Members deleting other members posts

Something I've noticed is that when a post is placed on the timeline or a member posts a photo etc other members get the option to edit or delete. 

I think that this may cause an issue with our members is this something that can be stopped ?

Go to your Admin > Settings > Member Levels > click on Standard Actions > and disable the DELETION you need..

Please note, since lots of Mods can be installed within D7, each mode has its own DELETION/EDIT option, so you will need to deactivate the DELETION for the desired Mod.. 

Also it maybe that you are looking from admin account, admin can delete almost any content.