Preferential attachment in randomly grown networks

Weaver, Iain S. (2015) Preferential attachment in randomly grown networks. Physica A: Statistical Mechanics and its Applications, 1-8. (doi:10.1016/j.physa.2015.06.019).

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Abstract

We reintroduce the model of Callaway et al. (2001) as a special case of a more general model for random network growth. Vertices are added to the graph at a rate of 1, while edges are introduced at rate δ. Rather than edges being introduced at random, we allow for a degree of preferential attachment with a linear attachment kernel, parametrised by m. The original model is recovered in the limit of no preferential attachment, m → ∞. As expected, even weak preferential attachment introduces a power-law tail to the degree distribution. Additionally, this generalisation retains a great deal of the tractability of the original along with a surprising range of behaviour, although key mathematical features are modified for finite mm. In particular, the critical edge density, δ_c which marks the onset of a giant network component is reduced with increasing tendency for preferential attachment. The positive degree–degree correlation introduced by the unbiased growth process is offset by the skewed degree distribution, reducing the network assortativity.

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