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Academic literature on the topic 'Hierarchical graphs'

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Published: 4 June 2021
Last updated: 27 April 2022

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Journal articles on the topic "Hierarchical graphs"

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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 (June 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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BUSATTO, GIORGIO, HANS-JÖRG KREOWSKI, and SABINE KUSKE. "Abstract hierarchical graph transformation." Mathematical Structures in Computer Science 15, no. 4 (July 15, 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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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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Faran, Rachel, and Orna Kupferman. "A Parametrized Analysis of Algorithms on Hierarchical Graphs." International Journal of Foundations of Computer Science 30, no. 06n07 (September 2019): 979–1003. http://dx.doi.org/10.1142/s0129054119400252.

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Hierarchical graphs are used in order to describe systems with a sequential composition of sub-systems. A hierarchical graph consists of a vector of subgraphs. Vertices in a subgraph may “call” other subgraphs. The reuse of subgraphs, possibly in a nested way, causes hierarchical graphs to be exponentially more succinct than equivalent flat graphs. Early research on hierarchical graphs and the computational price of their succinctness suggests that there is no strong correlation between the complexity of problems when applied to flat graphs and their complexity in the hierarchical setting. That is, the complexity in the hierarchical setting is higher, but all “jumps” in complexity up to an exponential one are exhibited, including no jumps in some problems. We continue the study of the complexity of algorithms for hierarchical graphs, with the following contributions: (1) In many applications, the subgraphs have a small, often a constant, number of exit vertices, namely vertices from which control returns to the calling subgraph. We offer a parameterized analysis of the complexity and point to problems where the complexity becomes lower when the number of exit vertices is bounded by a constant. (2) We describe a general methodology for algorithms on hierarchical graphs. The methodology is based on an iterative compression of subgraphs in a way that maintains the solution to the problems and results in subgraphs whose size depends only on the number of exit vertices, and (3) we handle labeled hierarchical graphs, where edges are labeled by letters from some alphabet, and the problems refer to the languages of the graphs.
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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 (January 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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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 (September 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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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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WANG, XIAOQIAN, HUILING XU, and CHANGBING MA. "CONSENSUS PROBLEMS IN WEIGHTED HIERARCHICAL GRAPHS." Fractals 27, no. 06 (September 2019): 1950086. http://dx.doi.org/10.1142/s0218348x19500865.

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We present the hierarchical graph for the growth of weighted networks in which the structural growth is coupled with the edges’ weight dynamical evolution. We investigate consensus problems of the graph from weighted Laplacian spectra perspective, focusing on three important quantities of consensus problems, convergence speed, delay robustness, and first-order coherence, which are determined by the second smallest eigenvalue, largest eigenvalue, and sum of reciprocals of each nonzero eigenvalue of weighted Laplacian matrix, respectively. Unlike previous enquiries, we want to emphasize the importance of weight factor in the study of coherence problems. In what follows, we attempt to study that the weighted Laplacian eigenvalues of the weighted hierarchical graphs, which are determined through analytic recursive equations. We find in our study that the value of convergence speed and delay robustness in weighted hierarchical graphs increases as weight factor increases and the value of first-order coherence decreases as weight factor increases. Moreover, as is expected, weight factor affects the performance of consensus behavior and can be regarded as a leverage in the problem of consensus problems. This paper puts forward the proposal and the countermeasure for stability optimization of networks from the perspective of weight factor for future researchers.
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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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Krinkin, Kirill, Alexander Ivanovich Vodyaho, Igor Kulikov, and Nataly Zhukova. "Deductive Synthesis of Networks Hierarchical Knowledge Graphs." International Journal of Embedded and Real-Time Communication Systems 12, no. 3 (July 2021): 32–48. http://dx.doi.org/10.4018/ijertcs.2021070103.

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The article focuses on developing of a deductive synthesis method for building telecommunications networks (TN) hierarchical knowledge graphs (KG). Synthesized KGs can be used to solve search, analytical, and recommendation (forecast) problems. TNs are complex heterogeneous objects. The synthesis of knowledge graphs of such objects requires much computational resources. The proposed method provides a low complexity of the synthesis of KG of TN by taking into account their hierarchical structure. The authors propose to do synthesis by direct downward multilevel inference and reverse multilevel inference. The article analyses existing graph models of TNs and methods for their building. Detailed description of the proposed method of networks hierarchical KGs synthesis is given. In order to evaluate the deductive synthesis method, a prototype of the system is developed. The provided real-world example shows how telecommunications networks hierarchical knowledge graphs are synthesized and used in practice. Finally, conclusions are formulated, and the areas of further research are identified.
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Dissertations / Theses on the topic "Hierarchical graphs"

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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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Dorrian, Henry Joseph. "Hierarchical graphs and oscillator dynamics." Thesis, Manchester Metropolitan University, 2015. http://e-space.mmu.ac.uk/580120/.

