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

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

Arnab K. Ray
Department of Physics, Jaypee University of Engineering and Technology
Raghogarh, Guna 473226, Madhya Pradesh, India


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.