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
if task.depends_on_past:
                node['depends_on_past'] = task.depends_on_past
            if task.start_date:
                
                node['start_ts'] = int(task.start_date.timestamp())
                if task.end_date:
                    
                    node['end_ts'] = int(task.end_date.timestamp())
            if task.extra_links:
                node['extra_links'] = task.extra_links
            return node
        return {
            'name': '[DAG]',
            'children': [recurse_nodes(t, set()) for t in dag.roots],
            'instances': [dag_runs.get(d) or {'execution_date': d.isoformat()} for d in dates],
        }
    @expose('/tree')
    @auth.has_access(
        [
            (permissions.ACTION_CAN_READ, permissions.RESOURCE_DAG),
            (permissions.ACTION_CAN_READ, permissions.RESOURCE_TASK_INSTANCE),
            (permissions.ACTION_CAN_READ, permissions.RESOURCE_TASK_LOG),
        ]
    )
    @gzipped  
    @action_logging  
    def tree(self):
        """Get Dag as tree."""
        dag_id = request.args.get('dag_id')
        dag = current_app.dag_bag.get_dag(dag_id)