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After installation, Jira Administrator can decide if the graph should be visible or hidden by default:

Issue Links Viewer > Settings [2.x] > Ability to show or hide graph by default.png

This setting could be overridden by user preferences - even if the graph is hidden by default, it could be displayed after pressing that big blue button "Show links graph":

Issue Links Viewer > Settings [2.x] > Graph hidden.png

Expanded graph could be hidden again with the use of the "Hide" option in the top right corner (above the mark):

Issue Links Viewer > Settings [2.x] > Graph visible.png