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Journal articles on the topic 'Hierarchical graph'

Author: Grafiati

Published: 4 June 2021

Last updated: 18 June 2025

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EADES, PETER, XUEMIN LIN, and ROBERTO TAMASSIA. "AN ALGORITHM FOR DRAWING A HIERARCHICAL GRAPH." International Journal of Computational Geometry & Applications 06, no. 02 (1996): 145–55. http://dx.doi.org/10.1142/s0218195996000101.

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Hierarchical graphs appear in several graph drawing applications, where nodes are assigned layers for semantic reasons. More importantly, general methods for drawing directed graphs usually begin by transforming the input digraph into a hierarchical graph, then applying a hierarchical graph drawing algorithm. This paper introduces the Degree Weighted Barycentre (DWB) algorithm for drawing hierarchical graphs. We show that drawings output by DWB satisfy several important aesthetic criteria: under certain connectivity conditions, they are planar, convex, and symmetric whenever such drawings are possible. The algorithm can be implemented as a simple Gauss — Seidel iteration.

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Qian, Feifei, Lu Bai, Lixin Cui, et al. "DHAKR: Learning Deep Hierarchical Attention-Based Kernelized Representations for Graph Classification." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 19 (2025): 19995–20003. https://doi.org/10.1609/aaai.v39i19.34202.

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Graph-based representations are powerful tools for analyzing structured data. In this paper, we propose a novel model to learn Deep Hierarchical Attention-based Kernelized Representations (DHAKR) for graph classification. To this end, we commence by learning an assignment matrix to hierarchically map the substructure invariants into a set of composite invariants, resulting in hierarchical kernelized representations for graphs. Moreover, we introduce the feature-channel attention mechanism to capture the interdependencies between different substructure invariants that will be converged into the composite invariants, addressing the shortcoming of discarding the importance of different substructures arising in most existing R-convolution graph kernels. We show that the proposed DHAKR model can adaptively compute the kernel-based similarity between graphs, identifying the common structural patterns over all graphs. Experiments demonstrate the effectiveness of the proposed DHAKR model.

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BUSATTO, GIORGIO, HANS-JÖRG KREOWSKI, and SABINE KUSKE. "Abstract hierarchical graph transformation." Mathematical Structures in Computer Science 15, no. 4 (2005): 773–819. http://dx.doi.org/10.1017/s0960129505004846.

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In this paper we introduce a new hierarchical graph model to structure large graphs into small components by distributing the nodes (and, likewise, edges) into a hierarchy of packages. In contrast to other known approaches, we do not fix the type of underlying graphs. Moreover, our model is equipped with a rule-based transformation concept such that hierarchical graphs are not restricted to being used only for the static representation of complex system states, but can also be used to describe dynamic system behaviour.

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Wen, Lingfeng, Xuan Tang, Mingjie Ouyang, et al. "Hyperbolic Graph Diffusion Model." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 14 (2024): 15823–31. http://dx.doi.org/10.1609/aaai.v38i14.29512.

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Diffusion generative models (DMs) have achieved promising results in image and graph generation. However, real-world graphs, such as social networks, molecular graphs, and traffic graphs, generally share non-Euclidean topologies and hidden hierarchies. For example, the degree distributions of graphs are mostly power-law distributions. The current latent diffusion model embeds the hierarchical data in a Euclidean space, which leads to distortions and interferes with modeling the distribution. Instead, hyperbolic space has been found to be more suitable for capturing complex hierarchical structures due to its exponential growth property. In order to simultaneously utilize the data generation capabilities of diffusion models and the ability of hyperbolic embeddings to extract latent hierarchical distributions, we propose a novel graph generation method called, Hyperbolic Graph Diffusion Model (HGDM), which consists of an auto-encoder to encode nodes into successive hyperbolic embeddings, and a DM that operates in the hyperbolic latent space. HGDM captures the crucial graph structure distributions by constructing a hyperbolic potential node space that incorporates edge information. Extensive experiments show that HGDM achieves better performance in generic graph and molecule generation benchmarks, with a 48% improvement in the quality of graph generation with highly hierarchical structures.

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Chen, Fukun, Guisheng Yin, Yuxin Dong, Gesu Li, and Weiqi Zhang. "KHGCN: Knowledge-Enhanced Recommendation with Hierarchical Graph Capsule Network." Entropy 25, no. 4 (2023): 697. http://dx.doi.org/10.3390/e25040697.

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Knowledge graphs as external information has become one of the mainstream directions of current recommendation systems. Various knowledge-graph-representation methods have been proposed to promote the development of knowledge graphs in related fields. Knowledge-graph-embedding methods can learn entity information and complex relationships between the entities in knowledge graphs. Furthermore, recently proposed graph neural networks can learn higher-order representations of entities and relationships in knowledge graphs. Therefore, the complete presentation in the knowledge graph enriches the item information and alleviates the cold start of the recommendation process and too-sparse data. However, the knowledge graph’s entire entity and relation representation in personalized recommendation tasks will introduce unnecessary noise information for different users. To learn the entity-relationship presentation in the knowledge graph while effectively removing noise information, we innovatively propose a model named knowledge—enhanced hierarchical graph capsule network (KHGCN), which can extract node embeddings in graphs while learning the hierarchical structure of graphs. Our model eliminates noisy entities and relationship representations in the knowledge graph by the entity disentangling for the recommendation and introduces the attentive mechanism to strengthen the knowledge-graph aggregation. Our model learns the presentation of entity relationships by an original graph capsule network. The capsule neural networks represent the structured information between the entities more completely. We validate the proposed model on real-world datasets, and the validation results demonstrate the model’s effectiveness.

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Zhang, H., J. J. Zhou, and R. Li. "Enhanced Unsupervised Graph Embedding via Hierarchical Graph Convolution Network." Mathematical Problems in Engineering 2020 (July 26, 2020): 1–9. http://dx.doi.org/10.1155/2020/5702519.

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Graph embedding aims to learn the low-dimensional representation of nodes in the network, which has been paid more and more attention in many graph-based tasks recently. Graph Convolution Network (GCN) is a typical deep semisupervised graph embedding model, which can acquire node representation from the complex network. However, GCN usually needs to use a lot of labeled data and additional expressive features in the graph embedding learning process, so the model cannot be effectively applied to undirected graphs with only network structure information. In this paper, we propose a novel unsupervised graph embedding method via hierarchical graph convolution network (HGCN). Firstly, HGCN builds the initial node embedding and pseudo-labels for the undirected graphs, and then further uses GCNs to learn the node embedding and update labels, finally combines HGCN output representation with the initial embedding to get the graph embedding. Furthermore, we improve the model to match the different undirected networks according to the number of network node label types. Comprehensive experiments demonstrate that our proposed HGCN and HGCN∗ can significantly enhance the performance of the node classification task.

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Kasyanov, Victor N. "Methods and tools for information visualization on the basis of attributed hierarchical graphs with ports." Siberian Aerospace Journal 24, no. 1 (2023): 8–17. http://dx.doi.org/10.31772/10.31772/2712-8970-2023-24-1-8-17.

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At present visualization of graph models is an inherent part of the processing of complex information about the structure of objects, systems and processes in many applications in science and technology, and at the market there are widely presented science-intensive software products, using the information visualization on the basis of graph models. Since the information that it is desirable to visualize is constantly growing and becoming more complex, more and more situations arise in which classical graph models cease to be adequate. More powerful graph-theoretic formalisms are required and appear to represent information models with a hierarchical structure, since hierarchy is the basis of numerous methods for visual processing of complex big data in various fields of application. One of these formalisms is the so-called hierarchical graphs. This formalism allows selecting in the given classical graph a set of such its parts (so-called fragments) that all elements of each selected fragment deserve separate joint consideration, and all fragments of the selected set form a nesting hierarchy. At the A. P. Ershov Institute of Informatics Systems constructed the Visual Graph visualization system, which is based on hierarchical graphs and allows exploring complex structured big data through their visual representations. In many applications, objects modeled by graph vertices are complex and contain non-intersecting logical parts (so-called ports) through which these objects are in a relationship modeled by arcs. In the paper the formalism of attributed hierarchical graphs with ports is introduced and new possibilities of the Visual Graph system for visualization of large structured data based on attributed hierarchical graphs with ports are considered.

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Kasyanov, V. N., A. M. Merculov, and T. A. Zolotuhin. "A circular layout algorithm for attributed hierarchical graphs with ports." Journal of Physics: Conference Series 2099, no. 1 (2021): 012051. http://dx.doi.org/10.1088/1742-6596/2099/1/012051.

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Abstract Information visualization based on graph models is a key component of support tools for many applications in science and engineering. The Visual Graph system is intended for visualization of big amounts of complex information on the basis of attributed hierarchical graph models. In this paper, a circular layout algorithm for attributed hierarchical graphs with ports and its effective implementation in the Visual Graph system are presented.

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Kasyanov, V. N. "Methods and Tools for Visualization of Graphs and Graph Algorithms." International Journal of Applied Mathematics and Informatics 15 (November 16, 2021): 78–84. http://dx.doi.org/10.46300/91014.2021.15.13.

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Graphs are the most common abstract structure encountered in computer science and are widely used for structural information visualization. In the paper, we consider practical and general graph formalism of so called hierarchical graphs and present the Higres and ALVIS systems aimed at supporting of structural information visualization on the base of hierarchical graph models.

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Jingyi, Zhan, and Li Ming. "Research on the Revitalization of the Defensive Fortress of the Great Wall Based on the Adversarial Interpretive-Structure Model." Information 26, no. 2 (2023): 71–79. http://dx.doi.org/10.47880/inf2602-03.

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This article aims to formulate a revitalization strategy for the affiliated fortress of the Ming Great Wall. The Adversarial Interpretive-Structure Model (AISM) extracts the opposite hierarchical rules and obtains a pair of simplified hierarchical topology graphs. The directed line segments in the adversarial hierarchical topology graph represent the interrelationships between the elements, which are presented in a topological hierarchy and can easily compare the advantages and disadvantages of the revitalization factors, which provides a basis for subsequent revitalization strategy formulation. The adversarial hierarchical topology graph provides a new method for conserving and reusing architectural heritage. Key Words: adversarial hierarchical topology graph, fortress, architectural heritage, conservation and reuse

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Oggier, Frédérique, and Anwitaman Datta. "Renyi entropy driven hierarchical graph clustering." PeerJ Computer Science 7 (February 25, 2021): e366. http://dx.doi.org/10.7717/peerj-cs.366.

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This article explores a graph clustering method that is derived from an information theoretic method that clusters points in ${{\mathbb{R}}^{n}}$ relying on Renyi entropy, which involves computing the usual Euclidean distance between these points. Two view points are adopted: (1) the graph to be clustered is first embedded into ${\mathbb{R}}^{d}$ for some dimension d so as to minimize the distortion of the embedding, then the resulting points are clustered, and (2) the graph is clustered directly, using as distance the shortest path distance for undirected graphs, and a variation of the Jaccard distance for directed graphs. In both cases, a hierarchical approach is adopted, where both the initial clustering and the agglomeration steps are computed using Renyi entropy derived evaluation functions. Numerical examples are provided to support the study, showing the consistency of both approaches (evaluated in terms of F-scores).

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Abello, James. "Hierarchical graph maps." Computers & Graphics 28, no. 3 (2004): 345–59. http://dx.doi.org/10.1016/j.cag.2004.03.012.

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Cazaux, Bastien, and Eric Rivals. "Hierarchical Overlap Graph." Information Processing Letters 155 (March 2020): 105862. http://dx.doi.org/10.1016/j.ipl.2019.105862.

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Drewes, Frank, Berthold Hoffmann, and Detlef Plump. "Hierarchical Graph Transformation." Journal of Computer and System Sciences 64, no. 2 (2002): 249–83. http://dx.doi.org/10.1006/jcss.2001.1790.

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Gu, Mei-Mei, Jou-Ming Chang, and Rong-Xia Hao. "On Component Connectivity of Hierarchical Star Networks." International Journal of Foundations of Computer Science 31, no. 03 (2020): 313–26. http://dx.doi.org/10.1142/s0129054120500100.

