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© 2011

Random Walks and Diffusions on Graphs and Databases

An Introduction

Benefits

  • 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

Book

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

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Philippe Blanchard, Dimitri Volchenkov
    Pages 1-17
  3. Philippe Blanchard, Dimitri Volchenkov
    Pages 19-41
  4. Philippe Blanchard, Dimitri Volchenkov
    Pages 43-54
  5. Philippe Blanchard, Dimitri Volchenkov
    Pages 55-72
  6. Philippe Blanchard, Dimitri Volchenkov
    Pages 73-84
  7. Philippe Blanchard, Dimitri Volchenkov
    Pages 85-91
  8. Philippe Blanchard, Dimitri Volchenkov
    Pages 93-106
  9. Philippe Blanchard, Dimitri Volchenkov
    Pages 107-170
  10. Philippe Blanchard, Dimitri Volchenkov
    Pages 219-235
  11. Back Matter
    Pages 237-262

About this book

Introduction

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.

Keywords

Complex Networks Diffusion metric Effective resistance metric Markov Chain Analysis Path integral approach to graphs Probabilistic embedding of graphs

Authors and affiliations

  1. 1.Fakultät für Physik, Abt. Theoretische PhysikUniversität BielefeldBielefeldGermany
  2. 2.Fak. PhysikUniversität BielefeldBielefeldGermany

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)

Bibliographic information