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In many types of network, the relationship between structure and function is of great significance. This work is particularly concerned with community structures, which arise in a wide variety of domains. A simple oscillator model is applied to networks with community structures and shows that waves of regular oscillation are caused by synchronised clusters of nodes. Moreover, we demonstrate that such global oscillations may arise as a direct result of network topology. We also observe that additional modes of oscillation (as detected through frequency analysis) occur in networks with additional levels of hierarchy and that such modes may be directly related to network structure. This method is applied in two specific domains (metabolic networks and metropolitan transport), demonstrating the robustness of the results when applied to real world systems. A topological analysis is also applied to the real world networks of metabolism and metropolitan transport using standard graphical measures. This yields a new artificial network growth model, which agrees closely with the graphical measures taken on metabolic pathway networks. This new model demonstrates a simple mechanism to produce the particular features found in these networks. We conclude that (where the distribution of oscillator frequencies and the interactions between them are known to be unimodal) the observations may be applicable to the detection of underlying community structure in networks, shedding further light on the general relationship between structure and function in complex systems.
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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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Puch-Solis, Roberto O. "Hierarchical junction trees." Thesis, University of Warwick, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.365243.

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Reynolds, Jason. "A hierarchical layout algorithm for drawing directed graphs." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp04/mq20694.pdf.

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Wallgrün, Jan Oliver. "Hierarchical Voronoi graphs spatial representation and reasoning for mobile robots." Berlin Heidelberg Springer, 2008. http://d-nb.info/99728210X/04.

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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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Santana, Maia Deise. "A study of hierarchical watersheds on graphs with applications to image segmentation." Thesis, Paris Est, 2019. http://www.theses.fr/2019PESC2069.

