Network Growth with Preferential Attachment for High Indegree and Low Outdegree

We study the growth of a directed transportation network, such as a food web, in which links carry resources. We propose a growth process in which new nodes (or species) preferentially attach to existing nodes with high indegree (in food-web language, number of prey) and low outdegree (or number of predators). This scheme, which we call inverse preferential attachment, is intended to maximize the amount of resources available to each new node. We show that the outdegree (predator) distribution decays at least exponentially fast for large outdegree and is continuously tunable between an exponential distribution and a delta function. The indegree (prey) distribution is poissonian in the large-network limit.

💡 Research Summary

The paper introduces a novel growth mechanism for directed transportation networks, exemplified by ecological food webs, where links represent the flow of resources. Traditional network models often rely on preferential attachment, which causes new nodes to connect preferentially to already highly connected nodes. However, in resource‑driven directed systems the simple degree of a node does not capture the ecological pressures that shape connections. To address this, the authors propose “inverse preferential attachment”: a new node attaches with probability proportional to the indegree (number of prey) of an existing node and inversely proportional to its outdegree (number of predators). Formally, the attachment probability for node i is

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