Geodesic
Emergence of the~giant component in preferential-attachment growing networks
Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 3, pp. 496-507

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We study the percolation transition in evolving scale-free networks. A new node is added at each step and is connected to a random number of old nodes according to the preferential attachment mechanism. We give the critical value of the emergence of the giant component and prove that the transition is of infinite order. We also obtain asymptotic expressions for the cluster size distribution in the subcritical, critical, and supercritical regimes.
Keywords: scale-free network, percolation, cluster size distribution.
Mots-clés : Kosterlitz–Thouless transition 
@article{TMF_2016_186_3_a9,
     author = {Yan Li and Yuan Sun},
     title = {Emergence of the~giant component in preferential-attachment growing networks},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {496--507},
     publisher = {mathdoc},
     volume = {186},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_186_3_a9/}
}
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Yan Li; Yuan Sun. Emergence of the~giant component in preferential-attachment growing networks. Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 3, pp. 496-507. http://geodesic.mathdoc.fr/item/TMF_2016_186_3_a9/