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Exponential Growth and Dynamic Local World of Scale-Free Network

Qian Xing-san

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Abstract

Started from exponential growth of scale-free network, the analytic and simulated results of the modified BA model are presented in the paper. The analytic results show that the evolution speed of scale-free network satisfies 05β≤1 and the index of power-law distribution satisfies r=2β+1. Based on this process, we find that preferential attachment takes place in a dynamic local world whose size is in direct proportion to the size of whole networks.

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What this paper is about

Started from exponential growth of scale-free network, the analytic and simulated results of the modified BA model are presented in the paper. The analytic results show that the evolution speed of scale-free network satisfies 05β≤1 and the index of power-law distribution satisfies r=2β+1. Based on this process, we find that preferential attachment takes place in a dynamic local world whose size is in direct proportion to the size of whole networks.

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Available abstract

Started from exponential growth of scale-free network, the analytic and simulated results of the modified BA model are presented in the paper. The analytic results show that the evolution speed of scale-free network satisfies 05β≤1 and the index of power-law distribution satisfies r=2β+1. Based on this process, we find that preferential attachment takes place in a dynamic local world whose size is in direct proportion to the size of whole networks.

Key concepts: Preferential attachment, Scale-free network, Exponential function, Scale (ratio), Power law, Exponential growth, Statistical physics, Exponential distribution

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