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In this paper, benzene-core photonic crystal fibers (B-PCFs) with non-uniform air holes for the square lattice are studied by controlling the air-filling factor of the air holes in the first ring and increasing those up to a maximum for external holes. Commercial Mode Solutions software is used to study the influence of structural parameters on the nonlinear coefficient, dispersion, effective mode area, and attenuation. It can be seen that this design affects the linear and nonlinear properties at the same time. In other words, it has a crucial effect on either the near-zero flatness of dispersion or going up the nonlinearity and falling the loss of the B-PCFs. The above benefits make the optimized fibers suitable for supercontinuum (SC) generation applications. [ABSTRACT FROM AUTHOR]