Scale-Free Property for Degrees and Weights in a Preferential Attachment Random Graph Model

الملخص EN

A random graph evolution mechanism is defined.

The evolution studied is a combination of the preferential attachment model and the interaction of four vertices.

The asymptotic behaviour of the graph is described.

It is proved that the graph exhibits a power law degree distribution; in other words, it is scale-free.

It turns out that any exponent in (2,∞) can be achieved.

The proofs are based on martingale methods.