In several real-world networks like the Internet, WWW etc., the number of
links grow in time in a non-linear fashion. We consider growing networks in
which the number of outgoing links is a non-linear function of time but new
links between older nodes are forbidden. The attachments are made using a
preferential attachment scheme. In the deterministic picture, the number of
outgoing links m(t) at any time t is taken as N(t)θ where N(t) is
the number of nodes present at that time. The continuum theory predicts a power
law decay of the degree distribution: P(k)∝k−1−1−θ2, while the degree of the node introduced at time ti is given by
k(ti,t)=tiθ[tit]21+θ when the
network is evolved till time t. Numerical results show a growth in the degree
distribution for small k values at any non-zero θ. In the stochastic
picture, m(t) is a random variable. As long as isindependentoftime,thenetworkshowsabehavioursimilartotheBarabaˊsi−Albert(BA)model.Differentresultsareobtainedwhen is time-dependent, e.g.,
when m(t) follows a distribution P(m)∝m−λ. The behaviour
of P(k) changes significantly as λ is varied: for λ>3, the
network has a scale-free distribution belonging to the BA class as predicted by
the mean field theory, for smaller values of λ it shows different
behaviour. Characteristic features of the clustering coefficients in both
models have also been discussed.Comment: Revised text, references added, to be published in PR