  The distributions of stars and prestellar cores by mass (initial and dense
core mass functions, IMF/DCMF) are among the key factors regulating star
formation and are the 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, and on the scaling relation between the
amplitude and mass of a fluctuation. 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. We effectively combine gravoturbulent and
competitive accretion approaches and predict the accretion rate to be
proportional to the dense core mass: $dM/dt \propto M$. Then we describe 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.
