Del. Code tit. 15, § 5944

When an election is contested because of alleged malconduct of the election officers holding the election or because the person whose right to office is contested was not eligible for such office, a proceeding may be instituted under this chapter against such person by the person who received the next highest number of votes for the office at the election under which such ineligible person was declared elected, notwithstanding the person so contesting the election does not claim to have been elected.