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

A continuum model has been proposed to fit the data pertaining to the directed networks in free and opensource software. While the degree distributions of links in both the in-directed and out-directed dependency networks follow Zipf’s law for the intermediate nodes, the most richly linked nodes, as well as the most 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. Dynamic evolution of free software releases shows that the finite-size properties of the in-directed and out-directed networks are opposite in nature. For the out-degree distribution, the initial condition for a dynamic evolution also corresponds to the limiting count of rich nodes that the mature out-directed network can have. The number of nodes contributing out-directed links grows with each passing generation of software release, but this growth ultimately saturates towards a finite value due to the finiteness of semantic possibilities in the network.