Random Walks and Diffusions on Graphs and Databases An Introduction /

• Main Authors: Blanchard, Philippe (Author), Volchenkov, Dimitri (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2011.
• Series: Springer Series in Synergetics, 10
• Subjects: Physics.; Data structures (Computer science).; Manifolds (Mathematics).; Complex manifolds.; Complexity, Computational.; Complex Networks.; Manifolds and Cell Complexes (incl. Diff.Topology).; Data Structures, Cryptology and Information Theory.; Complexity.

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...

Table of Contents:

• Introduction to Permutations, Markov Chains, and Partitions
• Worth Another Binary Relation: Graphs
• Permutations Sieved Through Adjacency: Garph Autormorphisms
• Exploring Undirected Graphs by Random Walks
• Embedding of Graphs in Probabilistic Euclidean Space
• Random Walks and Electric Resistance Networks
• Random Walks and Diffusions on Directed Graphs and Interacting Networks
• Structural Analysis of Networks and Databases
• When Feedbacks Matter: Epidemics, Synchronization, and Self-Regulation in Complex Networks
• Critical Phenomena on Large Graphs With Regular Subgraphs
• Glossary of Graph Theory.