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For an integer [Formula: see text], the [Formula: see text]-component connectivity of a graph [Formula: see text], denoted by [Formula: see text], is the minimum number of vertices whose removal from [Formula: see text] results in a disconnected graph with at least [Formula: see text] components or a graph with fewer than [Formula: see text] vertices. This naturally generalizes the classical connectivity of graphs defined in term of the minimum vertex-cut. This kind of connectivity can help us to measure the robustness of the graph corresponding to a network. The hierarchical star networks [Formula: see text], proposed by Shi and Srimani, is a new level interconnection network topology, and uses the star graphs as building blocks. In this paper, by exploring the combinatorial properties and fault-tolerance of [Formula: see text], we study the [Formula: see text]-component connectivity of hierarchical star networks [Formula: see text]. We obtain the results: [Formula: see text], [Formula: see text] and [Formula: see text] for [Formula: see text].

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Dutta, Anjan, Pau Riba, Josep Lladós, and Alicia Fornés. "Hierarchical stochastic graphlet embedding for graph-based pattern recognition." Neural Computing and Applications 32, no. 15 (2019): 11579–96. http://dx.doi.org/10.1007/s00521-019-04642-7.

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AbstractDespite being very successful within the pattern recognition and machine learning community, graph-based methods are often unusable because of the lack of mathematical operations defined in graph domain. Graph embedding, which maps graphs to a vectorial space, has been proposed as a way to tackle these difficulties enabling the use of standard machine learning techniques. However, it is well known that graph embedding functions usually suffer from the loss of structural information. In this paper, we consider the hierarchical structure of a graph as a way to mitigate this loss of information. The hierarchical structure is constructed by topologically clustering the graph nodes and considering each cluster as a node in the upper hierarchical level. Once this hierarchical structure is constructed, we consider several configurations to define the mapping into a vector space given a classical graph embedding, in particular, we propose to make use of the stochastic graphlet embedding (SGE). Broadly speaking, SGE produces a distribution of uniformly sampled low-to-high-order graphlets as a way to embed graphs into the vector space. In what follows, the coarse-to-fine structure of a graph hierarchy and the statistics fetched by the SGE complements each other and includes important structural information with varied contexts. Altogether, these two techniques substantially cope with the usual information loss involved in graph embedding techniques, obtaining a more robust graph representation. This fact has been corroborated through a detailed experimental evaluation on various benchmark graph datasets, where we outperform the state-of-the-art methods.

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Han, Wenhao, Xuemei Liu, Jianhao Zhang, and Hairui Li. "Hierarchical Perceptual Graph Attention Network for Knowledge Graph Completion." Electronics 13, no. 4 (2024): 721. http://dx.doi.org/10.3390/electronics13040721.

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Knowledge graph completion (KGC), the process of predicting missing knowledge through known triples, is a primary focus of research in the field of knowledge graphs. As an important graph representation technique in deep learning, graph neural networks (GNNs) perform well in knowledge graph completion, but most existing graph neural network-based knowledge graph completion methods tend to aggregate neighborhood information directly and individually, ignoring the rich hierarchical semantic structure of KGs. As a result, how to effectively deal with multi-level complex relations is still not well resolved. In this study, we present a hierarchical knowledge graph completion technique that combines both relation-level and entity-level attention and incorporates a weight matrix to enhance the significance of the embedded information under different semantic conditions. Furthermore, it updates neighborhood information to the central entity using a hierarchical aggregation approach. The proposed model enhances the capacity to capture hierarchical semantic feature information and is adaptable to various scoring functions as decoders, thus yielding robust results. We conducted experiments on a public benchmark dataset and compared it with several state-of-the-art models, and the experimental results indicate that our proposed model outperforms existing models in several aspects, proving its superior performance and validating the effectiveness of the model.

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Landmark, K., and E. Messel. "HIERARCHICAL PATH PLANNING FOR WALKING (ALMOST) ANYWHERE." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-4/W8 (July 11, 2018): 109–16. http://dx.doi.org/10.5194/isprs-archives-xlii-4-w8-109-2018.

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<p><strong>Abstract.</strong> Computerized path planning, not constrained to transportation networks, may be useful in a range of settings, from search and rescue to archaeology. This paper develops a method for general path planning intended to work across arbitrary distances and at the level of terrain detail afforded by aerial LiDAR scanning. Relevant information about terrain, trails, roads, and other infrastructure is encoded in a large directed graph. This basal graph is partitioned into strongly connected subgraphs such that the generalized diameter of each subgraphs is constrained by a set value, and with nominally as few subgraphs as possible. This is accomplished using the k-center algorithm adapted with heuristics suitable for large spatial graphs. A simplified graph results, with reduced (but known) position accuracy and complexity. Using a hierarchy of simplified graphs adapted to different length scales, and with careful selection of levels in the hierarchy based on geodesic distance, a shortest path search can be restricted to a small subset of the basal graph. The method is formulated using matrix-graph duality, suitable for linear algebra-oriented software. Extensive use is also made of public data, including LiDAR, as well as free and open software for geospatial data processing.</p>

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Goedicke, M., P. Tröpfner, and B. Enders-Sucrow. "HIERARCHICAL SPECIFICATION OF GRAPHICAL USER INTERFACES USING A GRAPH GRAMMAR APPROACH." Journal of Integrated Design and Process Science: Transactions of the SDPS, Official Journal of the Society for Design and Process Science 5, no. 1 (2001): 67–86. http://dx.doi.org/10.3233/2001-jid5_05.

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In this contribution we consider a rule based visual language for the specification of graphical user interfaces (GUIs). Our approach uses a graph rewrite approach in such a way that the state of a GUI is represented as a complex visual graph. An action is represented by a visual rewrite rule applicable to a graph of this form. Since the GUI features are represented as little pictures like windows, listboxes etc. it is necessary to define these problem oriented representa-tions by a more abstract mathematical formalism. We use graphs to represent the semantics of the problem oriented representation. Complex actions and events are modelled by rewrite steps on these graphs. Usually complex GUIs are described by a hierarchy of interaction objects. Such a hierarchy is adequately expressed as a hierarchy of graph layers. We present how the various descriptions of picture graphs and graphs as well as visual rules and graph rewrite rules, respectively, are integrated by a method using special mappings.

