Mr Abdi was found seriously injured within Abercorn Avenue in the early hours on Sunday morning and was rushed to the Royal Infirmary of Edinburgh, where he later passed away.
The cordon has now been reduced although uniformed officers continue to provide a high-visibility presence in the area to engage with local residents and offer reassurance to the community.
Since launching the enquiry, police have received a high volume of calls from the public which are now being processed by Police Scotland’s Specialist Crime Division.
Officers want to thank those who have already come forward but are continuing to urge anyone with information that can assist their enquiries to get in touch.
Chief Inspector Mark Patterson, of Police Scotland’s Edinburgh Division, said:- “It is firstly important to remember that incidents like this are incredibly rare within Edinburgh, and the Capital remains a safe place to live, work and visit.
“However, when such events do occur, it can have a significant impact on the local community and we continue to deploy a large number of officers to the Willowbrae area to speak with residents and address their concerns. In addition, people can approach these officers and pass on information to them.
“I would like to extend my sincere thanks to those who live and work in the area for all of their assistance, patience, support and understanding while the cordons were in place. They can rest assured that Police Scotland is working tirelessly to find those responsible and bring a sense of normality back to the area.
“We remain keen to speak with anyone who saw anything suspicious in the general area surrounding Abercorn Avenue and Paisley Crescent in the early hours of Sunday morning or who saw vehicles travelling at speed or being driven erratically.
“Anyone who believes they have information that can help with our ongoing investigation, and who has yet to speak with our officers, should contact police immediately.”