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La littérature abondante sur la théorie des graphes invite de nombreux problèmes à être modélisés dans ce cadre. En particulier, les algorithmes de regroupement et de segmentation conçus dans ce cadre peuvent être utilisés pour résoudre des problèmes dans de nombreux domaines tels que l'analyse d'image qui est le principal domaine d'application de cette thèse. Dans ce travail, nous nous concentrons sur un outil de segmentation semi-supervisé largement étudié dans la morphologie mathématique et appliqué à l'analyse d'image, notamment les Ligne de Partage des Eaux (LPE). Nous étudions la notion de hiérarchie de LPE, qui est une extension multi-échelle de la notion de LPE permettant de décrire une image ou, plus généralement, un ensemble de donnés par des partitions à plusieurs niveaux de détail. Les contributions principales de cette étude sont les suivantes : - Reconnaissance de hiérarchies de LPE : nous proposons une caractérisation des hiérarchies de LPE qui mène à un algorithme efficace pour déterminer si une hiérarchie est une hiérarchie de LPE d'un graphe donné. - Opérateur watersheding : nous présentons l'opérateur watersheding, qui, étant donné un graphe pondéré, associe n'importe quelle hiérarchie à une hiérarchie de LPE de ce graphe. Nous montrons que cet opérateur est idempotent et que ses points fixes sont les hiérarchies de LPE. Nous proposons également un algorithme efficace pour calculer le résultat de cet opérateur. - Probabilité de hiérarchies de LPE : nous proposons et étudions une notion de probabilité d'une hiérarchie de LPE, et nous concevons un algorithme pour calculer la probabilité d'une hiérarchie de LPE. De plus, nous présentons des algorithmes pour calculer des hiérarchies de LPE de probabilité minimale et maximale pour un graphe pondéré donné. - Combinaison de hiérarchies : nous étudions une famille d'opérateurs pour combiner des hiérarchies de partitions et nous étudions les propriétés de ces opérateurs lorsqu'ils sont appliqués à des hiérarchies de LPE. En particulier, nous prouvons que, dans certaines conditions, la famille des hiérarchies de LPE est fermée pour l'opérateur de combinaison. - Évaluation de hiérarchies : nous proposons un cadre d'évaluation de hiérarchies, qui est également utilisé pour évaluer les hiérarchies de LPE et les combinaisons des hiérarchies. En conclusion, cette thèse révise des propriétés existantes et des nouvelles propriétés liées aux hiérarchies de LPE, montrant la richesse théorique de ce cadre et fournissant une vue d'ensemble des ses applications dans l'analyse d'image et dans la vision par ordinateur et, plus généralement, dans le traitement de donnés et dans l'apprentissage automatique
The wide literature on graph theory invites numerous problems to be modeled in the framework of graphs. In particular, clustering and segmentation algorithms designed this framework can be applied to solve problems in various domains, including image processing, which is the main field of application investigated in this thesis. In this work, we focus on a semi-supervised segmentation tool widely studied in mathematical morphology and used in image analysis applications, namely the watershed transform. We explore the notion of a hierarchical watershed, which is a multiscale extension of the notion of watershed allowing to describe an image or, more generally, a dataset with partitions at several detail levels. The main contributions of this study are the following : - Recognition of hierarchical watersheds : we propose a characterization of hierarchical watersheds which leads to an efficient algorithm to determine if a hierarchy is a hierarchical watershed of a given edge-weighted graph. - Watersheding operator : we introduce the watersheding operator, which, given an edge-weighted graph, maps any hierarchy of partitions into a hierarchical watershed of this edge-weighted graph. We show that this operator is idempotent and its fixed points are the hierarchical watersheds. We also propose an efficient algorithm to compute the result of this operator. - Probability of hierarchical watersheds : we propose and study a notion of probability of hierarchical watersheds, and we design an algorithm to compute the probability of a hierarchical watershed. Furthermore, we present algorithms to compute the hierarchical watersheds of maximal and minimal probabilities of a given weighted graph. - Combination of hierarchies : we investigate a family of operators to combine hierarchies of partitions and study the properties of these operators when applied to hierarchical watersheds. In particular, we prove that, under certain conditions, the family of hierarchical watersheds is closed for the combination operator. - Evaluation of hierarchies : we propose an evaluation framework of hierarchies, which is further used to assess hierarchical watersheds and combinations of hierarchies. In conclusion, this thesis reviews existing and introduces new properties and algorithms related to hierarchical watersheds, showing the theoretical richness of this framework and providing insightful view for its applications in image analysis and computer vision and, more generally, for data processing and machine learning
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Charpentier, Bertrand. "Multi-scale clustering in graphs using modularity." Thesis, KTH, Skolan för elektroteknik och datavetenskap (EECS), 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-244847.

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This thesis provides a new hierarchical clustering algorithm for graphs, named Paris, which can be interpreted through the modularity score and its resolution parameter. The algorithm is agglomerative and based on a simple distance between clusters induced by the probability of sampling node pairs. It tries to approximate the optimal partitions with respect to the modularity score at any resolution in one run. In addition to the Paris hierarchical algorithm, this thesis proposes four algorithms that compute rankings of the sharpest clusters, clusterings and resolutions by processing the hierarchy output by Paris. These algorithms are based on a new measure of stability for clusterings, named sharp-score. Key outcomes of these four algorithms are the possibility to rank clusters, detect sharpest clusterings scale, go beyond the resolution limit and detect relevant resolutions. All these algorithms have been tested on both synthetic and real datasets to illustrate the efficiency of their approaches.
Denna avhandling ger en ny hierarkisk klusteralgoritm för grafer, som heter Paris, vilket kan tolkas av modularitetsresultatet och dess upplösningsparameter. Algoritmen är agglomerativ och är baserad på ett enda avstånd mellan kluster som induceras av sannolikheten för sampling av nodpar. Det försöker att approximera de optimala partitionerna vid vilken upplösning som helst i en körning. Förutom en hierarkisk algoritm föreslår denna avhandling fyra algoritmer som beräknar rankningar av de bästa grupperna, kluster och resolutioner genom att bearbeta hierarkiproduktionen i Paris. Dessa algoritmer bygger på ett nytt koncept av klusterstabilitet, kallad sharpscore. Viktiga resultat av dessa fyra algoritmer är förmågan att rangordna kluster, upptäcka bästa klusterskala, gå utöver upplösningsgränsen och upptäcka de mest relevanta resolutionerna. Alla dessa algoritmer har testats på både syntetiska och verkliga datamängder för att illustrera effektiviteten i deras metoder.
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Books on the topic "Hierarchical graphs"

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Wallgrün, Jan Oliver. Hierarchical Voronoi Graphs. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-10345-2.

