In configuration->graphs, if graph contains items (including items in Y Min/Max axis which will be fixed in ZBX-6678) and user doesn't have write permissions on that host, graphs are not displayed. Although user is able to see the total number of graphs in host navigation bar. This is because there is no write permission check on related objects in CHostGeneral ($options['selectGraphs']).
This issue also applies to other objects like graphprototypes, triggers and screens.