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 \cite{red2}. In this directed network, a new node gets attached to an older node with the probability $\sim K(k)f(t)$ where the degree and age of the older node are $k$ and $t$ respectively. Several functional forms of $K(k)$ and $f(t)$ have been considered. The desirable features of the citation network can be reproduced with $K(k) \sim k^{-\beta}$ and $f(t) \sim \exp(\alpha t)$ with $\beta =2.0$ and $\alpha = -0.2$ and with simple modifications in the growth scheme.