New figures obtained by the Evening News show that both North Edinburgh and Pentlands areas have seen big jumps in their pervert population.
At the same time, the number living in the city centre policing area has fallen from 73 in 2007 to just 24 this year.
Overall, the number of registered sex offenders (RSOs) being monitored in Edinburgh and the Lothians has changed little in the last two years.
Around two thirds of the Lothians' 676 sex offenders are free to live where they please as long as they register with the police.
However, Edinburgh North and Leith MSP Malcolm Chisolm has pledged to challenge the city council's housing department over what he sees as an increasingly disproportionate number of offenders being housed in his constituency.
Two years ago, the Evening News revealed that the area already contained the highest concentration of sex offenders per head of population in Scotland – and the number has since increased by 17 per cent to 92.
Mr Chisholm said: "Sex offenders need to be housed somewhere but it's important to spread them evenly throughout the city and avoid a disproportionate build-up in one area.
"I will be taking this matter up with the housing department."
The largest rise in the city was in the Pentlands policing zone, where the number of sex offenders living in the area has increased by nearly 50 per cent from 41 to 77.
Edinburgh Pentlands MSP David McLetchie said: "My concern with all of this moving around would be the potential for sex offenders to slip through the net, with the constant moving making it difficult to keep track of them. I'd also be concerned that the places that they're moving to may be less secure than the address that they were originally released into."
Only one in seven sex offenders on the register is currently in prison, with the remainder being managed in the community. Around a third of offenders are subject to licensing conditions or sexual offences prevention orders (SOPOs) forbidding them from living in certain areas, but the remainder are free to move around.
A police spokesman maintained there was no policy or concerted effort to move RSOs from central Edinburgh to other areas.
A spokesman said: "RSOs have the same rights as any member of the public to bid for council housing stock in Edinburgh.
"However, Edinburgh council do ensure that where sex offenders are accommodated in council housing, they are not placed near to victims and there is communication between the other key agencies."
Of the sex offenders currently being monitored by Lothian and Borders Police, 47 per cent live in social rented housing managed by local councils or housing associations, and 53 per cent live in owner occupied, privately rented, or friend and family accommodation.
The spokesman added: "Offenders are subject to pre-arranged home visits by police offender management units on a regular basis, and risk assessment is conducted on an ongoing basis."