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Random Walks and Diffusions on Graphs and Databases

An Introduction

  • Book
  • © 2011

Overview

Authors:
  1. Philippe Blanchard

    1. Fakultät für Physik, Abt. Theoretische Physik, Universität Bielefeld, Bielefeld, Germany

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  2. Dimitri Volchenkov

    1. Fak. Physik, Universität Bielefeld, Bielefeld, Germany

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    You can also search for this author in PubMed   Google Scholar

  • Written by the experts who have contributed to the original development of the field
  • Offers a lecture-based pedagogical approach for a broad audience
  • Includes detailed benchmarking of theory with diverse real-word applications
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Series in Synergetics (SSSYN, volume 10)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Introduction to Permutations, Markov Chains, and Partitions

    • Philippe Blanchard, Dimitri Volchenkov
    Pages 1-17

  3. Worth Another Binary Relation: Graphs

    • Philippe Blanchard, Dimitri Volchenkov
    Pages 19-41

  4. Permutations Sieved Through Adjacency: Graph Automorphisms

    • Philippe Blanchard, Dimitri Volchenkov
    Pages 43-54

  5. Exploring Undirected Graphs by Random Walks

    • Philippe Blanchard, Dimitri Volchenkov
    Pages 55-72

  6. Embedding of Graphs in Probabilistic Euclidean Space

    • Philippe Blanchard, Dimitri Volchenkov
    Pages 73-84

  7. Random Walks and Electric Resistance Networks

    • Philippe Blanchard, Dimitri Volchenkov
    Pages 85-91

  8. Random Walks and Diffusions on Directed Graphs and Interacting Networks

    • Philippe Blanchard, Dimitri Volchenkov
    Pages 93-106

  9. Structural Analysis of Networks and Databases

    • Philippe Blanchard, Dimitri Volchenkov
    Pages 107-170

  10. When Feedbacks Matter: Epidemics, Synchronization, and Self-regulation in Complex Networks

    • Philippe Blanchard, Dimitri Volchenkov
    Pages 171-217

  11. Critical Phenomena on Large Graphs with Regular Subgraphs

    • Philippe Blanchard, Dimitri Volchenkov
    Pages 219-235

  12. Back Matter

    Pages 237-262
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Keywords

About this book

Most networks and databases that humans have to deal with contain large, albeit finite number of units. Their structure, for maintaining functional consistency of the components, is essentially not random and calls for a precise quantitative description of relations between nodes (or data units) and all network components. This book is an introduction, for both graduate students and newcomers to the field, to the theory of graphs and random walks on such graphs. The methods based on random walks and diffusions for exploring the structure of finite connected graphs and databases are reviewed (Markov chain analysis). This provides the necessary basis for consistently discussing a number of applications such diverse as electric resistance networks, estimation of land prices, urban planning, linguistic databases, music, and gene expression regulatory networks.

Authors and Affiliations

  • Fakultät für Physik, Abt. Theoretische Physik, Universität Bielefeld, Bielefeld, Germany

    Philippe Blanchard

  • Fak. Physik, Universität Bielefeld, Bielefeld, Germany

    Dimitri Volchenkov

About the authors

Philippe Blanchard is a mathematical physicist of international stature. He has edited/authored a number of books for Springer and is member of various editorial boards (e.g. Fundamental Theories of Physics)

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