The Connector tool (Ctrl+F2 or the 'o' key) is used to create and reroute connectors.
Connection point handles are shown while the mouse cursor is hovering over a non-connector object in the connector tool. They are shown at the center of objects. When creating a connector, if the connector is started or ended over a connection point, then the connector will be attached to that object. From then on the connector will be automatically rerouted whenever the attached object is moved.
A selected connector will show two endpoint handles. By clicking and dragging these, the connector can be rerouted and attached/detached from objects.
Once selected, a connector's stroke paint and stroke style can be modified. Here, it's possible to add arrows onto connectors.
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† Discusses the "avoid selected objects" and "ignore selected objects" features.
Copyright: This document is licensed as GPL v2. It incorporates text from: FLOSS Manuals (GPL v2); and Inkscape release notes for 0.43, 0.44, 0.48, and 1.1 (GPL v2).