Sustainable Growth in Complex Networks

CCSS Working Paper No. 10-008

7 Pages Posted: 12 Jul 2010 Last revised: 24 Jul 2010

See all articles by Frank Schweitzer

Frank Schweitzer

ETH Zürich

Claudio J. Tessone

ETH Zürich

Markus Michael Geipel

ETH Zürich - Department of Management, Technology, and Economics (D-MTEC)

Date Written: July 8, 2010

Abstract

Based on the empirical analysis of the dependency network in 18 Java projects, we develop a novel model of network growth which considersboth: an attachment mechanism and the addition of new nodes with a heterogeneous distribution of their initial degree, k0. Empirically we find that the cumulative degree distributions of initial degrees and of the final network, follow power-law behaviors: P(k0) ∝ k01−α, and P(k) ∝ k1−γ, respectively. For the total number of links as a function of the network size, we find empirically K(N) ∝ Nβ, where β is (at the beginning of thenetwork evolution) between 1.25 and 2, while converging to  ∼ 1 for large N. This indicates a transition from a growth regime with increasing network density towards a sustainable regime, which revents a collapse because of ever increasing dependencies. Our theoretical framework is able to predict relations between the exponents α, β, γ, which also link issues of software engineering and developer activity.

These relations are verified by means of computer simulations and empirical investigations. They indicate that the growth of real Open Source Software networks occurs on the edge between two regimes, which are either dominated by the initial degree distribution of added nodes, or by the preferential attachment mechanism. Hence, the heterogeneous degree distribution of newly added nodes, found empirically, is essential to describe the laws of sustainable growth in networks.

Keywords: Complex networks, Sustainable growth, Stochastic growth

Suggested Citation

Schweitzer, Frank and Tessone, Claudio J. and Geipel, Markus Michael, Sustainable Growth in Complex Networks (July 8, 2010). CCSS Working Paper No. 10-008. Available at SSRN: https://ssrn.com/abstract=1638866 or http://dx.doi.org/10.2139/ssrn.1638866

Frank Schweitzer

ETH Zürich ( email )

Weinbergstrasse 56/58
WEV Room G 211
Zurich, CH-8032
Switzerland
+41 44 632 83 50 (Phone)

HOME PAGE: http://www.sg.ethz.ch

Claudio J. Tessone (Contact Author)

ETH Zürich ( email )

Zürichbergstrasse 18
8092 Zurich, CH-1015
Switzerland

HOME PAGE: http://www.sg.ethz.ch/people/tessonec

Markus Michael Geipel

ETH Zürich - Department of Management, Technology, and Economics (D-MTEC) ( email )

ETH-Zentrum
Zurich, CH-8092
United States

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