The design of the low- and high-pass filters is a characteristic
example of the relevance of quantum graphs in applications. This
motivated the present study in which the new form of boundary
conditions at a vertex is introduced and advocated. Mathematically,
it is a reduced form of the general boundary condition. By its
construction it proves most effective when the number of independent
parameters is to be identified for two connection matrices of given
(and equally weighted) ranks. Its merits are fine-tuned to the
calculations of the scattering off the vertex when both the
connection matrices are singular and when the dynamics at both the
large and small momenta is interesting.

MR2737903 Cheon, Taksu; Exner, Pavel; Turek, Ondrej Tripartite
connection condition for a quantum graph vertex. Phys. Lett. A 375
(2010), no. 2, 113--118. 81Q35