Models of networks with preferential attachment

Modeling is one of the methods of analyzing organizational principles of complex networks that define their topology and behavior. Traditionally networks with no apparent design principles were described as random graph that were first studied by Paul Erdos and Alfred Rcnyi fl, 2]. But it is known that the topology of real networks deviates from a random graph and many of them sclf-organizc into scale-free (SF) state. The basic motivation of main theoretical models that come under review in this article is to explain the origin of this scale invariance. The example of a network with in-degree and out-degree power-law distribution is the citation network observed by Derek do Sofia Price in [4, 5]. He discovered that in order the network to have these properties the rate at which a paper gets new citations should be proportional to the number that it already has. He called the process cumulative, advantage.Now it is known as preferential attachmentdue to [6].