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Li, Jiangmeng, Yifan Jin, Hang Gao, Wenwen Qiang, Changwen Zheng, and Fuchun Sun. "Hierarchical Topology Isomorphism Expertise Embedded Graph Contrastive Learning." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 12 (2024): 13518–27. http://dx.doi.org/10.1609/aaai.v38i12.29255.

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Graph contrastive learning (GCL) aims to align the positive features while differentiating the negative features in the latent space by minimizing a pair-wise contrastive loss. As the embodiment of an outstanding discriminative unsupervised graph representation learning approach, GCL achieves impressive successes in various graph benchmarks. However, such an approach falls short of recognizing the topology isomorphism of graphs, resulting in that graphs with relatively homogeneous node features cannot be sufficiently discriminated. By revisiting classic graph topology recognition works, we disclose that the corresponding expertise intuitively complements GCL methods. To this end, we propose a novel hierarchical topology isomorphism expertise embedded graph contrastive learning, which introduces knowledge distillations to empower GCL models to learn the hierarchical topology isomorphism expertise, including the graph-tier and subgraph-tier. On top of this, the proposed method holds the feature of plug-and-play, and we empirically demonstrate that the proposed method is universal to multiple state-of-the-art GCL models. The solid theoretical analyses are further provided to prove that compared with conventional GCL methods, our method acquires the tighter upper bound of Bayes classification error. We conduct extensive experiments on real-world benchmarks to exhibit the performance superiority of our method over candidate GCL methods, e.g., for the real-world graph representation learning experiments, the proposed method beats the state-of-the-art method by 0.23% on unsupervised representation learning setting, 0.43% on transfer learning setting. Our code is available at https://github.com/jyf123/HTML.

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Ranjan, Ekagra, Soumya Sanyal, and Partha Talukdar. "ASAP: Adaptive Structure Aware Pooling for Learning Hierarchical Graph Representations." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (2020): 5470–77. http://dx.doi.org/10.1609/aaai.v34i04.5997.

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Graph Neural Networks (GNN) have been shown to work effectively for modeling graph structured data to solve tasks such as node classification, link prediction and graph classification. There has been some recent progress in defining the notion of pooling in graphs whereby the model tries to generate a graph level representation by downsampling and summarizing the information present in the nodes. Existing pooling methods either fail to effectively capture the graph substructure or do not easily scale to large graphs. In this work, we propose ASAP (Adaptive Structure Aware Pooling), a sparse and differentiable pooling method that addresses the limitations of previous graph pooling architectures. ASAP utilizes a novel self-attention network along with a modified GNN formulation to capture the importance of each node in a given graph. It also learns a sparse soft cluster assignment for nodes at each layer to effectively pool the subgraphs to form the pooled graph. Through extensive experiments on multiple datasets and theoretical analysis, we motivate our choice of the components used in ASAP. Our experimental results show that combining existing GNN architectures with ASAP leads to state-of-the-art results on multiple graph classification benchmarks. ASAP has an average improvement of 4%, compared to current sparse hierarchical state-of-the-art method. We make the source code of ASAP available to encourage reproducible research 1.

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Fujita, Takaaki. "Modeling Hierarchical Systems in Graph Signal Processing, Electric Circuits, and Bond Graphs Via Hypergraphs and Superhypergraphs." Journal of Engineering Research and Reports 27, no. 5 (2025): 542–92. https://doi.org/10.9734/jerr/2025/v27i51522.

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Graph theory is a core branch of mathematics concerned with representing and analyzing relationships among discrete elements. These concepts are widely used in fields such as electrical engineering. For example, graphs play a crucial role in important frameworks including Graph Signal Processing, Electric Circuits, and Bond Graphs. A hypergraph generalizes the concept of a traditional graph by allowing edges—called hyperedges—to connect more than two vertices simultaneously (Berge, 1984). A superhypergraph further extends this idea by incorporating recursively defined powerset layers, enabling hierarchical and self-referential relationships among hyperedges (Smarandache, 2020). In this paper, we extend the frameworks of Graph Signal Processing, Electric Circuits, and Bond Graphs using hypergraphs and superhypergraphs, and investigate their mathematical properties and illustrative examples. These extensions enable the representation of hierarchical structures inherent in Graph Signal Processing, Electric Circuits, and Bond Graphs, providing a more expressive modeling framework. We anticipate that future research will advance computational experiments and practical applications in these domains.

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Lin, Zhe, Fan Zhang, Xuemin Lin, Wenjie Zhang, and Zhihong Tian. "Hierarchical core maintenance on large dynamic graphs." Proceedings of the VLDB Endowment 14, no. 5 (2021): 757–70. http://dx.doi.org/10.14778/3446095.3446099.

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The model of k -core and its decomposition have been applied in various areas, such as social networks, the world wide web, and biology. A graph can be decomposed into an elegant k -core hierarchy to facilitate cohesive subgraph discovery and network analysis. As many real-life graphs are fast evolving, existing works proposed efficient algorithms to maintain the coreness value of every vertex against structure changes. However, the maintenance of the k -core hierarchy in existing studies is not complete because the connections among different k -cores in the hierarchy are not considered. In this paper, we study hierarchical core maintenance which is to compute the k -core hierarchy incrementally against graph dynamics. The problem is challenging because the change of hierarchy may be large and complex even for a slight graph update. In order to precisely locate the area affected by graph dynamics, we conduct in-depth analyses on the structural properties of the hierarchy, and propose well-designed local update techniques. Our algorithms significantly outperform the baselines on runtime by up to 3 orders of magnitude, as demonstrated on 10 real-world large graphs.

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Bruni, Roberto, FABIO GADDUCCI, and Alberto Lluch-Lafuente. "An Algebra of Hierarchical Graphs and its Application to Structural Encoding." Scientific Annals of Computer Science XX (June 5, 2010): 53–96. https://doi.org/10.5281/zenodo.12720483.

