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Existence of a persistent hub in the convex preferential attachment model

Galashin P.

Probability and Mathematical Statistics

2016

Vol. 36, Fasc. 1

59--74

A vertex of a randomly growing graph is called a persistent hub if at all but finitely many moments of time it has the maximal degree in the graph. We establish the existence of a persistent hub in the Barabási-Albert random graph model with probability one. We also extend this result to the class of convex preferential attachment graphs, where a vertex of degree k gets a new edge with probability proportional to some convex function of k.

Simulation and Measurement of Complex Network Growth: the Interplay of Uniform and Preferential Attachment

Luo H., Horadam K.

Fundamenta Informaticae

2008

Vol. 84, nr 1

61-79

The main discovery of the paper is the introduction and study of a new U-P complex network model, which aims to describe and analyze many common-featured real-world complex networks. This model employs a new functional form of the network growth rule: a linear combination of preferential and uniform attachment. In particular, the degree distribution of the model is first studied by using the computer simulation method, while the exact solution is also obtained analytically.