The influence of preferential attachment on evolving networks

With the consideration of local events and preferential attachment, the extended model proposed by Albert and Barabási is studied. Firstly, the extended model is built only by local events. It is found that without preferential attachment the networks' connectivity distribution decays exponentially for large connectivity, and the decaying exponent varies with different probabilities of the addition of new links and rewiring. Secondly, the extended model with partial preferential attachment is studied. When preferential attachment only presents in the addition of new links or new nodes, there is scale-free regime in the phase diagram; while preferential attachment is brought into the rewiring, there coexist two regimes, i.e., the exponential regime and the scale-free regime. Thirdly, fitness is introduced to the extended model with complete preferential attachment. It is obtained that the network's connectivity distribution is a result affected by many factors, including the fitness, the local events and preferential attachment.