A preferential attachment model with random initial degrees

• Autores: Maria Deijfen, Henri van den Esker, Remco van der Hofstad, Gerard Hooghiemstra
• Localización: Arkiv för matematik, ISSN 0004-2080, Vol. 47, Nº 1, 2009, págs. 41-72
• Idioma: inglés
• DOI: 10.1007/s11512-007-0067-4
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• Resumen

  • In this paper, a random graph process {G(t)}t.1 is studied and its degree sequence is analyzed. Let {Wt}t.1 be an i.i.d. sequence. The graph process is defined so that, at each integer time t, a new vertex with Wt edges attached to it, is added to the graph. The new edges added at time t are then preferentially connected to older vertices, i.e., conditionally on G(t.1), the probability that a given edge of vertex t is connected to vertex i is proportional to di(t.1)+¿Â, where di(t.1) is the degree of vertex i at time t.1, independently of the other edges.

    The main result is that the asymptotical degree sequence for this process is a power law with exponent T=min{TW, TP}, where TW is the power-law exponent of the initial degrees {Wt}t.1 and TP the exponent predicted by pure preferential attachment. This result extends previous work by Cooper and Frieze.