It is possible to enable security for web parts from the Central Administration. Enabling or disabling this option will establish the webpart connections in the Page.
Navigate to Central Administration-> Application Management - > Application Security
In the "Security for WebPart Pages" page, Select the web application for which the web part connections need to be disabled,
In the Web part connections sections enable the Prevents users from creating connections between webparts, and helps to improve security and performance.
The webparts connections will not be enabled and the users are prevented from creating webpart connections
Before Enabling:
After Enabling:
