Relevant bibliographies by topics / Hierarchical graph

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Hierarchical graph'

Author: Grafiati
Published: 4 June 2021
Last updated: 18 June 2025

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Journal articles on the topic "Hierarchical graph"

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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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Dissertations / Theses on the topic "Hierarchical graph"

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Busatto, Giorgio. "An abstract model of hierarchical graphs and hierarchical graph transformation." Oldenburg : Univ., Fachbereich Informatik, 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=967851955.

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Busatto, Giorgio [Verfasser]. "An abstract model of hierarchical graphs and hierarchical graph transformation / von Giorgio Busatto." Oldenburg : Univ., Fachbereich Informatik, 2002. http://d-nb.info/967851955/34.

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Slade, Michael L. "A layout algorithm for hierarchical graphs with constraints /." Online version of thesis, 1994. http://hdl.handle.net/1850/11724.

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Kakraba, Samuel. "A Hierarchical Graph for Nucleotide Binding Domain 2." Digital Commons @ East Tennessee State University, 2015. https://dc.etsu.edu/etd/2517.

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One of the most prevalent inherited diseases is cystic fibrosis. This disease is caused by a mutation in a membrane protein, the cystic fibrosis transmembrane conductance regulator (CFTR). CFTR is known to function as a chloride channel that regulates the viscosity of mucus that lines the ducts of a number of organs. Generally, most of the prevalent mutations of CFTR are located in one of two nucleotide binding domains, namely, the nucleotide binding domain 1 (NBD1). However, some mutations in nucleotide binding domain 2 (NBD2) can equally cause cystic fibrosis. In this work, a hierarchical graph is built for NBD2. Using this model for NBD2, we examine the consequence of single point mutations on NBD2. We collate the wildtype structure with eight of the most prevalent mutations and observe how the NBD2 is affected by each of these mutations.
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Choset, Howie M. Burdick Joel Wakeman Burdick Joel Wakeman. "Sensor based motion planning : the hierarchical generalized Voronoi graph /." Diss., Pasadena, Calif. : California Institute of Technology, 1996. http://resolver.caltech.edu/CaltechETD:etd-12182007-090504.

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Wengle, Emil. "Modelling Hierarchical Structures in Networks Using Graph Theory : With Application to Knowledge Networks in Graph Curricula." Thesis, Uppsala universitet, Signaler och system, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-415044.

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Community detection is a topic in network theory that involves assigning labels to nodes based on some distance measure or centrality index. Detecting communities within a network can be useful to perform information condensation. In this thesis we explore how to use the approach for pedagogical purposes, and more precisely to condense and visualise the networks of facts, concepts and procedures (also called Knowledge Components (KCs)) that are offered in higher education programmes. In details, we consider one of the most common quantities used to evaluate the goodness of a community classification, which is the concept of modularity. Detecting communities by computing the maximum possible modularity indexes is indeed usually desired, but this approach is generally unavailable because the associated optimisation problem is NP-complete. This is why practitioners use other algorithms, that instead of computing the optimum they rely on various heuristics to find communities: some use modularity directly, some start from the entire graph and divide it repeatedly, and some contain random elements. This thesis investigates the trade-offs of using different community detection algorithms and variations of the concept of modularity first in general terms, and then for the purpose of identifying communities in knowledge graphs associated to higher education programmes, which can be modelled as directed graphs of KCs. We discover, tweaking and applying these algorithms both on synthetic but also field data that the Louvain algorithm is among the better algorithms of those that we considered, which is mostly thanks to its efficiency. It does not produce a full hierarchy, however, so we recommend Fast Newman if hierarchy is important.
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Spisla, Christiane [Verfasser]. "Compaction of Orthogonal and Hierarchical Graph Drawings Using Constraint Graphs and Minimum Cost Flows / Christiane Spisla." München : Verlag Dr. Hut, 2019. http://d-nb.info/119641467X/34.

