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We study the effect of primordial non‐Gaussianity on the development of large‐scale cosmic structure using high‐resolution  N ‐body simulations. In particular, we focus on the topological properties of the ‘cosmic web’, quantitatively characterized by the Minkowski functionals (MFs), for models with quadratic non‐linearities with different values of the usual non‐Gaussianity parameter  f  NL . In the weakly non‐linear regime (the amplitude of mass density fluctuations σ 0  &lt; 0.1), we find that analytic formulae derived from perturbation theory agree with the numerical results within a few per cent of the amplitude of each MF when | f  NL | &lt; 1000. In the non‐linear regime, the detailed behaviour of the MFs as functions of threshold density deviates more strongly from the analytical curves, while the overall amplitude of the primordial non‐Gaussian effect remains comparable to the perturbative prediction. When smaller‐scale information is included, the influence of primordial non‐Gaussianity becomes increasingly significant statistically due to decreasing sample variance. We find that the effect of the primordial non‐Gaussianity with  | f  NL | = 50  is comparable to the sample variance of mass density fields with a volume of 0.125( h  −1  Gpc) 3  when they are smoothed by Gaussian filter at a scale of 5  h  −1  Mpc. The detectability of this effect in actual galaxy surveys will strongly depend on residual uncertainties in cosmological parameters and galaxy biasing.

The effect of primordial non‐Gaussianity on the topology of large‐scale structure