Connected components and evolution of random graphs: an algebraic approach
Identifieur interne : 002728 ( Main/Exploration ); précédent : 002727; suivant : 002729Connected components and evolution of random graphs: an algebraic approach
Auteurs : René Schott [France] ; G. Stacey Staples [États-Unis]Source :
- Journal of Algebraic Combinatorics [ 0925-9899 ] ; 2012-02-01.
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Abstract
Abstract: Questions about a graph’s connected components are answered by studying appropriate powers of a special “adjacency matrix” constructed with entries in a commutative algebra whose generators are idempotent. The approach is then applied to the Erdös–Rényi model of sequences of random graphs. Developed herein is a method of encoding the relevant information from graph processes into a “second quantization” operator and using tools of quantum probability and infinite-dimensional analysis to derive formulas that reveal the exact values of quantities that otherwise can only be approximated. In particular, the expected size of a maximal connected component, the probability of existence of a component of particular size, and the expected number of spanning trees in a random graph are obtained.
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DOI: 10.1007/s10801-011-0297-1
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The approach is then applied to the Erdös–Rényi model of sequences of random graphs. Developed herein is a method of encoding the relevant information from graph processes into a “second quantization” operator and using tools of quantum probability and infinite-dimensional analysis to derive formulas that reveal the exact values of quantities that otherwise can only be approximated. 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Stacey Staples</name></region><name sortKey="Staples, G Stacey" sort="Staples, G Stacey" uniqKey="Staples G" first="G. Stacey" last="Staples">G. Stacey Staples</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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