We discuss formulations of boundary conditions in a quantum graph vertex and demonstrate that the so-called ST-form can be further reduced up to a form more effective in certain applications: In particular, in identifying the number of independent parameters for given ranks of two connection matrices, or in calculating the scattering matrix when both matrices are singular. The new form of boundary conditions, called the PQ RS-form, also gives a natural scheme to design generalized low and high pass quantum filters. (C) 2010 Elsevier B.V. All rights reserved.