Random Walks and Diffusions on Graphs and Databases: An Introduction

Front Cover
Springer Science & Business Media, May 26, 2011 - Science - 262 pages
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.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Introduction to Permutations Markov Chains and Partitions
1
Worth Another Binary Relation Graphs
18
Permutations Sieved Through Adjacency Graph Automorphisms
43
Exploring Undirected Graphs by Random Walks
55
Embedding of Graphs in Probabilistic Euclidean Space
73
Random Walks and Electric Resistance Networks
85
Random Walks and Diffusions on Directed Graphs and Interacting Networks
92
Structural Analysis of Networks and Databases
107
When Feedbacks Matter Epidemics Synchronization and Selfregulation in Complex Networks
171
Critical Phenomena on Large Graphs with Regular Subgraphs
219
References
236
Glossary of Graph Theory
253
Index
259
Copyright

Other editions - View all

Common terms and phrases

About the author (2011)

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)