Evolution of Reference Networks with Fitness Inheritance

The vertex connectivity of many large networks follows a scale-free power-law distribution. BA model and many other BA-derived models reproduce such property and acquire a special status. The most distinct characteristic of these models is that during the preferential attachment process the choice of old vertices is based on the connectivity of the old vertices and there is no relationship between new vertices´ property and old ones´. In this article we present a new model that bases its choice of old vertices on the fitness of the old vertices and the fitness of new vertices is partially determined by the old ones. Based on the new model, both theoretical analysis and simulation show that the connectivity distribution of networks generated by our model follows an exponential distribution and loses the scale-free property. Also the differences between our model and existing models and the relationships between them are discussed.