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  • 1
    Book chapter
    Book chapter
    Berlin, Heidelberg: Springer Berlin Heidelberg
    Language: English
    In: Lecture Notes in Computer Science, Graph Drawing: 14th International Symposium, GD 2006, Karlsruhe, Germany, September 18-20, 2006. Revised Papers, pp.240-251
    Description: The need to visualize large and complex networks has strongly increased in the last decade. Although networks with more than 1000 vertices seem to be prohibitive for a comprehensive layout, real-world networks exhibit a very inhomogenous edge density that can be harnessed to derive an aesthetic and structured layout. Here, we will present a heuristic that finds a spanning tree with a very low average spanner property for the non-tree edges, the so-called backbone of a network. This backbone can then be used to apply a modified tree-layout algorithm to draw the whole graph in a way that highlights dense parts of the graph, so-called clusters, and their inter-connections.
    Keywords: Computer Science ; Discrete Mathematics in Computer Science ; Algorithm Analysis and Problem Complexity ; Computer Graphics ; Data Structures ; Engineering ; Computer Science
    ISBN: 9783540709039
    ISBN: 3540709037
    Source: SpringerLink Books
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  • 2
    Book chapter
    Book chapter
    Berlin, Heidelberg: Springer Berlin Heidelberg
    Language: English
    In: Lecture Notes in Computer Science, Peer-to-Peer Systems and Applications, pp.57-76
    Description: 6.1 Introduction 6.2 Definitions 6.3 The Riddle – Analysis of Real Networks 6.4 Families and Models 6.4.1 Random Graphs 6.4.2 Small-Worlds – The Riddle’s First Solution 6.4.3 Scale-Free Networks: How the Rich Get Richer 6.5 Applications to Peer-to-Peer Systems 6.5.1 Navigating in Small-Worlds 6.5.2 Small-World Overlay Networks in P2P Systems 6.5.3 Scale-Free Overlay Networks in P2P Systems 6.6 Summary
    Keywords: Computer Science ; Computer Communication Networks ; Information Systems Applications (Incl.Internet) ; Information Storage and Retrieval ; Algorithm Analysis and Problem Complexity ; Software Engineering ; Engineering ; Computer Science
    ISBN: 9783540291923
    ISBN: 354029192X
    Source: SpringerLink Books
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  • 3
    Language: English
    In: Lecture Notes in Computer Science, Network Analysis: Methodological Foundations, pp.16-61
    Description: 3.1. Introductory Examples 3.2. A Loose Definition 3.3. Distances and Neighborhoods 3.3.1. Degree 3.3.2. Facility Location Problems 3.3.3. Structural Properties 3.4. Shortest Paths 3.4.1. Stress Centrality 3.4.2. Shortest-Path Betweenness Centrality 3.4.3. Reach 3.4.4. Traversal Sets 3.5. Derived Edge Centralities 3.5.1. Edge Centralities Derived from Vertex Centralities 3.6. Vitality 3.6.1. Flow Betweenness Vitality 3.6.2. Closeness Vitality 3.6.3. Shortcut Values as a Vitality-Like Index 3.6.4. Stress Centrality as a Vitality-Like Index 3.7. Current Flow 3.7.1. Electrical Networks 3.7.2. Current-Flow Betweenness Centrality 3.7.3. Current-Flow Closeness Centrality 3.8. Random Processes 3.8.1. Random Walks and Degree Centrality 3.8.2. Random-Walk Betweenness Centrality 3.8.3. Random-Walk Closeness Centrality 3.9. Feedback 3.9.1. Counting All Paths – The Status Index of Katz 3.9.2. General Feedback Centralities 3.9.3. Web Centralities 3.10. Dealing with Insufficient Connectivity 3.10.1. Intuitive Approaches 3.10.2. Cumulative Nominations 3.11. Graph- vs. Vertex-Level Indices 3.12. Chapter Notes
    Keywords: Computer Science ; Discrete Mathematics in Computer Science ; Computer Communication Networks ; Data Structures ; Algorithm Analysis and Problem Complexity ; Algorithms ; Communications Engineering, Networks ; Engineering ; Computer Science
    ISBN: 9783540249795
    ISBN: 3540249796
    Source: SpringerLink Books
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  • 4
    Book chapter
    Book chapter
    Berlin, Heidelberg: Springer Berlin Heidelberg
    Language: English
    In: Lecture Notes in Computer Science, Network Analysis: Methodological Foundations, pp.62-82
    Description: 4.1. Basic Algorithms 4.1.1. Shortest Paths 4.1.2. Shortest Paths Between All Vertex Pairs 4.1.3. Dynamic All-Pairs Shortest Paths 4.1.4. Maximum Flows and Minimum-Cost Flows 4.1.5. Computing the Largest Eigenvector 4.2. Centrality-Specific Algorithms 4.2.1. Betweenness Centrality 4.2.2. Shortcut Values 4.3. Fast Approximation 4.3.1. Approximation of Centralities Based on All Pairs Shortest Paths Computations 4.3.2. Approximation of Web Centralities 4.4. Dynamic Computation 4.4.1. Continuously Updated Approximations of PageRank 4.4.2. Dynamically Updating PageRank
    Keywords: Computer Science ; Discrete Mathematics in Computer Science ; Computer Communication Networks ; Data Structures ; Algorithm Analysis and Problem Complexity ; Algorithms ; Communications Engineering, Networks ; Engineering ; Computer Science
    ISBN: 9783540249795
    ISBN: 3540249796
    Source: SpringerLink Books
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  • 5
    Book chapter
    Book chapter
    Berlin, Heidelberg: Springer Berlin Heidelberg
    Language: English
    In: Lecture Notes in Computer Science, Network Analysis: Methodological Foundations, pp.83-111
    Description: 5.1. Normalization 5.1.1. Comparing Elements of a Graph 5.1.2. Comparing Elements of Different Graphs 5.2. Personalization 5.2.1. Personalization for Distance and Shortest Paths Based Centralities 5.2.2. Personalization for Web Centralities 5.3. Four Dimensions of a Centrality Index 5.4. Axiomatization 5.4.1. Axiomatization for Distance-Based Vertex Centralities 5.4.2. Axiomatization for Feedback-Centralities 5.5. Stability and Sensitivity 5.5.1. Stability of Distance-Based Centralities 5.5.2. Stability and Sensitivity of Web-Centralities
    Keywords: Computer Science ; Discrete Mathematics in Computer Science ; Computer Communication Networks ; Data Structures ; Algorithm Analysis and Problem Complexity ; Algorithms ; Communications Engineering, Networks ; Engineering ; Computer Science
    ISBN: 9783540249795
    ISBN: 3540249796
    Source: SpringerLink Books
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