Logarithmic growth dynamics in software networks

– In a recent paper, Krapivsky and Redner [1] proposed a new growing network model with new nodes being attached to a randomly selected node, as well to all ancestors of the target node. The model leads to a sparse graph with an average degree growing logarithmically with the system size. Here we present compeling evidence for software networks being the result of a similar class of growing dynamics. The predicted patternd of network growth, as well as the stationary inand out-degree distributions are consistent with the model. Our results confirm the view of large-scale software topology being generated through duplication-rewiring mechanisms. Implications of these findings are outlined. Introduction. – The structure of many natural and artificial systems can be depicted with networks. Empirical studies on these networks have revealed that many of them display a heterogenous degree distribution p(k) ≈ k , where few nodes (hubs) have a large number of connections while the majority of nodes have one or two links [2]. The existence of hubs has been related to multiplicative effects affecting network evolution [3]. Such topological patterns have been explained by a number of mechanisms, including preferential attachment rules [4] and network models based on simple rules of node duplication [5]. A very simple approach is given by the growing network model with copying (GNC) [1]. The network grows by introducing a single node at a time. This new node links to m randomly selected target node(s) with probability p as well to all ancestor nodes of each target, with probability q (see fig. 1). The discrete dynamics follows a rate equation [1] L(N + 1) = L(N) + m N 〈