The component structure of random graphs: Phase transitions in random graphs and random graph processes

Seierstad, Taral Guldahl

ISBN 10: 363943286X / ISBN 13: 9783639432862

Published by AV Akademikerverlag, 2012

About this Item

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Bibliographic Details

• Title: The component structure of random graphs: Phase transitions in random graphs and random graph processes
• Publisher: AV Akademikerverlag
• Publication Date: 2012
• Language: English
• ISBN 10: 363943286X
• ISBN 13: 9783639432862
• Binding: Soft cover
• Condition: New

About this title

Synopsis

Revision with unchanged content. Many random graph processes exhibit a phase transition, where the compo-nent structure of the graph changes radically caused by the addition of relatively few random edges. Before the phase transition the graph consists, with high probability, of many small components, while after the phase transition it contains, with high probability, a unique component of linear size, called the giant component, which is much larger than every other component in the graph. This book treats the phase transition and the emergence of the giant component in three different random graph models. It presents several techniques that are useful for studying this type of problem, including generating functions, branching processes and differential equations. The book is aimed at mathematicians interested in random graphs in general, and in the phase transition and the giant component in particular.

About the Author

Dr. rer. nat. in computer science at the Humboldt University Berlin; currently postdoctoral fellow in biostatistics at the University of Oslo.