The family of graphynes, novel two-dimensional semiconductors with various and fascinating chemical and physical properties, has attracted great interest from both science and industry. Currently, the focus of graphynes is on graphdiyne, or graphyne-2. In this work, we systematically study the effect of acetylene, i.e., carbon-carbon triple bond, links on the electronic and optical properties of a series of graphynes (graphyne-n, where n = 1-5, the number of acetylene bonds) using the ab initio calculations. We find an even-odd pattern, i.e., n = 1, 3, 5 and n = 2, 4 having different features, which has not be discovered in studying graphyne or graphdyine only. It is found that as the number of acetylene bonds increases, the electron effective mass increases continuously in the low energy range because of the flatter conduction band induced by the longer acetylene links. Meanwhile, longer acetylene links result in larger redshift of the imaginary part of the dielectric function, loss function, and extinction coefficient. In this work, we propose an effective method to tune and manipulate both the electronic and optical properties of graphynes for the applications in optoelectronic devices and photo-chemical catalysis.