Time evolution of a random graph

Alex A Lushnikov

doi:10.1088/0305-4470/38/46/L02

Time evolution of a random graph

Alex A Lushnikov

Tutkimustuotos: Artikkelijulkaisu › Artikkeli › Tieteellinen › vertaisarvioitu

Abstrakti

An initially empty (no edges) graph of the order of M is assumed to evolve by adding one edge at a time. This edge can connect either two linked components and form a new component of a larger order (coalescence of graphs) or increase (by one) the number of edges in a given linked component. The evolution equation for the generating functional of the probability to find in the system a given set of occupation numbers (the numbers of graphs of the order of g having exactly v edges) at time t is formulated and solved exactly. The expression for the graph composition spectrum is derived and analysed in the limit of large M.

Alkuperäiskieli	englanti
Lehti	Journal of Physics A : Mathematical and General
Vuosikerta	38
Sivut	L777-L782
ISSN	0305-4470
DOI - pysyväislinkit	https://doi.org/10.1088/0305-4470/38/46/L02
Tila	Julkaistu - 2005
OKM-julkaisutyyppi	A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä, vertaisarvioitu

Pääsy asiakirjaan

10.1088/0305-4470/38/46/L02

Siteeraa tätä

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AB - An initially empty (no edges) graph of the order of M is assumed to evolve by adding one edge at a time. This edge can connect either two linked components and form a new component of a larger order (coalescence of graphs) or increase (by one) the number of edges in a given linked component. The evolution equation for the generating functional of the probability to find in the system a given set of occupation numbers (the numbers of graphs of the order of g having exactly v edges) at time t is formulated and solved exactly. The expression for the graph composition spectrum is derived and analysed in the limit of large M.

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