Topic
Book embedding
About: Book embedding is a research topic. Over the lifetime, 1977 publications have been published within this topic receiving 52030 citations.
Papers published on a yearly basis
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Papers
Book•
30 Dec 1998TL;DR: In this article, the authors present a model for drawing graphs and digraphs based on the topology of low dimensions Higher-Order Surfaces and a model of a graph.
Abstract: INTRODUCTION TO GRAPH MODELS Graphs and Digraphs Common Families of Graphs Graph Modeling Applications Walks and Distance Paths, Cycles, and Trees Vertex and Edge Attributes: More Applications STRUCTURE AND REPRESENTATION Graph Isomorphism Revised! Automorphisms and Symmetry Moved and revised! Subgraphs Some Graph Operations Tests for Non-Isomorphism Matrix Representation More Graph Operations TREES Reorganized and revised! Characterizations and Properties of Trees Rooted Trees, Ordered Trees, and Binary Trees Binary-Tree Traversals Binary-Search Trees Huffman Trees and Optimal Prefix Codes Priority Trees Counting Labeled Trees: Prufer Encoding Counting Binary Trees: Catalan Recursion SPANNING TREES Reorganized and revised! Tree-Growing Depth-First and Breadth-First Search Minimum Spanning Trees and Shortest Paths Applications of Depth-First Search Cycles, Edge Cuts, and Spanning Trees Graphs and Vector Spaces Matroids and the Greedy Algorithm CONNECTIVITY Revised! Vertex- and Edge-Connectivity Constructing Reliable Networks Max-Min Duality and Menger's Theorems Block Decompositions OPTIMAL GRAPH TRAVERSALS Eulerian Trails and Tours DeBruijn Sequences and Postman Problems Hamiltonian Paths and Cycles Gray Codes and Traveling Salesman Problems PLANARITY AND KURATOWSKI'S THEOREM Reorganized and revised! Planar Drawings and Some Basic Surfaces Subdivision and Homeomorphism Extending Planar Drawings Kuratowski's Theorem Algebraic Tests for Planarity Planarity Algorithm Crossing Numbers and Thickness DRAWING GRAPHS AND MAPS Reorganized and revised! The Topology of Low Dimensions Higher-Order Surfaces Mathematical Model for Drawing Graphs Regular Maps on a Sphere Imbeddings on Higher-Order Surfaces Geometric Drawings of Graphs New! GRAPH COLORINGS Vertex-Colorings Map-Colorings Edge-Colorings Factorization New! MEASUREMENT AND MAPPINGS New Chapter! Distance in Graphs New! Domination in Graphs New! Bandwidth New! Intersection Graphs New! Linear Graph Mappings Moved and revised! Modeling Network Emulation Moved and revised! ANALYTIC GRAPH THEORY New Chapter! Ramsey Graph Theory New! Extremal Graph Theory New! Random Graphs New! SPECIAL DIGRAPH MODELS Reorganized and revised! Directed Paths and Mutual Reachability Digraphs as Models for Relations Tournaments Project Scheduling and Critical Paths Finding the Strong Components of a Digraph NETWORK FLOWS AND APPLICATIONS Flows and Cuts in Networks Solving the Maximum-Flow Problem Flows and Connectivity Matchings, Transversals, and Vertex Covers GRAPHICAL ENUMERATION Reorganized and revised! Automorphisms of Simple Graphs Graph Colorings and Symmetry Burnside's Lemma Cycle-Index Polynomial of a Permutation Group More Counting, Including Simple Graphs Polya-Burnside Enumeration ALGEBRAIC SPECIFICATION OF GRAPHS Cyclic Voltages Cayley Graphs and Regular Voltages Permutation Voltages Symmetric Graphs and Parallel Architectures Interconnection-Network Performance NON-PLANAR LAYOUTS Reorganized and revised! Representing Imbeddings by Rotations Genus Distribution of a Graph Voltage-Graph Specification of Graph Layouts Non KVL Imbedded Voltage Graphs Heawood Map-Coloring Problem APPENDIX Logic Fundamentals Relations and Functions Some Basic Combinatorics Algebraic Structures Algorithmic Complexity Supplementary Reading BIBLIOGRAPHY General Reading References SOLUTIONS AND HINTS New! INDEXES Index of Applications Index of Algorithms Index of Notations General Index
1,746 citations
13 Aug 2016
TL;DR: A novel graph embedding algorithm, High-Order Proximity preserved Embedding (HOPE for short), is developed, which is scalable to preserve high-order proximities of large scale graphs and capable of capturing the asymmetric transitivity.