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We define an algebraic theory of hierarchical graphs, whose axioms characterise graph isomorphism: two terms are equated exactly when they represent the same graph. Our algebra can be understood as a high-level language for describing graphs with a node-sharing, embedding structure, and it is then well suited for defining graphical representations of software models where nesting and linking are key aspects. In particular, we propose the use of our graph formalism as a convenient way to describe configurations in process calculi equipped with inherently hierarchical features such as sessions, locations, transactions, membranes or ambients. The graph syntax can be seen as an intermediate representation language, that facilitates the encodings of algebraic specifications, since it provides primitives for nesting, name restriction and parallel composition. In addition, proving soundness and correctness of an encoding (i.e. proving that structurally equivalent processes are mapped to isomorphic graphs) becomes easier as it can be done by induction over the graph syntax.

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Engels, Gregor, and Andy Schürr. "Encapsulated Hierarchical Graphs, Graph Types, and Meta Types." Electronic Notes in Theoretical Computer Science 2 (1995): 101–9. http://dx.doi.org/10.1016/s1571-0661(05)80186-0.

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Babanov, Alexey M., and Elena S. Kvach. "IS-THE graphs usage to analyze hierarchical data structures." Vestnik Tomskogo gosudarstvennogo universiteta. Upravlenie, vychislitel'naya tekhnika i informatika, no. 66 (2024): 87–96. http://dx.doi.org/10.17223/19988605/66/9.

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The article defines the general principles for representing hierarchical structures, such as specializations and categorizations in data models, and class hierarchies in OOP. This representation allows a deeper analysis of the semantics of the subject area and solving the problem of optimal universal implementation of these structures in database systems and object-oriented applications. The possibility for such a generalization is provided by IS-THE relations and IS-THE mappings, on the basis of which IS-THE graphs are constructed. The selection of subgraphs of these graphs according to certain rules generates types of hierarchical structures known in computer science: a single inheritance hierarchy (a specialization hierarchy), a selective inheritance graph (a two-level categorization graph), a two-level multiple inheritance graph.

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Yang, Jinyu, Peilin Zhao, Yu Rong, et al. "Hierarchical Graph Capsule Network." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 12 (2021): 10603–11. http://dx.doi.org/10.1609/aaai.v35i12.17268.

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Graph Neural Networks (GNNs) draw their strength from explicitly modeling the topological information of structured data. However, existing GNNs suffer from limited capability in capturing the hierarchical graph representation which plays an important role in graph classification. In this paper, we innovatively propose hierarchical graph capsule network (HGCN) that can jointly learn node embeddings and extract graph hierarchies. Specifically, disentangled graph capsules are established by identifying heterogeneous factors underlying each node, such that their instantiation parameters represent different properties of the same entity. To learn the hierarchical representation, HGCN characterizes the part-whole relationship between lower-level capsules (part) and higher-level capsules (whole) by explicitly considering the structure information among the parts. Experimental studies demonstrate the effectiveness of HGCN and the contribution of each component. Code: https://github.com/uta-smile/HGCN

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Hausner, Alejo. "Hierarchical graph color dither." Journal of Electronic Imaging 17, no. 2 (2008): 023001. http://dx.doi.org/10.1117/1.2916703.

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Palacz, Wojciech. "Algebraic hierarchical graph transformation." Journal of Computer and System Sciences 68, no. 3 (2004): 497–520. http://dx.doi.org/10.1016/s0022-0000(03)00064-3.

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Perret, B., G. Chierchia, J. Cousty, S. J. F. Guimarães, Y. Kenmochi, and L. Najman. "Higra: Hierarchical Graph Analysis." SoftwareX 10 (July 2019): 100335. http://dx.doi.org/10.1016/j.softx.2019.100335.

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Lam, Ho-Ching, and Ivo D. Dinov. "Hyperbolic Wheel: A Novel Hyperbolic Space Graph Viewer for Hierarchical Information Content." ISRN Computer Graphics 2012 (October 31, 2012): 1–10. http://dx.doi.org/10.5402/2012/609234.

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Tree and graph structures have been widely used to present hierarchical and linked data. Hyperbolic trees are special types of graphs composed of nodes (points or vertices) and edges (connecting lines), which are visualized on a non-Euclidean space. In traditional Euclidean space graph visualization, distances between nodes are measured by straight lines. Displays of large graphs in Euclidean spaces may not utilize efficiently the available space and may impose limitations on the number of graph nodes. The special hyperbolic space rendering of tree-graphs enables adaptive and efficient use of the available space and facilitates the display of large hierarchical structures. In this paper we report on a newly developed advanced hyperbolic graph viewer, Hyperbolic Wheel, which enables the navigation, traversal, discovery and interactive manipulation of information stored in large hierarchical structures. Examples of such structures include personnel records, disc directory structures, ontological constructs, web-pages and other nested partitions. The Hyperbolic Wheel framework provides an intuitive and dynamic graphical interface to explore and retrieve information about individual nodes (data objects) and their relationships (data associations). The Hyperbolic Wheel is freely available online for educational and research purposes.

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DICKINSON, P. J., M. KRAETZL, H. BUNKE, M. NEUHAUS, and A. DADEJ. "SIMILARITY MEASURES FOR HIERARCHICAL REPRESENTATIONS OF GRAPHS WITH UNIQUE NODE LABELS." International Journal of Pattern Recognition and Artificial Intelligence 18, no. 03 (2004): 425–42. http://dx.doi.org/10.1142/s021800140400323x.

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A hierarchical abstraction scheme based on node contraction and two related similarity measures for graphs with unique node labels are proposed in this paper. The contraction scheme reduces the number of nodes in a graph and leads to a speed-up in the computation of graph similarity. Theoretical properties of the new graph similarity measures are derived and experimentally verified. A potential application of the proposed graph abstraction scheme in the domain of computer network monitoring is discussed.

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Han, Qiuhan, Atsushi Yoshikawa, and Masayuki Yamamura. "Hierarchical Graph Learning with Cross-Layer Information Propagation for Next Point of Interest Recommendation." Applied Sciences 15, no. 9 (2025): 4979. https://doi.org/10.3390/app15094979.

