Directed Accelerated Growth: Application in Citation Network

Abstract

In many real world networks, the number of links increases nonlinearly with the number of nodes. Models of such accelerated growth have been considered earlier with deterministic and stochastic number of links. Here we consider stochastic accelerated growth in a network where links are directed. With the number of out-going links following a power law distribution, the results are similar to the undirected case. As the accelerated growth is enhanced, the degree distribution becomes independent of the ``initial attractiveness'', a parameter which plays a key role in directed networks. As an example of a directed model with accelerated growth, the citation network is considered, in which the distribution of the number of outgoing link has an exponential tail. The role of accelerated growth is examined here with two different growth laws.