In the UI it would be nice to duplicate the selected connection, in the menu "With Selected". 

The copy would be set with the same name plus some suffix (_copy, _1, whatever) and it is useful for when you have a connection with all equal fields except something in a particular one. 
airflow/www/views.py
"""Update edges_to_add and edges_to_skip according to TaskGroups."""
        if isinstance(task_group, BaseOperator):
            return
        for target_id in task_group.downstream_group_ids:
            
            
            target_group = task_group_map[target_id]
            edges_to_add.add((task_group.downstream_join_id, target_group.upstream_join_id))
            for child in task_group.get_leaves():
                edges_to_add.add((child.task_id, task_group.downstream_join_id))
                for target in target_group.get_roots():
                    edges_to_skip.add((child.task_id, target.task_id))
                edges_to_skip.add((child.task_id, target_group.upstream_join_id))
            for child in target_group.get_roots():
                edges_to_add.add((target_group.upstream_join_id, child.task_id))
                edges_to_skip.add((task_group.downstream_join_id, child.task_id))
        
        
        
        for target_id in task_group.downstream_task_ids:
            edges_to_add.add((task_group.downstream_join_id, target_id))
            for child in task_group.get_leaves():
                edges_to_add.add((child.task_id, task_group.downstream_join_id))
                edges_to_skip.add((child.task_id, target_id))