The default in LinkedIn is to send a notification to your 1st degree connections when you update your profile. If you want to disable this default, there are the steps as of July 11, 2018.
1) Login to your profile
2) In the top menu ribbon, find "Me" and click on the arrow to expand the menu. The "Me" is to the right of "Notifications" and to the left of "Work"
3) Click "Settings & Privacy"
4) Click "Privacy"
5) Scroll down and find "Sharing profile edits" which is below the sub-header "How others see your LinkedIn activity"
6) Click on the radio button so that is shows "No" and is not highlighted in blue
It should indicate "Saved" when you make this selection to "No".
Now your 1st degree connections will not be notified of any edits made to your LinkedIn profile.