(10 votes from 9 institutions)
The distributions of stars and prestellar cores by mass (initial and dense core mass functions, IMF/DCMF) stay among the key factors regulating star formation and are subject of detailed theoretical and observational studies. Results from numerical simulations of star formation qualitatively resemble an observed mass function, a scale free power law with a sharp decline at low masses. However, most analytic IMF theories critically depend on the empirically chosen input spectrum of mass fluctuations which evolve into dense cores and, subsequently, stars. Here we propose a new approach exploiting the techniques from the field of network science. We represent a system of dense cores accreting gas from the surrounding diffuse interstellar medium (ISM) as a spatial network growing by preferential attachment and assume that the ISM density has a self-similar fractal distribution following the Kolmogorov turbulence theory. As opposed to gravoturbulent fragmentation theories, we consider the dense core growth and demonstrate that the power law core mass function emerges independently of the initial distribution of density fluctuations by mass. Our model yields a power law solely defined by the fractal dimensionalities of the ISM and accreting gas. With a proper choice of the low mass cut-off, it reproduces observations over three decades in mass. We also rule out a low mass star dominated ``bottom-heavy'' IMF in a single star forming region.