initial findings unveil a compelling pattern: speedup generally correlates positively with the number of active threads. However, if the thread count breaches the system's inherent capacity, the speedup hits a plateau, showing only marginal fluctuations without significant increases. These statistical revelations not only vouch for the advantages of BFS parallelization but also emphasize a critical insight: judiciously increasing thread count, up to a system-specified limit, can yield peak efficiency.

A parallel Breadth-First Search using shared memory level-synchronization

Breadth-first search (BFS) stands as a cornerstone in graph exploration techniques, enabling systematic traversal of a provided graph. As the digital era continues to burgeon, there has been a marked upswing in the need to process vast graph-based data sets. To harness the power of such data effectively, it becomes imperative to use computational tools efficiently. Parallelizing BFS emerges as a pivotal strategy in this regard, leveraging the expansive capabilities of multiprocessor systems to maximize efficiency. This manuscript introduces a level-synchronous parallel BFS that is predicated on the shared-memory model. Recognizing the potential pitfalls of such an approach, especially regarding overhead induced by implicit barriers and critical sections, meticulous optimization techniques are infused into the model. These strategies are not mere afterthoughts; they are woven into the fabric of the design, ensuring smooth operations even when scaled. To validate the efficacy of this model, a rigorous assessment is carried out using the Graph500 benchmark. This offers insights into the performance scale of the parallel BFS algorithm, especially focusing on its speedup in relation to the number of operational threads. Concluding this exploration, the paper delineates prospective avenues for refining and further enhancing the proposed parallel implementation, aiming for even greater efficiencies in future endeavors.

ExEmPLAR (Extracting, Exploring, and Embedding Pathways Leading to Actionable Research): a user-friendly interface for knowledge graph mining.

Knowledge graphs are being increasingly used in biomedical research to link large amounts of heterogenous data and facilitate reasoning across diverse knowledge sources. Wider adoption and exploration of knowledge graphs in the biomedical research community is limited by requirements to understand the underlying graph structure in terms of entity types and relationships, represented as nodes and edges, respectively, and learn specialized query languages for graph mining and exploration. We have developed a user-friendly interface dubbed ExEmPLAR (Extracting, Exploring, and Embedding Pathways Leading to Actionable Research) to aid reasoning over biomedical knowledge graphs and assist with data-driven research and hypothesis generation. We explain the key functionalities of ExEmPLAR and demonstrate its use with a case study considering the relationship of Trypanosoma cruzi, the etiological agent of Chagas disease, to frequently associated cardiovascular conditions. ExEmPLAR is freely accessible at https://www.exemplar.mml.unc.edu/. For code and instructions for the using the application, see: https://github.com/beasleyjonm/AOP-COP-Path-Extractor.

Temporally-aware node embeddings for evolving networks topologies

Static node embedding algorithms applied to snapshots of real-world applications graphs are unable to capture their evolving process. As a result, the absence of information about the dynamics in these node representations can harm the accuracy and increase processing time of machine learning tasks related to these applications. Aiming at fill the gap regarding the inability of static methods to capture evolving processes on dynamic networks, we propose a biased random walk method named Evolving Node Embedding (EVNE). EVNE leverages the sequential relationship of graph snapshots by incorporating historic information when generating embeddings for the next snapshot. It learns node representations through a neural network, but differs from existing methods as it: (i) incorporates previously run walks at each step; (ii) starts the optimization of the current embedding from the parameters obtained in the previous iteration; and (iii) uses two time-varying parameters to regulate the behavior of the biased random walks over the process of graph exploration. Through a wide set of experiments we show that our approach generates better embeddings, outperforming baselines by up to 20% in a downstream node classification task. EVNE’s embeddings achieve better performance than others, based on experiments with four classifiers and five datasets. In addition, we present seven variations of our model to show the impact of each of EVNE’s mechanisms.

Graph Exploration With Embedding-Guided Layouts.

