Abstract In the last few years it has been established that the connectivity distribution of the large real-world networks often follows the power-law, i.e., they are scale-free networks. In this article stochastic models leading to scale-free network are considered and a model close to them is proposed. Deterministic models for creating scale-free networks with given nodes (static model) are demonstrated. A characteristic of graphs, which could be used for determining the scale-free topology of networks, is suggested.