We study the growth of a directed network, in which the growth is constrained
by the cost of adding links to the existing nodes. We propose a new
preferential-attachment scheme, in which a new node attaches to an existing
node i with probability proportional to 1/k_i, where k_i is the number of
outgoing links at i. We calculate the degree distribution for the outgoing
links in the asymptotic regime (t->infinity), both analytically and by Monte
Carlo simulations. The distribution decays like k c^k/Gamma(k) for large k,
where c is a constant. We investigate the effect of this
preferential-attachment scheme, by comparing the results to an equivalent
growth model with a degree-independent probability of attachment, which gives
an exponential outdegree distribution. Also, we relate this mechanism to simple
food-web models by implementing it in the cascade model. We show that the
low-degree preferential-attachment mechanism breaks the symmetry between in-
and outdegree distributions in the cascade model. It also causes a faster decay
in the tails of the outdegree distributions for both our network growth model
and the cascade model.Comment: 10 pages, 7 figures. A new figure added. Minor modifications made in
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