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Mikov, Aleksandr. Generalized graphs and grammars. ru: 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: Spatial representation and reasoning for mobile robots. Heidelberg: Springer, 2010.

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Computer Systems Laboratory (U.S.), ed. Programmer's Hierarchical Interactive Graphics System (PHIGS). Gaithersburg, MD: U.S. Dept. of Commerce, Technology Administration, National Institute of Standards and Technology, Computer Systems Laboratory, 1995.

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Bos, Jan van den, 1939-, ed. 3D interactive computer graphics: The hierarchical modelling system HIRASP. New York: Ellis Horwood, 1990.

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

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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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Programmer's Hierarchical Interactive Graphics System by Example. Springer Verlag, 1991.

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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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Farin, Gerald, Bernd Hamann, and Hans Hagen. Hierarchical and Geometrical Methods in Scientific Visualization. Springer, 2011.

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Book chapters on the topic "Hierarchical graphs"

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Wallgrün, Jan Oliver. "Introduction." In Hierarchical Voronoi Graphs, 1–9. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-10345-2_1.

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Wallgrün, Jan Oliver. "Robot Mapping." In Hierarchical Voronoi Graphs, 11–43. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-10345-2_2.

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Wallgrün, Jan Oliver. "Voronoi-Based Spatial Representations." In Hierarchical Voronoi Graphs, 45–58. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-10345-2_3.

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Wallgrün, Jan Oliver. "Simplification and Hierarchical Voronoi Graph Construction." In Hierarchical Voronoi Graphs, 59–84. Berlin, Heidelberg: 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, 85–111. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-10345-2_5.

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Wallgrün, Jan Oliver. "Global Mapping: Minimal Route Graphs Under Spatial Constraints." In Hierarchical Voronoi Graphs, 113–46. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-10345-2_6.

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Wallgrün, Jan Oliver. "Experimental Evaluation." In Hierarchical Voronoi Graphs, 147–76. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-10345-2_7.

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Wallgrün, Jan Oliver. "Conclusions and Outlook." In Hierarchical Voronoi Graphs, 177–86. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-10345-2_8.

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Palomo, E. J., J. M. Ortiz-de-Lazcano-Lobato, Domingo López-Rodríguez, and R. M. Luque. "Hierarchical Graphs for Data Clustering." In Lecture Notes in Computer Science, 432–39. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02478-8_54.

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Fernández-Baca, David, and Mark A. Williams. "On matroids and hierarchical graphs." In SWAT 90, 320–31. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/3-540-52846-6_101.

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Conference papers on the topic "Hierarchical graphs"

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Li, Chong, Kunyang Jia, Dan Shen, C. J. Richard Shi, and Hongxia Yang. "Hierarchical Representation Learning for Bipartite Graphs." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. California: International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/398.

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Recommender systems on E-Commerce platforms track users' online behaviors and recommend relevant items according to each user’s interests and needs. Bipartite graphs that capture both user/item feature and use-item interactions have been demonstrated to be highly effective for this purpose. Recently, graph neural network (GNN) has been successfully applied in representation of bipartite graphs in industrial recommender systems. Providing individualized recommendation on a dynamic platform with billions of users is extremely challenging. A key observation is that the users of an online E-Commerce platform can be naturally clustered into a set of communities. We propose to cluster the users into a set of communities and make recommendations based on the information of the users in the community collectively. More specifically, embeddings are assigned to the communities and the user embedding is decomposed into two parts, each of which captures the community-level generalizations and individualized preferences respectively. The community embedding can be considered as an enhancement to the GNN methods that are inherently flat and do not learn hierarchical representations of graphs. The performance of the proposed algorithm is demonstrated on a public dataset and a world-leading E-Commerce company dataset.
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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}. California: 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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Ismaeel, Alaa A. K., Pradyumn Kumar Shukla, and Hartmut Schmeck. "Dynamic Drawing of Hierarchical Graphs." In Annual International Conference on Computational Mathematics, Computational Geometry & Statistics. Global Science and Technology Forum (GSTF), 2012. http://dx.doi.org/10.5176/2251-1911_cmcgs52.