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With the vast quantity of GPS data that have been collected from location-based social networks, Point-of-Interest (POI) recommendation aims to predict users’ next locations by learning from their historical check-in trajectories. While Graph Neural Network (GNN)-based models have shown promising results in this field, they typically construct single-layer graphs that fail to capture the hierarchical nature of human mobility patterns. To address this limitation, we propose a novel Hierarchical Graph Learning (HGL) framework that models POI relationships at multiple scales. Specifically, we construct a three-level graph structure: a base-level graph capturing direct POI transitions, a region-level graph modeling area-based interactions through spatio-temporal clustering, and a global-level graph representing category-based patterns. To effectively utilize this hierarchical structure, we design a cross-layer information propagation mechanism that enables bidirectional message passing between different levels, allowing the model to capture both fine-grained POI interactions and coarse-grained mobility patterns. Compared to traditional models, our hierarchical structure improves cold-start robustness and achieves superior performance on real-world datasets. While the incorporation of multi-layer attention and clustering introduces moderate computational overhead, the cost remains acceptable for offline recommendation contexts.

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Li, Zitong, Xiang Cheng, Lixiao Sun, Ji Zhang, and Bing Chen. "A Hierarchical Approach for Advanced Persistent Threat Detection with Attention-Based Graph Neural Networks." Security and Communication Networks 2021 (May 4, 2021): 1–14. http://dx.doi.org/10.1155/2021/9961342.

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Advanced Persistent Threats (APTs) are the most sophisticated attacks for modern information systems. Currently, more and more researchers begin to focus on graph-based anomaly detection methods that leverage graph data to model normal behaviors and detect outliers for defending against APTs. However, previous studies of provenance graphs mainly concentrate on system calls, leading to difficulties in modeling network behaviors. Coarse-grained correlation graphs depend on handcrafted graph construction rules and, thus, cannot adequately explore log node attributes. Besides, the traditional Graph Neural Networks (GNNs) fail to consider meaningful edge features and are difficult to perform heterogeneous graphs embedding. To overcome the limitations of the existing approaches, we present a hierarchical approach for APT detection with novel attention-based GNNs. We propose a metapath aggregated GNN for provenance graph embedding and an edge enhanced GNN for host interactive graph embedding; thus, APT behaviors can be captured at both the system and network levels. A novel enhancement mechanism is also introduced to dynamically update the detection model in the hierarchical detection framework. Evaluations show that the proposed method outperforms the state-of-the-art baselines in APT detection.

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SHARMA, ROHAN, BIBHAS ADHIKARI, and TYLL KRUEGER. "SELF-ORGANIZED CORONA GRAPHS: A DETERMINISTIC COMPLEX NETWORK MODEL WITH HIERARCHICAL STRUCTURE." Advances in Complex Systems 22, no. 06 (2019): 1950019. http://dx.doi.org/10.1142/s021952591950019x.

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In this paper, we propose a self-organization mechanism for newly appeared nodes during the formation of corona graphs that define a hierarchical pattern in the resulting corona graphs and we call it self-organized corona graphs (SoCG). We show that the degree distribution of SoCG follows power-law in its tail with power-law exponent approximately 2. We also show that the diameter is less equal to 4 for SoCG defined by any seed graph and for certain seed graphs, the diameter remains constant during its formation. We derive lower bounds of clustering coefficients of SoCG defined by certain seed graphs. Thus, the proposed SoCG can be considered as a growing network generative model which is defined by using the corona graphs and a self-organization process such that the resulting graphs are scale-free small-world highly clustered growing networks. The SoCG defined by a seed graph can also be considered as a network with a desired motif which is the seed graph itself.

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Kuznetsov, Maksim, and Daniil Polykovskiy. "MolGrow: A Graph Normalizing Flow for Hierarchical Molecular Generation." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 9 (2021): 8226–34. http://dx.doi.org/10.1609/aaai.v35i9.17001.

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We propose a hierarchical normalizing flow model for generating molecular graphs. The model produces new molecular structures from a single-node graph by recursively splitting every node into two. All operations are invertible and can be used as plug-and-play modules. The hierarchical nature of the latent codes allows for precise changes in the resulting graph: perturbations in the first layer cause global structural changes, while perturbations in the consequent layers change the resulting molecule only marginally. Proposed model outperforms existing generative graph models on the distribution learning task. We also show successful experiments on global and constrained optimization of chemical properties using latent codes of the model.

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Guo, Kan, Yongli Hu, Yanfeng Sun, Sean Qian, Junbin Gao, and Baocai Yin. "Hierarchical Graph Convolution Network for Traffic Forecasting." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 1 (2021): 151–59. http://dx.doi.org/10.1609/aaai.v35i1.16088.

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Traffic forecasting is attracting considerable interest due to its widespread application in intelligent transportation systems. Given the complex and dynamic traffic data, many methods focus on how to establish a spatial-temporal model to express the non-stationary traffic patterns. Recently, the latest Graph Convolution Network (GCN) has been introduced to learn spatial features while the time neural networks are used to learn temporal features. These GCN based methods obtain state-of-the-art performance. However, the current GCN based methods ignore the natural hierarchical structure of traffic systems which is composed of the micro layers of road networks and the macro layers of region networks, in which the nodes are obtained through pooling method and could include some hot traffic regions such as downtown and CBD etc., while the current GCN is only applied on the micro graph of road networks. In this paper, we propose a novel Hierarchical Graph Convolution Networks (HGCN) for traffic forecasting by operating on both the micro and macro traffic graphs. The proposed method is evaluated on two complex city traffic speed datasets. Compared to the latest GCN based methods like Graph WaveNet, the proposed HGCN gets higher traffic forecasting precision with lower computational cost.The website of the code is https://github.com/guokan987/HGCN.git.

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Krleza, Dalibor, and Kresimir Fertalj. "Graph Matching Using Hierarchical Fuzzy Graph Neural Networks." IEEE Transactions on Fuzzy Systems 25, no. 4 (2017): 892–904. http://dx.doi.org/10.1109/tfuzz.2016.2586962.

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Béthune, Louis, Yacouba Kaloga, Pierre Borgnat, Aurélien Garivier, and Amaury Habrard. "Hierarchical and Unsupervised Graph Representation Learning with Loukas’s Coarsening." Algorithms 13, no. 9 (2020): 206. http://dx.doi.org/10.3390/a13090206.

