Unconnected links represent a service that is not connected to some other host (e.g., an unused interface on a router). They are drawn as short lines extending out from the host. The first unconnected interface is drawn straight up ("12 noon") and the rest are evenly distributed around the host in a clockwise fashion. You can choose to display or not display the unconnected links.
Because unconnected links illustrate any service for which a device has an active monitor, you can use this feature to show a visual status of the services for which monitors are configured. For example, though the device is up (green), you may see that one of the unconnected links is down (red) and will know to check the device's services.