  We claim that networks are created according to the priority attachment
mechanism and we show a simple model which uses the priority attachment to
generate both synthetic and close to empirical networks. Priority attachment is
a mechanism which generalizes previously proposed mechanisms, such as small
world creation or preferential attachment, but we also observe its presence in
a range of real-world networks. In this paper we show that by using priority
attachment we can generate networks of very diverse topologies, as well as
recreate empirical networks. An additional advantage of the priority attachment
mechanism is an easy interpretation of the latent processes of network
formation. We substantiate our claims by performing numerical experiments on
synthetic and empirical networks. The two main contributions of the paper are:
the introduction of the priority attachment mechanism, and the design of the
Priority Rank: a simple network generative model based on the priority
attachment mechanism.