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We propose a novel algorithm for unsupervised graph representation learning with attributed graphs. It combines three advantages addressing some current limitations of the literature: (i) The model is inductive: it can embed new graphs without re-training in the presence of new data; (ii) The method takes into account both micro-structures and macro-structures by looking at the attributed graphs at different scales; (iii) The model is end-to-end differentiable: it is a building block that can be plugged into deep learning pipelines and allows for back-propagation. We show that combining a coarsening method having strong theoretical guarantees with mutual information maximization suffices to produce high quality embeddings. We evaluate them on classification tasks with common benchmarks of the literature. We show that our algorithm is competitive with state of the art among unsupervised graph representation learning methods.

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Duan, Ziheng, Yi Dai, Ahyeon Hwang, et al. "iHerd: an integrative hierarchical graph representation learning framework to quantify network changes and prioritize risk genes in disease." PLOS Computational Biology 19, no. 9 (2023): e1011444. http://dx.doi.org/10.1371/journal.pcbi.1011444.

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Different genes form complex networks within cells to carry out critical cellular functions, while network alterations in this process can potentially introduce downstream transcriptome perturbations and phenotypic variations. Therefore, developing efficient and interpretable methods to quantify network changes and pinpoint driver genes across conditions is crucial. We propose a hierarchical graph representation learning method, called iHerd. Given a set of networks, iHerd first hierarchically generates a series of coarsened sub-graphs in a data-driven manner, representing network modules at different resolutions (e.g., the level of signaling pathways). Then, it sequentially learns low-dimensional node representations at all hierarchical levels via efficient graph embedding. Lastly, iHerd projects separate gene embeddings onto the same latent space in its graph alignment module to calculate a rewiring index for driver gene prioritization. To demonstrate its effectiveness, we applied iHerd on a tumor-to-normal GRN rewiring analysis and cell-type-specific GCN analysis using single-cell multiome data of the brain. We showed that iHerd can effectively pinpoint novel and well-known risk genes in different diseases. Distinct from existing models, iHerd’s graph coarsening for hierarchical learning allows us to successfully classify network driver genes into early and late divergent genes (EDGs and LDGs), emphasizing genes with extensive network changes across and within signaling pathway levels. This unique approach for driver gene classification can provide us with deeper molecular insights. The code is freely available at https://github.com/aicb-ZhangLabs/iHerd. All other relevant data are within the manuscript and it supporting information files.

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Piekarczyk, Marcin, and Marek Ogiela. "Hierarchical Graph-Grammar Model for Secure and Efficient Handwritten Signatures Classification." JUCS - Journal of Universal Computer Science 17, no. (6) (2011): 926–43. https://doi.org/10.3217/jucs-017-06-0926.

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One important subject associated with personal authentication capabilities is the analysis of handwritten signatures. Among the many known techniques, algorithms based on linguistic formalisms are also possible. However, such techniques require a number of algorithms for intelligent image analysis to be applied, allowing the development of new solutions in the field of personal authentication and building modern security systems based on the advanced recognition of such patterns. The article presents the approach based on the usage of syntactic methods for the static analysis of handwritten signatures. The graph linguistic formalisms applied, such as the IE graph and ETPL(k) grammar, are characterised by considerable descriptive strength and a polynomial membership problem of the syntactic analysis. For the purposes of representing the analysed handwritten signatures, new hierarchical (two-layer) HIE graph structures based on IE graphs have been defined. The two-layer graph description makes it possible to take into consideration both local and global features of the signature. The usage of attributed graphs enables the storage of additional semantic information describing the properties of individual signature strokes. The verification and recognition of a signature consists in analysing the affiliation of its graph description to the language describing the specimen database. Initial assessments display a precision of the method at a average level of under 75%.

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Wang, Yuxiang, Zhangyang Peng, Xiangyu Ke, Xiaoliang Xu, Tianxing Wu, and Yuan Gao. "Cohesiveness-aware Hierarchical Compressed Index for Community Search on Attributed Graphs." Proceedings of the ACM on Management of Data 3, no. 1 (2025): 1–27. https://doi.org/10.1145/3709672.

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Community search on attributed graphs (CSAG) is a fundamental topic in graph data mining. Given an attributed graph G and a query node q , CSAG seeks a structural- and attribute-cohesive subgraph from G that contains q . Exact methods based on graph traversal are time-consuming, especially for large graphs. Approximate methods improve efficiency by pruning the search space with heuristics but still take hundreds of milliseconds to tens of seconds to respond, hindering their use in time-sensitive applications. Moreover, pruning strategies are typically tailored to specific algorithms and their cohesiveness metrics, making them difficult to generalize. To address this, we study a general approach to accelerate various CSAG methods. We first present a proximity graph-based, cohesiveness-aware hierarchical index that accommodates different cohesiveness metrics. Then, we present two optimizations to enhance the index's navigability and reliability. Finally, we design a compressed storage structure for space-efficient indexing. Experiments on real-world datasets show that integrating our index with existing mainstream CSAG methods results in an average 30.7× speedup while maintaining a comparable or even better attribute cohesiveness.

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Haga, Tatsuya, and Tomoki Fukai. "Multiscale representations of community structures in attractor neural networks." PLOS Computational Biology 17, no. 8 (2021): e1009296. http://dx.doi.org/10.1371/journal.pcbi.1009296.

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Our cognition relies on the ability of the brain to segment hierarchically structured events on multiple scales. Recent evidence suggests that the brain performs this event segmentation based on the structure of state-transition graphs behind sequential experiences. However, the underlying circuit mechanisms are poorly understood. In this paper we propose an extended attractor network model for graph-based hierarchical computation which we call the Laplacian associative memory. This model generates multiscale representations for communities (clusters) of associative links between memory items, and the scale is regulated by the heterogenous modulation of inhibitory circuits. We analytically and numerically show that these representations correspond to graph Laplacian eigenvectors, a popular method for graph segmentation and dimensionality reduction. Finally, we demonstrate that our model exhibits chunked sequential activity patterns resembling hippocampal theta sequences. Our model connects graph theory and attractor dynamics to provide a biologically plausible mechanism for abstraction in the brain.

