Modelling aging characteristics in citation networks

Growing network models with preferential attachment dependent on both age and degree are proposed to simulate certain features of citation network noted in [Redner, arXiv: physics/0407137 (2004)]. In this directed network, a new node gets attached to an older node with the probability ∼K(k)f(t)∼K(k)f(t) where the degree and age of the older node are k and t  , respectively. Several functional forms of K(k)K(k) and f(t)f(t) have been considered. The desirable features of the citation network can be reproduced with K(k)∼k-βK(k)∼k-β and f(t)∼exp(αt)f(t)∼exp(αt) with β=2.0β=2.0 and α=-0.2α=-0.2 and with simple modifications in the growth scheme.