RUN»REGEDIT
Computer\HKEY_LOCAL_MACHINE\SOFWARE\Microsoft\Windows\ CurrentVersion\Explorer\Desktop\NameSpace
In the NameSpace folder, there will be a folder (key) with the name
{B4FB3F98-C1EA-428d-A78A-D1F5659CBA93}
The value of the default item should be “Other users”. This is the registry entry Homegroup icon. Delete the folder from the registry.
In the NameSpace folder, there will be a folder (key) with the name
{031E4825-7B94-4dc3-B131-E946B44C8DD5}
The value of the default item should be “Libraries”. This is the registry entry This is the Libraries icon. Delete the folder from the registry.
Go to your desktop and hit F5, the icons should disappear. Libraries and Homegroup have retained their full functionality as far as I can tell, so it hasn’t appeared to have affected the programs at all.