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Holzer, Martin. "Hierarchical speed-up techniques for shortest-path algorithms." [S.l. : s.n.], 2003. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB10605142.

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Ismaeel, Alaa Aly Khalaf [Verfasser], and H. [Akademischer Betreuer] Schmeck. "Dynamic Hierarchical Graph Drawing / Alaa Aly Khalaf Ismaeel. Betreuer: H. Schmeck." Karlsruhe : KIT-Bibliothek, 2012. http://d-nb.info/1023081776/34.

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Cybis, Gabriela Bettella. "Phenotypic Bayesian phylodynamics : hierarchical graph models, antigenic clustering and latent liabilities." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2014. http://hdl.handle.net/10183/132858.

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Combining models for phenotypic and molecular evolution can lead to powerful inference tools. Under the flexible framework of Bayesian phylogenetics, I develop statistical methods to address phylodynamic problems in this intersection. First, I present a hierarchical phylogeographic method that combines information across multiple datasets to draw inference on a common geographical spread process. Each dataset represents a parallel realization of this geographic process on a different group of taxa, and the method shares information between these realizations through a hierarchical graph structure. Additionally, I develop a multivariate latent liability model for assessing phenotypic correlation among sets of traits, while controlling for shared evolutionary history. This method can efficiently estimate correlations between multiple continuous traits, binary traits and discrete traits with many ordered or unordered outcomes. Finally, I present a method that uses phylogenetic information to study the evolution of antigenic clusters in influenza. The method builds an antigenic cartography map informed by the assignment of each influenza strain to one of the antigenic clusters.
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Books on the topic "Hierarchical graph"

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Mikov, Aleksandr. Generalized graphs and grammars. INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/1013698.

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The textbook deals with ordinary graphs and their generalizations-hypergraphs, hierarchical structures, geometric graphs, random and dynamic graphs. Graph grammars are considered in detail.
 Meets the requirements of the federal state educational standards of higher education of the latest generation.
 For master's students studying in the areas of the 02.00.00 group "Computer and Information Sciences", and can also be used in senior bachelor's courses and other areas in the field of computer science and computer engineering.
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Wallgrün, Jan Oliver. Hierarchical Voronoi Graphs. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-10345-2.

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Wallgrün, Jan Oliver. Hierarchical Voronoi graphs: Spatial representation and reasoning for mobile robots. Springer, 2010.

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Yust, Jason. Graph Theory for Temporal Structure. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780190696481.003.0014.

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This chapter introduces mathematical graph theory and develops graph-theory concepts that are useful for temporal networks. By generating chord progressions from networks, the potential musical and temporal meaning of graph-theory concepts, especially cycles, is emphasized. A number of concepts related to trees are introduced to show hierarchical aspects of temporal structure, and to allow for a comparison of Fred Lerdahl and Ray Jackendoff’s prolongational trees to temporal structures. This suggests an enrichment of MOPs through spanning trees, and is channelled into a discussion of graph-theoretic algebras, cycle and edge-cut algebras, as they apply to temporal structures.
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(Editor), Andreas Dress, and A. Von Haeseler (Editor), eds. Trees and Hierarchical Structures: Proceedings of Conference Held at Bielefeld, Frg, Oct. 1987 (Lecture Notes in Biomathematics). Springer, 1990.

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Coolen, A. C. C., A. Annibale, and E. S. Roberts. Specific constructions. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198709893.003.0009.

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This chapter presents network-generating models which cannot be neatly categorized as growing, nor as defined primarily through a target degree distribution. They are best understood as mechanistic constructions designed to elucidate a particular feature of the network. In the first sub-section, the Watts–Strogatz model is introduced and motivated as a construction to achieve both a high degree of clustering and a low average path length. Geometric graphs, in their Euclidian flavour, are shown to be a natural choice for broadcast networks. The Hyperbolic variant is informally described, because it is known to be a natural space in which to embed hierarchical graphs. Planar graphs have very specific real-world applications, but are extraordinarily challenging to analyze mathematically. Finally, weighted graphs allow for concepts such as traffic to be incorporated into the random graph model.
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Hierarchical Voronoi Graphs: Spatial Representation and Reasoning for Mobile Robots. Springer Berlin / Heidelberg, 2014.

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Wallgrün, Jan Oliver. Hierarchical Voronoi Graphs: Spatial Representation and Reasoning for Mobile Robots. Springer, 2010.

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Bisseling, Rob H. Parallel Scientific Computation. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198788348.001.0001.

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This book explains how to use the bulk synchronous parallel (BSP) model to design and implement parallel algorithms in the areas of scientific computing and big data. Furthermore, it presents a hybrid BSP approach towards new hardware developments such as hierarchical architectures with both shared and distributed memory. The book provides a full treatment of core problems in scientific computing and big data, starting from a high-level problem description, via a sequential solution algorithm to a parallel solution algorithm and an actual parallel program written in the communication library BSPlib. Numerical experiments are presented for parallel programs on modern parallel computers ranging from desktop computers to massively parallel supercomputers. The introductory chapter of the book gives a complete overview of BSPlib, so that the reader already at an early stage is able to write his/her own parallel programs. Furthermore, it treats BSP benchmarking and parallel sorting by regular sampling. The next three chapters treat basic numerical linear algebra problems such as linear system solving by LU decomposition, sparse matrix-vector multiplication (SpMV), and the fast Fourier transform (FFT). The final chapter explores parallel algorithms for big data problems such as graph matching. The book is accompanied by a software package BSPedupack, freely available online from the author’s homepage, which contains all programs of the book and a set of test programs.
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Raitner, Marcus. Efficient Visual Navigation- A Study by the Example of Hierarchically Structured Graphs. VDM Verlag Dr. Mueller e.K., 2007.

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Book chapters on the topic "Hierarchical graph"

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Woo, Sung-Ho, and Sung-Bong Yang. "Hierarchical Vertex Ordering." In Graph Transformation. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-45832-8_29.

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Padberg, Julia. "Hierarchical Graph Transformation Revisited." In Graph Transformation. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-61470-0_2.

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North, Stephen C., and Gordon Woodhull. "Online Hierarchical Graph Drawing." In Graph Drawing. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-45848-4_19.

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Drewes, Frank, Berthold Hoffmann, and Detlef Plump. "Hierarchical Graph Transformation." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/3-540-46432-8_7.

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Wallgrün, Jan Oliver. "Simplification and Hierarchical Voronoi Graph Construction." In Hierarchical Voronoi Graphs. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-10345-2_4.

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Wallgrün, Jan Oliver. "Voronoi Graph Matching for Data Association." In Hierarchical Voronoi Graphs. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-10345-2_5.

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Sander, G. "A fast heuristic for hierarchical Manhattan layout." In Graph Drawing. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/bfb0021828.

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Yan, Hao, Senzhang Wang, Jun Yin, Chaozhuo Li, Junxing Zhu, and Jianxin Wang. "Hierarchical Graph Contrastive Learning." In Machine Learning and Knowledge Discovery in Databases: Research Track. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-43415-0_41.

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Tapken, Josef. "Implementing Hierarchical Graph-Structures." In Fundamental Approaches to Software Engineering. Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-540-49020-3_15.

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Kakoulis, Konstantinos G., and Ioannis G. Tollis. "An algorithm for labeling edges of hierarchical drawings." In Graph Drawing. Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/3-540-63938-1_60.

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Conference papers on the topic "Hierarchical graph"

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Lin, Yao, Dong Zhu, Chenhui Zhang, Zhiqiang Zhang, and Le Wang. "Spherical Hierarchical Knowledge Graph Embeddings for Cybersecurity Knowledge Graph Completion." In 2024 IEEE 9th International Conference on Data Science in Cyberspace (DSC). IEEE, 2024. https://doi.org/10.1109/dsc63484.2024.00043.

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Wang, Qingsong, and Xin Lin. "Recommendation Model Based Hierarchical Knowledge Graph Embedding." In 2024 9th International Conference on Intelligent Computing and Signal Processing (ICSP). IEEE, 2024. http://dx.doi.org/10.1109/icsp62122.2024.10743380.

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Nguyen, Trong-Thuan, Pha Nguyen, and Khoa Luu. "HIG: Hierarchical Interlacement Graph Approach to Scene Graph Generation in Video Understanding." In 2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2024. http://dx.doi.org/10.1109/cvpr52733.2024.01740.

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Tang, Shuhao, Hao Tian, Xiaofeng Cao, and Wei Ye. "Deep Hierarchical Graph Alignment Kernels." In Thirty-Third International Joint Conference on Artificial Intelligence {IJCAI-24}. International Joint Conferences on Artificial Intelligence Organization, 2024. http://dx.doi.org/10.24963/ijcai.2024/549.

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Typical R-convolution graph kernels invoke the kernel functions that decompose graphs into non-isomorphic substructures and compare them. However, overlooking implicit similarities and topological position information between those substructures limits their performances. In this paper, we introduce Deep Hierarchical Graph Alignment Kernels (DHGAK) to resolve this problem. Specifically, the relational substructures are hierarchically aligned to cluster distributions in their deep embedding space. The substructures belonging to the same cluster are assigned the same feature map in the Reproducing Kernel Hilbert Space (RKHS), where graph feature maps are derived by kernel mean embedding. Theoretical analysis guarantees that DHGAK is positive semi-definite and has linear separability in the RKHS. Comparison with state-of-the-art graph kernels on various benchmark datasets demonstrates the effectiveness and efficiency of DHGAK. The code is available at Github (https://github.com/EWesternRa/DHGAK).
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Zhou, Kaixiong, Qingquan Song, Xiao Huang, Daochen Zha, Na Zou, and Xia Hu. "Multi-Channel Graph Neural Networks." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/188.

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The classification of graph-structured data has be-come increasingly crucial in many disciplines. It has been observed that the implicit or explicit hierarchical community structures preserved in real-world graphs could be useful for downstream classification applications. A straightforward way to leverage the hierarchical structure is to make use the pooling algorithms to cluster nodes into fixed groups, and shrink the input graph layer by layer to learn the pooled graphs.However, the pool shrinking discards the graph details to make it hard to distinguish two non-isomorphic graphs, and the fixed clustering ignores the inherent multiple characteristics of nodes. To compensate the shrinking loss and learn the various nodes’ characteristics, we propose the multi-channel graph neural networks (MuchGNN). Motivated by the underlying mechanisms developed in convolutional neural networks, we define the tailored graph convolutions to learn a series of graph channels at each layer, and shrink the graphs hierarchically to en-code the pooled structures. Experimental results on real-world datasets demonstrate the superiority of MuchGNN over the state-of-the-art methods.
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Zhu, Wenhao, Tianyu Wen, Guojie Song, Xiaojun Ma, and Liang Wang. "Hierarchical Transformer for Scalable Graph Learning." In Thirty-Second International Joint Conference on Artificial Intelligence {IJCAI-23}. International Joint Conferences on Artificial Intelligence Organization, 2023. http://dx.doi.org/10.24963/ijcai.2023/523.

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Graph Transformer is gaining increasing attention in the field of machine learning and has demonstrated state-of-the-art performance on benchmarks for graph representation learning. However, as current implementations of Graph Transformer primarily focus on learning representations of small-scale graphs, the quadratic complexity of the global self-attention mechanism presents a challenge for full-batch training when applied to larger graphs. Additionally, conventional sampling-based methods fail to capture necessary high-level contextual information, resulting in a significant loss of performance. In this paper, we introduce the Hierarchical Scalable Graph Transformer (HSGT) as a solution to these challenges. HSGT successfully scales the Transformer architecture to node representation learning tasks on large-scale graphs, while maintaining high performance. By utilizing graph hierarchies constructed through coarsening techniques, HSGT efficiently updates and stores multi-scale information in node embeddings at different levels. Together with sampling-based training methods, HSGT effectively captures and aggregates multi-level information on the hierarchical graph using only Transformer blocks. Empirical evaluations demonstrate that HSGT achieves state-of-the-art performance on large-scale benchmarks with graphs containing millions of nodes with high efficiency.
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Batisteli, João Pedro Oliveira, and Zenilton K. G. Patrocínio Jr. "Hierarchical Graph Neural Networks Based on Multi-Scale Image Representations." In Anais Estendidos da Conference on Graphics, Patterns and Images. Sociedade Brasileira de Computação - SBC, 2024. https://doi.org/10.5753/sibgrapi.est.2024.31646.

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Image representation as graphs can enhance the understanding of image semantics and facilitate multi-scale image representation. However, existing methods often overlook the significance of the relationship between elements at each scale or fail to encode the hierarchical relationship between graph elements. To cope with that, we introduce four novel approaches for graph construction from images. These approaches utilize hierarchical image segmentation techniques to generate segmentations at multiple scales, and one of them incorporates edges to encode the relationships at each scale. Leveraging these representations, we present two new models: the Hierarchical Graph Convolutional Network for Image Classification (HGCIC) and the Hierarchical Image Graph with Scale Importance (HIGSI). HGCIC uses an adaptive depth to capture significant features and patterns at different scales, while HIGSI employs a novel readout function that weighs the importance of each scale when generating a fixed-size graph representation. Experimental results with CIFAR-10 and STL-10 datasets show that the HIGSI model outperforms (or closely matches) state-of-the-art models. The model also utilizes smaller graphs, reaching the point of using graphs with 50% of the number of nodes compared to other approaches. Additionally, HIGSI outperforms models trained with only the base graph used to create the hierarchy, achieving up to 11.54% better performance while using fewer parameters.
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Kasyanov, Victor Nikolaevich, Elena Viktorovna Kasyanova, and Timur Alexandrovich Zolotuhin. "Information Visualization Based on Attributed Hierarchical Graphs with Ports." In 32nd International Conference on Computer Graphics and Vision. Keldysh Institute of Applied Mathematics, 2022. http://dx.doi.org/10.20948/graphicon-2022-211-217.

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Information visualization based on graph models has many applications in both real and theoretical fields. Since the information that it is desirable to visualize is constantly growing and becoming more complex, more powerful graph-theoretic formalisms are required and appear to represent structured information models with a hierarchical structure. One of these formalisms is the so-called attributed hierarchical graphs. It allows selecting in the original graph a set of such parts (so-called fragments) that all elements of each fragment deserve separate joint consideration, and all fragments of the selected set form a nesting hierarchy. Visual Graph is a visualization system which is constructed at the A.P. Ershov Institute of Informatics Systems to explore complex structured big data through their visual representations based on attributed hierarchical graphs. 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 this paper a formalism of attributed hierarchical graphs with ports and new possibilities of the Visual Graph system for information visualization based on this graph formalism are considered.
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Zhu, Yiheng, Zhenqiu Ouyang, Ben Liao, et al. "MolHF: A Hierarchical Normalizing Flow for Molecular Graph Generation." In Thirty-Second International Joint Conference on Artificial Intelligence {IJCAI-23}. International Joint Conferences on Artificial Intelligence Organization, 2023. http://dx.doi.org/10.24963/ijcai.2023/556.

