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Deon Swiggs lost his Central Ward seat to Jake McLellan after allegations were made that Mr Swiggs had engaged in inappropriate late-night messaging with young people and insisted on hugs instead of handshakes.
The reporting of the allegations derailed Mr Swiggs' campaign, although Cr McLellan has maintained he was always on track to win.
On Monday, supporters of Mr Swiggs were in court, claiming the allegations were deliberately released to the media by Cr McLellan's team to sabotage Mr Swiggs' campaign.
If the judge finds Cr McLellan was not duly elected, it could trigger a re-election in the ward.
The hearing is scheduled to last three days.
Last month the city council announced it had abandoned an investigation into the complaints because its code of conduct could only be enforced for sitting city councillors.