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A preferential attachment model with random initial degrees
Stockholm University, Faculty of Science, Department of Mathematics.
2009 (English)In: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 47, no 1, 42-72 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, a random graph process{G(t)}t1 is studied and its degreesequence is analyzed. Let {Wt}t1 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(t1), the probability that a given edge of vertex t is connected to vertex i is proportional to di (t1)+δ, where di(t1) is the degree of vertex i at time t1, independently of the other edges.

The main result is that the asymptotical degree sequence for this process is a power law with exponent τ=min{τW, τP}, where τW is the power-law exponent of the initial degrees {Wt}t1 and τP the exponent predicted by pure preferential attachment. This result extends previous work by Cooper and Frieze.

Place, publisher, year, edition, pages
2009. Vol. 47, no 1, 42-72 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-36103DOI: 10.1007/s11512-007-0067-4ISI: 000263486500003OAI: oai:DiVA.org:su-36103DiVA: diva2:288760
Available from: 2010-01-21 Created: 2010-01-21 Last updated: 2017-12-12Bibliographically approved

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