Node-link diagrams are widely used to visualize graphs. Most graph layout algorithms only use graph topology for aesthetic goals (e.g., minimize node occlusions and edge crossings) or use node attributes for exploration goals (e.g., preserve visible communities). Existing hybrid methods that bind the two perspectives still suffer from various generation restrictions (e.g., limited input types and required manual adjustments and prior knowledge of graphs) and the imbalance between aesthetic and exploration goals. In this article, we propose a flexible embedding-based graph exploration pipeline to enjoy the best of both graph topology and node attributes. First, we leverage embedding algorithms for attributed graphs to encode the two perspectives into latent space. Then, we present an embedding-driven graph layout algorithm, GEGraph, which can achieve aesthetic layouts with better community preservation to support an easy interpretation of the graph structure. Next, graph explorations are extended based on the generated graph layout and insights extracted from the embedding vectors. Illustrated with examples, we build a layout-preserving aggregation method with Focus+Context interaction and a related nodes searching approach with multiple proximity strategies. Finally, we conduct quantitative and qualitative evaluations, a user study, and two case studies to validate our approach.

Gradient-Based Local Causal Structure Learning.

Finding the causal structure from a set of variables given observational data is a crucial task in many scientific areas. Most algorithms focus on discovering the global causal graph but few efforts have been made toward the local causal structure (LCS), which is of wide practical significance and easier to obtain. LCS learning faces the challenges of neighborhood determination and edge orientation. Available LCS algorithms build on conditional independence (CI) tests, they suffer the poor accuracy due to noises, various data generation mechanisms, and small-size samples of real-world applications, where CI tests do not work. In addition, they can only find the Markov equivalence class, leaving some edges undirected. In this article, we propose a GradieNt-based LCS learning approach (GraN-LCS) to determine neighbors and orient edges simultaneously in a gradient-descent way, and, thus, to explore LCS more accurately. GraN-LCS formulates the causal graph search as minimizing an acyclicity regularized score function, which can be optimized by efficient gradient-based solvers. GraN-LCS constructs a multilayer perceptron (MLP) to simultaneously fit all other variables with respect to a target variable and defines an acyclicity-constrained local recovery loss to promote the exploration of local graphs and to find out direct causes and effects of the target variable. To improve the efficacy, it applies preliminary neighborhood selection (PNS) to sketch the raw causal structure and further incorporates an l1 -norm-based feature selection on the first layer of MLP to reduce the scale of candidate variables and to pursue sparse weight matrix. GraN-LCS finally outputs LCS based on the sparse weighted adjacency matrix learned from MLPs. We conduct experiments on both synthetic and real-world datasets and verify its efficacy by comparing against state-of-the-art baselines. A detailed ablation study investigates the impact of key components of GraN-LCS and the results prove their contribution.

Graph Exploration for Effective Multiagent Q-Learning.

This article proposes an exploration technique for multiagent reinforcement learning (MARL) with graph-based communication among agents. We assume that the individual rewards received by the agents are independent of the actions by the other agents, while their policies are coupled. In the proposed framework, neighboring agents collaborate to estimate the uncertainty about the state-action space in order to execute more efficient explorative behavior. Different from existing works, the proposed algorithm does not require counting mechanisms and can be applied to continuous-state environments without requiring complex conversion techniques. Moreover, the proposed scheme allows agents to communicate in a fully decentralized manner with minimal information exchange. And for continuous-state scenarios, each agent needs to exchange only a single parameter vector. The performance of the algorithm is verified with theoretical results for discrete-state scenarios and with experiments for the continuous ones.

NLP-Based Management of Large Multiple-Choice Test Item Repositories

Multiple-choice questions (MCQs) are widely used in educational assessments and professional certification exams. Managing large repositories of MCQs, however, poses several challenges due to the high volume of questions and the need to maintain their quality and relevance over time. One of these challenges is the presence of questions that duplicate concepts but are formulated differently. Such questions can indeed elude syntactic controls but provide no added value to the repository. In this paper, we focus on this specific challenge and propose a workflow for the discovery and management of potential duplicate questions in large MCQ repositories. Overall, the workflow comprises three main steps: MCQ preprocessing, similarity computation, and finally a graph-based exploration and analysis of the obtained similarity values. For the preprocessing phase, we consider three main strategies: (i) removing the list of candidate answers from each question, (ii) augmenting each question with the correct answer, or (iii) augmenting each question with all candidate answers. Then, we use deep learning–based natural language processing (NLP) techniques, based on the Transformers architecture, to compute similarities between MCQs based on semantics. Finally, we propose a new approach to graph exploration based on graph communities to analyze the similarities and relationships between MCQs in the graph. We illustrate the approach with a case study of the Competenze Digitali program, a large-scale assessment project by the Italian government.

