Journal of East China Normal University(Natural Sc ›› 2017, Vol. 2017 ›› Issue (6): 42-49.doi: 10.3969/j.issn.1000-5641.2017.06.004

• Mathematics • Previous Articles     Next Articles

One scale-free network model based on two different preferential attachment probabilities

MA Fei, YAO Bing   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
  • Received:2016-06-01 Online:2017-11-25 Published:2017-11-25

Abstract: Based on the classic scale-free network model, we set up the partial differential equation satisfied a more general network dynamic system, and then we not only find another important topological property of scale-free network, but also discuss the real background meaning of every function. Meanwhile, we extend the BA-network-model growth principle, degree-preferential attachment mechanism. Starting from a more general situation, we establish a network model containing degree-preferential attachment probability and special-graph-preferential attachment probability. By analysis, this model is scale-free. Finally, we distinguish the connect between the scope of the power law parameter γ of scale-free network and the phenomena all kinds of preferential attachment probabilities co-existing. According to the contribution level from the vertex to the whole network, we come up with a preferential attachment probability.

Key words: scale-free network model, dynamical evolution, partial differential equation, degree preferential attachment, graph preferential attachment

CLC Number: