Power-law accelerating growth complex networks with mixed attachment mechanisms

Tao Chen and Zhi-Gang Shao

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 8, 2778-2787

Abstract: In this paper, motivated by the thoughts and methods of the mixture of preferential and uniform attachments, we extend the Barabási–Albert (BA) model, and establish a network model with the power-law accelerating growth and the mixture of the two attachment mechanisms. In our model, the number of edges generated by each newly-introduced node is proportional to the power of θ (0≤θ<1) of time t, i.e., mtθ. By virtue of the continuum approach, we have deduced the degree distribution P(k,t) of our model with the extended power-law form P(k,t)=A(t)[k+B(t)]−γ. When the number of edges k generated by each new node is much greater than the value of B(t), the degree distribution P(k,t) will converge to the power-law form P(k,t)=A(t)k−γ. When k is much less than the value of B(t), the degree distribution P(k,t) will converge to the exponential-law form P(k,t)=A(t)[B(t)]γe−γk/B(t). By virtue of numerical simulations, we also discuss the dependence of the degree distribution P(k,t) on the model’s parameters (where t is considered as a constant in the simulations). Finally, we investigate the possible application of our model in the spreading and evolution of epidemics in some real-world systems.

Keywords: Preferential attachment; Uniform attachment; Power-law accelerating growth; The continuum approach (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:8:p:2778-2787

DOI: 10.1016/j.physa.2011.12.050

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