To disable debugging, right-click on the edge and select Debug  No records from the context menu. Disabled debugging is indicated by the icon

If you want to disable debugging on multiple edges simultaneously, select the edges by left-clicking while holding down the Ctrl key first.

If you want to turn off debugging, you can click the Graph editor in any place outside the components and the edges, switch to the Properties tab and set the Debug mode attribute to false. This way you can turn off all debugging at a time.

Bug icons do not disappear, but edge debugging is not performed. If you disable debugging this way, it can be enabled back keeping the original configuration.

Alternatively, you can select Run  Debug Configurations…​ on the menu bar and check the Disable edge debugging option.