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Malik, Nikita, Rahul Gupta, and Sandeep Kumar. "HyperDefender: A Robust Framework for Hyperbolic GNNs." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 18 (2025): 19396–404. https://doi.org/10.1609/aaai.v39i18.34135.

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Graph neural networks for hyperbolic space has emerged as a powerful tool for embedding datasets exhibiting a highly non-Euclidean latent anatomy e.g., graphs with hierarchical structures. While several Hyperbolic Graph Neural Networks (Hy-GNNs) have been developed to enhance the representation of hierarchical datasets, they remain susceptible to noise and adversarial attacks, posing serious risks in critical applications. The absence of robust Hy-GNN frameworks underscores a pressing problem. This research addresses this challenge by introducing HyperDefender—a robust and flexible approach designed to fortify Hy-GNNs against adversarial attacks and noises. HyperDefender aims to secure the reliability of applications that depend on the integrity of hierarchical graph-structured data in real-world scenarios. Experimental results demonstrate that HyperDefender significantly improves node classification accuracy across various attacks, effectively mitigating the performance degradation typically observed in Hy-GNNs when the hierarchy in original datasets is compromised.

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Irion, Jeff, and Naoki Saito. "Hierarchical graph Laplacian eigen transforms." JSIAM Letters 6 (2014): 21–24. http://dx.doi.org/10.14495/jsiaml.6.21.

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JONYER, ISTVAN, LAWRENCE B. HOLDER, and DIANE J. COOK. "GRAPH-BASED HIERARCHICAL CONCEPTUAL CLUSTERING." International Journal on Artificial Intelligence Tools 10, no. 01n02 (2001): 107–35. http://dx.doi.org/10.1142/s0218213001000441.

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Hierarchical conceptual clustering has proven to be a useful, although greatly under-explored data mining technique. A graph-based representation of structural information combined with a substructure discovery technique has been shown to be successful in knowledge discovery. The SUBDUE substructure discovery system provides the advantages of both approaches. This work presents SUBDUE and the development of its clustering functionalities. Several examples are used to illustrate the validity of the approach both in structured and unstructured domains, as well as compare SUBDUE to earlier clustering algorithms. Results show that SUBDUE successfully discovers hierarchical clusterings in both structured and unstructured data.

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Suzuki, Jun, Yutaka Sasaki, and Eisaku Maeda. "Hierarchical directed acyclic graph kernel." Systems and Computers in Japan 37, no. 10 (2006): 58–68. http://dx.doi.org/10.1002/scj.20485.

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Yoshikawa, Tomohiro, Yuki Uchida, Takeshi Furuhashi, Eiji Hirao, and Hiroto Iguchi. "Extraction of Evaluation Keywords for Analyzing Product Evaluation in User-Reviews Using Hierarchical Keyword Graph." Journal of Advanced Computational Intelligence and Intelligent Informatics 13, no. 4 (2009): 457–62. http://dx.doi.org/10.20965/jaciii.2009.p0457.

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Recently, the number of sites on the Internet which give users the opportunity to write their ideas and opinions for the public to read have been increasing. In addition, the number of people who want to know the opinions of others about interesting products has also been increasing. However, it is very difficult for people to read complete reviews on the Internet. This study tries to develop a new system for the analysis of reviews, a system which shows evaluation information about products using graphs of evaluation keywords. This paper focuses on the extraction of evaluation keywords from reviews on the Internet. This paper proposes a method for extracting evaluation keywords and displays its results as graphs. It employs HK Graph (Hierarchical Keyword Graph), which can visualize the relationship among words in a hierarchical network structure based on the co-occurrence information for the keyword graph.

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RAFE, VAHID, and ADEL T. RAHMANI. "A NOVEL APPROACH TO VERIFY GRAPH SCHEMA-BASED SOFTWARE SYSTEMS." International Journal of Software Engineering and Knowledge Engineering 19, no. 06 (2009): 857–70. http://dx.doi.org/10.1142/s0218194009004398.

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Graph Grammars have recently become more and more popular as a general formal modeling language. Behavioral modeling of dynamic systems and model to model transformations are a few well-known examples in which graphs have proven their usefulness in software engineering. A special type of graph transformation systems is layered graphs. Layered graphs are a suitable formalism for modeling hierarchical systems. However, most of the research so far concentrated on graph transformation systems as a modeling means, without considering the need for suitable analysis tools. In this paper we concentrate on how to analyze these models. We will describe our approach to show how one can verify the designed graph transformation systems. To verify graph transformation systems we use a novel approach: using Bogor model checker to verify graph transformation systems. The AGG-like graph transformation systems are translated to BIR — the input language of Bogor — and Bogor verifies that model against some properties defined by combining LTL and special purpose graph rules. Supporting schema-based and layered graphs characterize our approach among existing solutions for verification of graph transformation systems.

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Wang, Ke, Yanmin Zhu, Tianzi Zang, Chunyang Wang, and Mengyuan Jing. "Review-Enhanced Hierarchical Contrastive Learning for Recommendation." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 8 (2024): 9107–15. http://dx.doi.org/10.1609/aaai.v38i8.28761.

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Designed to establish potential relations and distill high-order representations, graph-based recommendation systems continue to reveal promising results by jointly modeling ratings and reviews. However, existing studies capture simple review relations, failing to (1) completely explore hidden connections between users (or items), (2) filter out redundant information derived from reviews, and (3) model the behavioral association between rating and review interactions. To address these challenges, we propose a review-enhanced hierarchical contrastive learning, namely ReHCL. First, ReHCL constructs topic and semantic graphs to fully mine review relations from different views. Moreover, a cross-view graph contrastive learning is used to achieve enhancement of node representations and extract useful review knowledge. Meanwhile, we design a neighbor-based positive sampling to capture the graph-structured similarity between topic and semantic views, further performing efficient contrast and reducing redundant noise. Next, we propose a cross-modal contrastive learning to match the rating and review representations, by exploring the association between ratings and reviews. Lastly, these two contrastive learning modes form a hierarchical contrastive learning task, which is applied to enhance the final recommendation task. Extensive experiments verify the superiority of ReHCL compared with state-of-the-arts.

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