We study the effect of subtle changes on the evolution in the scale-free (SF) networks. Three extended models are evolved based on competition and inner anti-preferential deletion in growth and preferential attachment processes. By nonlinear and dynamic controlling on randomness and determinacy, three models can self-organize into scale-free networks, and diverse scaling exponents appear. Moreover, the model with more determinacy has more stringent parameter control than randomness, especially in the edge deletion. Our results suggest that the nature of the topology universality and dissimilarity in SF networks may be the subtle changes of randomness and determinacy.
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