We present an imaging survey of the CO ( 1–0 ) , HCN ( 1–0 ) , and HCO ^ { + } ( 1–0 ) lines in the nearby Seyfert galaxies using the Nobeyama Millimeter Array and RAINBOW Interferometer . Some of the observed Seyfert galaxies including NGC 1068 , NGC 1097 , NGC 5033 , and NGC 5194 exhibit strong HCN ( 1–0 ) emission on a few 100 pc scales . The observed HCN ( 1–0 ) /CO ( 1–0 ) and HCN ( 1–0 ) /HCO ^ { + } ( 1–0 ) line ratios in the Seyfert nuclei ( > 0.2 and > 1.8 , respectively ) have never been observed in the central regions of nuclear starburst galaxies . On the other hand , the molecular line ratios in the nuclei of NGC 3079 , NGC 3227 , NGC 4051 , NGC 6764 , NGC 7479 , and NGC 7469 are comparable with those in the nuclear starburst galaxies . We propose that the elevated HCN emission originates from the X-ray irradiated dense molecular tori or X-ray dominated regions ( XDRs ) in close proximity to the active nuclei . Further , our HCN/CO and HCN/HCO ^ { + } diagrams will provide a new powerful diagnostic of the nuclear power source in active galaxies . Based on our diagnostic , we observe three of five type-1 Seyferts ( six of ten in total ) host compact nuclear starbursts . Our results are also supported by observations at other wavelengths such as those by infrared L-band PAH spectroscopy . The proposed method based on the HCN and HCO ^ { + } spectroscopies will be crucial for investigating extremely dusty nuclei , such as the ultraluminous infrared galaxies and high-redshift submillimeter galaxies , because these molecular lines are devoid of dust extinction . As an example , we present the HCN and HCO ^ { + } observations of the luminous infrared galaxy NGC 4418 . We have obtained a high HCN/HCO ^ { + } ratio of 1.8 , which suggests the presence of a buried active nucleus .