Finite-size effects in the dependency networks of free and open-source software

Abstract: We propose a continuum model for the degree distribution of directed networks in free and open-source software. The degree distributions of links in both the in-directed and out-directed dependency networks follow Zipf's law for the intermediate nodes, but the heavily linked nodes and the poorly linked nodes deviate from this trend and exhibit finite-size effects. The finite-size parameters make a quantitative distinction between the in-directed and out-directed networks. For the out-degree distribution, the initial condition for a dynamic evolution corresponds to the limiting count of the most heavily liked nodes that the out-directed network can finally have. The number of nodes contributing out-directed links grows with every generation of software release, but this growth ultimately saturates towards a terminal value due to the finiteness of semantic possibilities in the network.