Abstract
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 preferential-attachment scheme, in which a new node attaches to an existing node with probability , where is the number of outgoing links at . We calculate the degree distribution for the outgoing links in the asymptotic regime , , both analytically and by Monte Carlo simulations. The distribution decays like for large , where 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.
- Received 27 October 2005
DOI:https://doi.org/10.1103/PhysRevE.73.056115
©2006 American Physical Society