Parsing inflected forms may not always work as expected. If the following does not give the correct word, try Latin Words or Perseus.
Vergĭlĭus (not Virgĭlĭus; the form Ver- is supported by the ancient MSS. and inscriptions in unbroken succession, to the fourth century A.D.; v. Ritschl, Opusc. Phil. 2, 779 sq.), ii, m., the name of a Roman gens; so, esp., P. Vergilius Maro, a celebrated Roman poet, Hor. C. 1, 3, 6; 1, 24, 10; 4, 12, 13; id. S. 1, 5, 40.
Hence, Vergĭlĭ-ānus, a, um, adj., of or belonging to the poet Vergil, Vergilian: virtus, Plin. praef. § 22: illud, Quint. 1, 3, 13: VERGILIANVS POËTA, a writer of a cento of Vergilian verses, Inscr. Grut. 64, 5.