Abstract: Graph embedding algorithms embed a graph into a vector space where the structure and the inherent properties of the graph are preserved The existing graph embedding methods cannot preserve the asymmetric transitivity well, which is a critical property of directed graphs Asymmetric transitivity depicts the correlation among directed edges, that is, if there is a directed path from u to v, then there is likely a directed edge from u to v Asymmetric transitivity can help in capturing structures of graphs and recovering from partially observed graphs To tackle this challenge, we propose the idea of preserving asymmetric transitivity by approximating high-order proximity which are based on asymmetric transitivity In particular, we develop a novel graph embedding algorithm, High-Order Proximity preserved Embedding (HOPE for short), which is scalable to preserve high-order proximities of large scale graphs and capable of capturing the asymmetric transitivity More specifically, we first derive a general formulation that cover multiple popular high-order proximity measurements, then propose a scalable embedding algorithm to approximate the high-order proximity measurements based on their general formulation Moreover, we provide a theoretical upper bound on the RMSE (Root Mean Squared Error) of the approximation Our empirical experiments on a synthetic dataset and three real-world datasets demonstrate that HOPE can approximate the high-order proximities significantly better than the state-of-art algorithms and outperform the state-of-art algorithms in tasks of reconstruction, link prediction and vertex recommendation
1,573 citations
TL;DR: Efficient algorithms for embedding graphs low-dimensionally with a small distortion, and a new deterministic polynomial-time algorithm that finds a (nearly tight) cut meeting this bound.
Abstract: In this paper we explore some implications of viewing graphs asgeometric objects. This approach offers a new perspective on a number of graph-theoretic and algorithmic problems. There are several ways to model graphs geometrically and our main concern here is with geometric representations that respect themetric of the (possibly weighted) graph. Given a graphG we map its vertices to a normed space in an attempt to (i) keep down the dimension of the host space, and (ii) guarantee a smalldistortion, i.e., make sure that distances between vertices inG closely match the distances between their geometric images. In this paper we develop efficient algorithms for embedding graphs low-dimensionally with a small distortion. Further algorithmic applications include:
Given faithful low-dimensional representations of statistical data, it is possible to obtain meaningful and efficientclustering. This is one of the most basic tasks in pattern-recognition. For the (mostly heuristic) methods used in the practice of pattern-recognition, see [20], especially chapter 6. Our studies of multicommodity flows also imply that every embedding of (the metric of) ann-vertex, constant-degree expander into a Euclidean space (of any dimension) has distortion Ω(logn). This result is tight, and closes a gap left open by Bourgain [12].
1,212 citations
Book•
1 Jan 1985
TL;DR: In this paper, the authors introduce graphs and algorithmic complexity, including Spanning-tree, branchings and connectivity, and planar graphs, and graph problems and intractability.
Abstract: Preface 1 Introducing graphs and algorithmic complexity 2 Spanning-trees, branchings and connectivity 3 Planar graphs 4 Networks and flows 5 Matchings 6 Eulerian and Hamiltonian tours 7 Colouring graphs 8 Graph problems and intractability Appendix Author Index Subject Index
1,090 citations
1 Jan 1990
TL;DR: It is shown that each plane graph of order n 2 3 has a straight line embedding on the n-2 by n-1 grid that is computable in time O(n), and a nice feature of the vertex-coordinates is that they have a purely combinatorial meaning.
Abstract: We show that each plane graph of order n 2 3 has a straight line embedding on the n-2 by n-2 grid. This embedding is computable in time O(n). A nice feature of the vertex-coordinates is that they have a purely combinatorial meaning.
822 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 1 |
| 2024 | 5 |
| 2023 | 29 |
| 2022 | 35 |
| 2021 | 15 |
| 2020 | 21 |