When connecting notebook to Homegroup, the Router icon and its association are lost. I spent several hours with support whose only fix was to restore my PC. This Registry modification fixes the issue (found on web):
Windows Registry Editor Version 5.00
; Corrects blank router icon
[HKEY_CLASSES_ROOT\NetworkExplorerPlugins\VEN_0033&DEV_0008&REV_01\DefaultIcon]
@="%SystemRoot%\\System32\\DDORes.dll,-2372"
; Removes "Network Map" shell extension from 'Network' explorer
[-HKEY_CLASSES_ROOT\NetworkExplorerPlugins\VEN_0033&DEV_0008&REV_01\shell]
; Removes "Network Map" shell extension from 'Devices and Printers' control panel
[-HKEY_LOCAL_MACHINE\SOFTWARE\Classes\DeviceDisplayObject\HardwareId\UMB#VEN_0033&DEV_0008&REV_01]