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

TL;DR

This paper introduces a continuum model for the degree distribution in open-source software dependency networks, highlighting finite-size effects and deviations from Zipf's law in heavily and poorly linked nodes.

Contribution

It presents a novel continuum model capturing finite-size effects and differences between in- and out-directed networks in software dependencies.

Findings

Degree distributions follow Zipf's law for intermediate nodes.

Heavily linked and poorly linked nodes deviate from Zipf's law due to finite-size effects.

Out-degree growth saturates due to limited semantic possibilities.

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.