Geodesic
Connected components and evolution of random graphs: An algebraic approach
Journal of Algebraic Combinatorics, Tome 35 (2012) no. 1, pp. 141-156.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Keywords: keywords random graphs, graph processes, quantum probability 
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     title = {Connected components and evolution of random graphs: {An} algebraic approach},
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Schott, René; Staples, G.Stacey. Connected components and evolution of random graphs: An algebraic approach. Journal of Algebraic Combinatorics, Tome 35 (2012) no. 1, pp. 141-156. http://geodesic.mathdoc.fr/item/JAC_2012__35_1_a1/