Robust analysis of preferential attachment models with fitness

Steffen Dereich, Marcel Ortgiese

Research output: Contribution to journalArticlepeer-review

25 Citations (SciVal)


The preferential attachment network with fitness is a dynamic random graph model. New vertices are introduced consecutively and a new vertex is attached to an old vertex with probability proportional to the degree of the old one multiplied by a random fitness. We concentrate on the typical behaviour of the graph by calculating the fitness distribution of a vertex chosen proportional to its degree. For a particular variant of the model, this analysis was first carried out by Borgs, Chayes, Daskalakis and Roch. However, we present a new method, which is robust in the sense that it does not depend on the exact specification of the attachment law. In particular, we show that a peculiar phenomenon, referred to as Bose–Einstein condensation, can be observed in a wide variety of models. Finally, we also compute the joint degree and fitness distribution of a uniformly chosen vertex.
Original languageEnglish
Pages (from-to)386-411
Number of pages26
JournalCombinatorics, Probability and Computing
Issue number3
Publication statusPublished - May 2014


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