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Random Walks and Diffusions on Graphs and Databases

An Introduction

Philipp Blanchard, Dimitri Volchenkov (Autoren)

Buch | Hardcover

XIV, 262 Seiten

2011
Springer Berlin (Verlag)
978-3-642-19591-4 (ISBN)

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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.

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)

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.

Erscheint lt. Verlag	27.5.2011
Reihe/Serie	Springer Series in Synergetics
Zusatzinfo	XIV, 262 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	550 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Mathematik / Informatik ► Mathematik ► Graphentheorie
	Naturwissenschaften ► Physik / Astronomie ► Astronomie / Astrophysik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
	Technik
Schlagworte	Complexity • complex networks • Diffusion metric • Effective resistance metric • Markov Chain Analysis • Path integral approach to graphs • Probabilistic embedding of graphs
ISBN-10	3-642-19591-1 / 3642195911
ISBN-13	978-3-642-19591-4 / 9783642195914
Zustand	Neuware