Complex Systems

Finite-Size Effects in the Dependency Networks of Free and Open-Source Software Download PDF

Rajiv Nair
Tata Institute of Social Sciences
V. N. Purav Marg, Deonar, Mumbai 400088, India
rajiv@tiss.edu

G. Nagarjuna
Homi Bhabha Centre for Science Education
Tata Institute of Fundamental Research
V. N. Purav Marg, Mankhurd, Mumbai 400088, India
nagarjun@gnowledge.org

Arnab K. Ray
Department of Physics, Jaypee University of Engineering and Technology
Raghogarh, Guna 473226, Madhya Pradesh, India
arnab.kumar@juet.ac.in

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 linked 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 toward a terminal value, due to the finiteness of semantic possibilities in the network.