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Zhang, Ying, Lu Qin, Fan Zhang, and Wenjie Zhang. "Hierarchical Decomposition of Big Graphs." In 2019 IEEE 35th International Conference on Data Engineering (ICDE). IEEE, 2019. http://dx.doi.org/10.1109/icde.2019.00240.

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Pandey, Prashant, Brian Wheatman, Helen Xu, and Aydin Buluc. "Terrace: A Hierarchical Graph Container for Skewed Dynamic Graphs." In SIGMOD/PODS '21: International Conference on Management of Data. New York, NY, USA: ACM, 2021. http://dx.doi.org/10.1145/3448016.3457313.

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Leon, Leissi M. Castañeda, Krzysztof Chris Ciesielski, and Paulo A. Vechiatto Miranda. "An Efficient Hierarchical Layered Graph Approach for Multi-Region Segmentation." In XXXII Conference on Graphics, Patterns and Images. Sociedade Brasileira de Computação - SBC, 2019. http://dx.doi.org/10.5753/sibgrapi.est.2019.8301.

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We proposed a novel efficient seed-based method for the multiple region segmentation of images based on graphs, named Hierarchical Layered Oriented Image Foresting Transform (HLOIFT). It uses a tree of the relations between the image objects, represented by a node. Each tree node may contain different individual high-level priors and defines a weighted digraph, named as layer. The layer graphs are then integrated into a hierarchical graph, considering the hierarchical relations of inclusion and exclusion. A single energy optimization is performed in the hierarchical layered weighted digraph leading to globally optimal results satisfying all the high-level priors. The experimental evaluations of HLOIFT and its extensions, on medical, natural and synthetic images, indicate promising results comparable to the state-of-the-art methods, but with lower computational complexity. Compared to hierarchical segmentation by the min-cut/max-flow algorithm, our approach is less restrictive, leading to globally optimal results in more general scenarios, and has a better running time.
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Wang, Bin, Teruaki Hayashi, and Yukio Ohsawa. "Hierarchical Graph Convolutional Network for Data Evaluation of Dynamic Graphs." In 2020 IEEE International Conference on Big Data (Big Data). IEEE, 2020. http://dx.doi.org/10.1109/bigdata50022.2020.9377789.

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Chua, Freddy Chong Tat, and Ee-Peng Lim. "Modeling Bipartite Graphs Using Hierarchical Structures." In 2011 International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2011). IEEE, 2011. http://dx.doi.org/10.1109/asonam.2011.45.

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Gordeev, Dmitrii Stanislavovich. "Visualization and debugging on internal representation graph of Cloud-Sisal programs." In 31th International Conference on Computer Graphics and Vision. Keldysh Institute of Applied Mathematics, 2021. http://dx.doi.org/10.20948/graphicon-2021-1-54-62.

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This paper describes the solution of the tasks of visualizing the graphs of the internal representation of Cloud Sisal programs, visualizing the process of computing and debugging Cloud Sisal programs. The formal definitions of the graph with ports and the graph model with ports and attributes are shown. A model of the visualization of the graph model with ports and attributes is described using static images in the SVG format. A model of displaying changes in the graph model with ports and attributes using animations supported by the SVG vector graphics format is described. The connection of graphic animations displaying changes in visual styles and changes in the attributes of the graph model with ports is implemented using Petri nets. It describes the modeling of calculations corresponding to the functions of a given Cloud Sisal program using the hierarchical Petri nets, where the transitions correspond to the functions, and the places of arguments and the parameters of the corresponding functions. Also described modifications of hierarchical Petri nets, ensuring the functionality of the breakpoints and editing the arguments or the results of functions at activated breakpoints for debugging purposes by adding additional places and transitions. Thus, for the obtained Petri nets, the possibility of changing markup of places in the process of functioning is considered.
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Wang, Hanchen, Defu Lian, Ying Zhang, Lu Qin, and Xuemin Lin. "GoGNN: Graph of Graphs Neural Network for Predicting Structured Entity Interactions." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/183.