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Molecular de novo design is a critical yet challenging task in scientific fields, aiming to design novel molecular structures with desired property profiles. Significant progress has been made by resorting to generative models for graphs. However, limited attention is paid to hierarchical generative models, which can exploit the inherent hierarchical structure (with rich semantic information) of the molecular graphs and generate complex molecules of larger size that we shall demonstrate to be difficult for most existing models. The primary challenge to hierarchical generation is the non-differentiable issue caused by the generation of intermediate discrete coarsened graph structures. To sidestep this issue, we cast the tricky hierarchical generation problem over discrete spaces as the reverse process of hierarchical representation learning and propose MolHF, a new hierarchical flow-based model that generates molecular graphs in a coarse-to-fine manner. Specifically, MolHF first generates bonds through a multi-scale architecture, then generates atoms based on the coarsened graph structure at each scale. We demonstrate that MolHF achieves state-of-the-art performance in random generation and property optimization, implying its high capacity to model data distribution. Furthermore, MolHF is the first flow-based model that can be applied to model larger molecules (polymer) with more than 100 heavy atoms. The code and models are available at https://github.com/violet-sto/MolHF.
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Hajiaghayi, Mohammadtaghi, Theodore Johnson, Mohammad Reza Khani, and Barna Saha. "Hierarchical graph partitioning." In SPAA '14: 26th ACM Symposium on Parallelism in Algorithms and Architectures. ACM, 2014. http://dx.doi.org/10.1145/2612669.2612699.

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Reports on the topic "Hierarchical graph"

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Mathuria, Aakanksha. Approximate Pattern Matching using Hierarchical Graph Construction and Sparse Distributed Representation. Portland State University Library, 2000. http://dx.doi.org/10.15760/etd.7453.

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Sondheim, M., and C. Hodgson. Common hydrology features (CHyF) logical model. Natural Resources Canada/CMSS/Information Management, 2024. http://dx.doi.org/10.4095/328952.

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The Open Geospatial Consortium has defined "OGC WaterML 2: Part 3 - Surface Hydrology Features (HY_Features) - Conceptual Model", but not any particular implementation of it. The Common Hydrology Features (CHyF) model extends HY_Features and makes some minor changes to it required for implementation and the delivery of high performance services. HY_Features discusses catchment coverage and topological relations. In CHyF these are key ideas, as is the notion that hydrologically defined network components form elements of a mathematical graph, allowing for very fast network traversal. HY_Features defines catchments and catchment networks, as well as rivers, channels, flowpaths and hydrographic networks. The CHyF logical model specifies a profile and some extensions to HY_Features, as required to implement topological and graph relations. This starts with the definition of elementary catchments and elementary flowpaths, which are treated as fundamental elements. They are tightly specified terms corresponding to basic catchments and flowpaths in HY_Features and the basic components in the standard reach-catchment model (Maidment and Clark, 2016). If they are subdivided, the result is simply more elementary catchments and elementary flowpaths. Consequently, they are the building blocks used to form complementary coverages as well as a graph structure referred to as a hygraph. Building the hygraph necessitates that connections between features be manifest through their geometry. Divergences and distributaries are supported in CHyF, as the hygraph need not be hierarchical. Nevertheless, CHyF does recognize hierarchical drainage basins and the value in identifying them explicitly (Blodgett, et al, 2021). Different kinds of elementary catchments and elementary flowpaths are defined in CHyF. Of note is that polygonal waterbody features, or portions of such features, are treated as elementary catchments in their own right. In addition to these water catchments, several kinds of land-based elementary catchments are recognized. These model constructs are compatible with the higher level conceptual model in HY_Features, although they differ in detail from other popular implementation models. With the approach taken it becomes practical to handle very large lakes and rivers, as well as coastal ocean zones. CHyF also includes wetlands, glaciers and snowfields as kinds of hydro features; these features help complete the concept of a catchment coverage as put forward by HY_Features.
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Tripakis, Stavros, Dai Bui, Bert Rodiers, and Edward A. Lee. Compositionality in Synchronous Data Flow: Modular Code Generation from Hierarchical SDF Graphs. Defense Technical Information Center, 2009. http://dx.doi.org/10.21236/ada538756.

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