Quantum interference (QI) phenomena between electronic states in molecular circuits offer a new opportunity to design new types of molecular devices such as molecular sensors, interferometers, and thermoelectric devices. Controlling the QI effect is a key challenge for such applications. For the development of single molecular devices employing QI effects, a systematic study of the relationship between electronic structure and the quantum interference is needed. In order to uncover the essential topological requirements for the appearance of QI effects and the relationship between the QI-affected line shape of the transmission spectra and the electronic structures, we consider a homogeneous toy model where all on-site energies are identical and model four types of molecular junctions due to their topological connectivities. We systematically analyze their transmission spectra, density of states, and thermoelectric properties. Even without the degree of freedom for on-site energies an asymmetric Fano peak could be realized in the homogeneous systems with the cyclic configuration. We also calculate the thermoelectric properties of the model systems with and without fluctuation of on-site energies. Even under the fluctuation of the on-site energies, the finite thermoelectrics are preserved for the Fano resonance, thus cyclic configuration is promising for thermoelectric applications. This result also suggests the possibility to detect the cyclic configuration in the homogeneous systems and the presence of the QI features from thermoelectric measurements. (C) 2014 AIP Publishing LLC.