  Based on the empirical analysis of the dependency network in 18 Java
projects, we develop a novel model of network growth which considers both: an
attachment mechanism and the addition of new nodes with a heterogeneous
distribution of their initial degree, $k_0$. Empirically we find that the
cumulative degree distributions of initial degrees and of the final network,
follow power-law behaviors: $P(k_{0}) \propto k_{0}^{1-\alpha}$, and
$P(k)\propto k^{1-\gamma}$, respectively. For the total number of links as a
function of the network size, we find empirically $K(N)\propto N^{\beta}$,
where $\beta$ is (at the beginning of the network evolution) between 1.25 and
2, while converging to $\sim 1$ 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
$\alpha$, $\beta$, $\gamma$, 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.
