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Cores and filamentary structures are the prime birthplaces of stars, and play key roles in the process of star formation. Latest advances in the methods of multi-scale source and filament extraction, and in making high-resolution column density map from $Herschel$ multi-wavelength observations enable us to detect the filamentary network structures in highly complex molecular cloud environments. The statistics for physical parameters shows that core mass strongly correlates with core dust temperature, and $M/L$ strongly correlates with $M/T$, which is in line with the prediction of the blackbody radiation, and can be used to trace evolutionary sequence from unbound starless cores to robust prestellar cores. Crest column densities of the filamentary structures are clearly related with mass per unit length ($M_{\rm line}$), but are uncorrelated by three orders ranging from $\sim 10^{20}$ to $\sim 10^{22}$ $ \rm cm^{-2}$ with widths. Full width at half maximum (FWHM) have a median value of 0.15 pc, which is consistent with the 0.1 pc typical inner width of the filamentary structures reported by previous research. We find $\sim $70\% of robust prestellar cores (135/199) embedded in supercritical filaments with $M_{\rm line}>16~M_{\odot}/{\rm pc}$, which implies that the gravitationally bound cores come from fragmentation of supercritical filaments. And on the basis of observational evidences that probability distribution function (PDF) with power-law distribution in the Perseus south is flatter than north, YSO number is significantly less than that in the north, and dust temperature difference. We infer that south region is more gravitationally bound than north region.