In this work we investigate the extraordinary characteristics of one-dimensional (1D) finite periodic parity-time (PT) symmetric network. On the basis of the transfer matrix method, three simple expressions are analytically obtained for transmission, left reflection and right reflection coefficients. For this periodic structure, we provide new criteria for the PT-symmetry breaking transition in terms of the elements of the transfer matrix and the scattering matrix. These criteria indicate that the exceptional points are related only to the cell structure, but not to the cell number. Utilizing these criteria and expressions, the relationships between the transmittances (reflectances) and the cell number are considered in detail. Furthermore, the conditions for ultrastrong transmission are analytically derived. We also show how a PT-symmetric network can become unidirectionally and bidirectionally transparent at specific frequencies. The conditions and related properties of unidirectional and bidirectional transparencies are also examined. Finally, we find that the finite periodic PT-symmetric network with certain cell number can be viewed as a unidirectionally invisible structure at the exceptional points. Our work may pave the way for designing a diversefamily of optical structures and networks with new properties and functionalities.