Efficient live exploration of a dynamic ring with mobile robots

The graph exploration problem requires a group of mobile robots, initially placed arbitrarily on the nodes of a graph, to work collaboratively to explore the graph such that each node is eventually visited by at least one robot. One important requirement of exploration is the termination condition, i.e., the robots must know that exploration is completed. The problem of live exploration of a dynamic ring using mobile robots was recently introduced by Di Luna et al. [DC 2020]. More specifically, they studied the problem of live exploration in a dynamic ring and proposed multiple algorithms to solve this problem in the fully synchronous and semi-synchronous settings with various guarantees when 2 robots were involved. They also showed that, under certain assumptions, exploration of the ring using two robots was impossible. An important question left open was how the presence of 3 robots would affect the results. In this paper, we try to settle this question in a fully synchronous setting and also show how to extend our results to a semi-synchronous setting.In particular, we present algorithms for exploration with explicit termination using 3 robots in conjunction with either (i) unique IDs of the robots and edge crossing detection capability (i.e., two robots moving in opposite directions through an edge in the same round can detect each other), or (ii) access to randomness. The time complexity of our deterministic algorithm is asymptotically optimal. We also provide complementary impossibility results showing that there does not exist any explicit termination algorithm for 2 robots even when each robot has a unique ID, edge crossing detection capability, and access to randomness. The theoretical analysis and comprehensive simulations of our algorithm show the effectiveness and efficiency of the algorithm in dynamic rings. We also present an algorithm to achieve exploration with partial termination using 3 robots with unique IDs in the semi-synchronous setting, when robots have access to edge crossing detection capability and randomness but do not know a bound on the size of the ring or have access to a landmark or are guaranteed that robots have common chirality. Our algorithms are fully decentralized, lightweight, and easily implementable.

Sparse Subgraph Prediction Based on Adaptive Attention

Link prediction is a crucial problem in the analysis of graph-structured data, and graph neural networks (GNNs) have proven to be effective in addressing this problem. However, the computational and temporal costs associated with large-scale graphs remain a concern. This study introduces a novel method for link prediction called Sparse Subgraph Prediction Based on Adaptive Attention (SSP-AA). The method generates sparse subgraphs and utilizes Graph SAmple and aggreGatE (GraphSAGE) for prediction, aiming to reduce computation and time costs while providing a foundation for future exploration of large-scale graphs. Certain key issues in GraphSAGE are addressed by integrating an adaptive attention mechanism and a jumping knowledge module into the model. To address the issue of adaptive weight distribution in GraphSAGE, an aggregation function is employed, which is based on the attention mechanism. This modification enables the model to distribute weights adaptively among neighboring nodes, significantly improving its ability to capture node relationships. Furthermore, to tackle the common issue of over-smoothing in GNNs, a jumping knowledge module is integrated, enabling information sharing across different layers and providing the model with the flexibility to select the appropriate representation depth based on the specific situation. By enhancing the quality of node representations, SSP-AA further boosts the performance of GraphSAGE in various prediction tasks involving graph-structured data.

KNIT: Ontology reusability through knowledge graph exploration

Ontologies have become a standard for knowledge representation across several domains. In Life Sciences, numerous ontologies have been introduced to represent human knowledge, often providing overlapping or conflicting perspectives. These ontologies are usually published as OWL or OBO, and are often registered in open repositories, e.g., BioPortal. However, the task of finding the concepts (classes and their properties) defined in the existing ontologies and the relationships between these concepts across different ontologies – for example, for developing a new ontology aligned with the existing ones – requires a great deal of manual effort in searching through the public repositories for candidate ontologies and their entities. In this work, we develop a new tool, KNIT, to automatically explore open repositories to help users fetch the previously designed concepts using keywords. User-specified keywords are then used to retrieve matching names of classes or properties. KNIT then creates a draft knowledge graph populated with the concepts and relationships retrieved from the existing ontologies. Furthermore, following the process of ontology learning, our tool refines this first draft of an ontology. We present three BioPortal-specific use cases for our tool. These use cases outline the development of new knowledge graphs and ontologies in the sub-domains of biology: genes and diseases, virome and drugs.