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Entity interaction prediction is essential in many important applications such as chemistry, biology, material science, and medical science. The problem becomes quite challenging when each entity is represented by a complex structure, namely structured entity, because two types of graphs are involved: local graphs for structured entities and a global graph to capture the interactions between structured entities. We observe that existing works on structured entity interaction prediction cannot properly exploit the unique graph of graphs model. In this paper, we propose a Graph of Graphs Neural Network, namely GoGNN, which extracts the features in both structured entity graphs and the entity interaction graph in a hierarchical way. We also propose the dual-attention mechanism that enables the model to preserve the neighbor importance in both levels of graphs. Extensive experiments on real-world datasets show that GoGNN outperforms the state-of-the-art methods on two representative structured entity interaction prediction tasks: chemical-chemical interaction prediction and drug-drug interaction prediction. Our code is available at Github.
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Reports on the topic "Hierarchical graphs"

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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. Fort Belvoir, VA: Defense Technical Information Center, October 2009. http://dx.doi.org/10.21236/ada538756.

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

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Wells, Aaron, Tracy Christopherson, Gerald Frost, Matthew Macander, Susan Ives, Robert McNown, and Erin Johnson. Ecological land survey and soils inventory for Katmai National Park and Preserve, 2016–2017. National Park Service, September 2021. http://dx.doi.org/10.36967/nrr-2287466.

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This study was conducted to inventory, classify, and map soils and vegetation within the ecosystems of Katmai National Park and Preserve (KATM) using an ecological land survey (ELS) approach. The ecosystem classes identified in the ELS effort were mapped across the park, using an archive of Geo-graphic Information System (GIS) and Remote Sensing (RS) datasets pertaining to land cover, topography, surficial geology, and glacial history. The description and mapping of the landform-vegetation-soil relationships identified in the ELS work provides tools to support the design and implementation of future field- and RS-based studies, facilitates further analysis and contextualization of existing data, and will help inform natural resource management decisions. We collected information on the geomorphic, topographic, hydrologic, pedologic, and vegetation characteristics of ecosystems using a dataset of 724 field plots, of which 407 were sampled by ABR, Inc.—Environmental Research and Services (ABR) staff in 2016–2017, and 317 were from existing, ancillary datasets. ABR field plots were located along transects that were selected using a gradient-direct sampling scheme (Austin and Heligers 1989) to collect data for the range of ecological conditions present within KATM, and to provide the data needed to interpret ecosystem and soils development. The field plot dataset encompassed all of the major environmental gradients and landscape histories present in KATM. Individual state-factors (e.g., soil pH, slope aspect) and other ecosystem components (e.g., geomorphic unit, vegetation species composition and structure) were measured or categorized using standard classification systems developed for Alaska. We described and analyzed the hierarchical relationships among the ecosystem components to classify 92 Plot Ecotypes (local-scale ecosystems) that best partitioned the variation in soils, vegetation, and disturbance properties observed at the field plots. From the 92 Plot Ecotypes, we developed classifications of Map Ecotypes and Disturbance Landscapes that could be mapped across the park. Additionally, using an existing surficial geology map for KATM, we developed a map of Generalized Soil Texture by aggregating similar surficial geology classes into a reduced set of classes representing the predominant soil textures in each. We then intersected the Ecotype map with the General-ized Soil Texture Map in a GIS and aggregated combinations of Map Ecotypes with similar soils to derive and map Soil Landscapes and Soil Great Groups. The classification of Great Groups captures information on the soil as a whole, as opposed to the subgroup classification which focuses on the properties of specific horizons (Soil Survey Staff 1999). Of the 724 plots included in the Ecotype analysis, sufficient soils data for classifying soil subgroups was available for 467 plots. Soils from 8 orders of soil taxonomy were encountered during the field sampling: Alfisols (<1% of the mapped area), Andisols (3%), Entisols (45%), Gelisols (<1%), Histosols (12%), Inceptisols (22%), Mollisols (<1%), and Spodosols (16%). Within these 8 Soil Orders, field plots corresponded to a total of 74 Soil Subgroups, the most common of which were Typic Cryaquents, Typic Cryorthents, Histic Cryaquepts, Vitrandic Cryorthents, and Typic Cryofluvents.
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Federal Information Processing Standards Publication: programmer's hierarchial interactive graphics sytem (PHIGS). Gaithersburg, MD: National Institute of Standards and Technology, 1995. http://dx.doi.org/10.6028/nist.fips.153-1.

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User's guide for the Programmer's hierarchical interactive graphics system (PHIGS) C binding validation tests (version 2). Gaithersburg, MD: National Institute of Standards and Technology, 1993. http://dx.doi.org/10.6028/nist.ir.5238.

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