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We present the environmental properties around high-$z$ radio galaxies(HzRGs) at $z\sim4$, which have been poorly investigated because of theirrarity. We use the largest samples of HzRGs and $g$-dropout galaxy overdenseregions at $z\sim4$, which were constructed from Hyper Suprime-Cam SubaruStrategic Program, to characterize the HzRG environments statistically. Wemeasure the $g$-dropout galaxy overdensities around 21 HzRGs whose rest-frame1.4 GHz radio luminosities ($L_{1.4\mathrm{GHz}}$) are $10^{26-27}$ WHz$^{-1}$. We find that the overdensities around the faint HzRGs with$L_{1.4\mathrm{GHz}}\sim10^{26.0-26.5}$ W Hz$^{-1}$ tend to be higher than thatof the $g$-dropout galaxies. On the other hand, no significant difference ofdensity environments is found between the luminous HzRGs with $L_{1.4\mathrm{GHz}}\sim10^{26.5-27.0} $ W Hz$^{-1}$ and the $g$-dropoutgalaxies. The HzRGs are found to occupy more massive halos than $g$-dropoutgalaxies through a cross-correlation between the HzRGs and $g$-dropoutgalaxies. This trend is more pronounced in the faint HzRGs. These results areconsistent with a scenario where HzRGs get older and more massive as theradio-luminosity decreases. The HzRGs are expected to trace the progenitors oflocal cluster halos from their calculated halo mass. In addition, we find thatsurrounding galaxies tend to distribute along the radio-jet major axis of theHzRGs at angular distances less than $\lesssim500$ physical kpc. Our findingsimply the onset of the filamentary structures around the HzRGs at $z\sim4$.

A Wide and Deep Exploration of Radio Galaxies with Subaru HSC (WERGS). VI. Distant Filamentary Structures Pointed by High-z Radio Galaxies at z~4