Almost-Optimal Deterministic Treasure Hunt in Unweighted Graphs

A mobile agent navigating along edges of a simple connected unweighted graph, either finite or countably infinite, has to find an inert target (treasure) hidden in one of the nodes. This task is known as treasure hunt. The agent has no a priori knowledge of the graph, of the location of the treasure, or of the initial distance to it. The cost of a treasure hunt algorithm is the worst-case number of edge traversals performed by the agent until finding the treasure. Awerbuch et al. [ 3 ] considered graph exploration and treasure hunt for finite graphs in a restricted model where the agent has a fuel tank that can be replenished only at the starting node s . The size of the tank is B = 2 (1+α) r , for some positive real constant α, where r , called the radius of the graph, is the maximum distance from s to any other node. The tank of size B allows the agent to make at most ⌊ B ⌋ edge traversals between two consecutive visits at node s . Let e(d) be the number of edges whose at least one endpoint is at distance less than d from s . Awerbuch et al. [ 3 ] conjectured that it is impossible to find a treasure hidden in a node at distance at most d at cost nearly linear in e(d) . We first design a deterministic treasure hunt algorithm working in the model without any restrictions on the moves of the agent at cost 𝒪(e(d) log d ) and then show how to modify this algorithm to work in the model from Awerbuch et al. [ 3 ] with the same complexity. Thus, we refute the preceding 20-year-old conjecture. We observe that no treasure hunt algorithm can beat cost Θ ( e(d) ) for all graphs, and thus our algorithms are also almost optimal.

Effective Network Analytics: Network Visualization and Graph Data Management

Network analytics provides a scientific solution to interact with networks through effective management of network data and corresponding visualization. Network analytics has been considered essential in many research areas as well as in commercial applications, including use cases in bioinformatics, biomedicine, security, social science, and knowledge graph exploration. We see that networks and the associated analysis process are expected to be initially supported by graph databases with advanced query engines, and later the filtered contents are rendered using corresponding visualization approaches for better communication and knowledge exchange. For this special issue (SI), we recruited papers describing research based on graph database utilization and network visualization that potentially could be integrated as a full pipeline, as well as their synergy for various applied problems. Through the formal IEEE Computer Graphics and Applications review process of the four submissions, we accepted three papers for this SI, focusing on the novelty and potential integration within the network analytics pipeline. These selected papers demonstrate the wide potentiality of techniques for complex network analytics.

IMGC: Interactive Multiple Graph Clustering With Constrained Laplacian Rank

Numerous graph clustering methods have been proposed to explore aggregation structures across multiple graphs. In these methods, single-graph features are merely considered or multigraph features are simply weighted, which are insufficient for the construction of reasonable multiple graph clustering features, since the association information between pairwise graphs is ignored and the varied local correlations might influence the clustering preference. Thus, we propose an interactive multiple graph clustering model, iMGC, in this article, to achieve reasonable multiple graph clustering features, which cannot only express multiple relationships, but also preserve associations of nodes across multiple graphs. First, a unified graph matrix is constructed with the combination of structural differences quantified by graph representation learning, which is further optimized by minimizing the difference of structural characteristics between it and each single graph matrix. Thus, multiple relationships are well integrated and expressed, while the varied local correlations within different graphs are also balanced in the unified graph matrix. Then, a constrained Laplacian rank is applied on the unified graph matrix to generate the unified clustering result directly, which is able to preserve association features across multiple graphs. Furthermore, we provide a set of visualization and interaction interfaces, enabling users to intuitively optimize and evaluate the multiple graph clustering features, and interactively explore the multiple graphs. Case studies and quantitative comparisons based on real-world datasets have demonstrated the effectiveness of iMGC in the clustering performance from various perspectives and exploration of multiple graphs.