title: Effects of preference for attachment to low-degree nodes on the degree distributions of a growing directed network and a simple food-web model.
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 i with probability II(k(i)) approximately k(-1), 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, n(k) both analytically and by Monte Carlo simulations. The distribution decays like kmu(k)/Tau(k) for large k, 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.
authors.affiliation: School of Computational Science, Center for Materials Research and Technology, and Department of Physics, Florida State University, Tallahassee, 32306-4120, USA. sevin@scs.fsu.edu
authors.forename: Volkan
authors.initials: V
authors.lastname: Sevim
authors.forename: Per Arne
authors.initials: PA
authors.lastname: Rikvold