  We investigate the particle trapping and scattering properties in a
tight-binding network which consists of several subgraphs. The particle
trapping condition is proved under which particles can be trapped in a subgraph
without leaking. Based on exact solutions for the configuration of a
$\pi$-shaped lattice, it is argued that the bound states in a specified
subgraph are of two types, resonant and evanescent. It is also shown that, when
such a subgraph is embedded in a one-dimensional chain as the waveguide, an
incident wave experiences total reflection if its energy matches the resonant
bound state energy.
