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
nodes = []
        edges = []
        for dag, dependencies in SerializedDagModel.get_dag_dependencies().items():
            dag_node_id = f"dag:{dag}"
            nodes.append(self._node_dict(dag_node_id, dag, "dag"))
            for dep in dependencies:
                nodes.append(self._node_dict(dep.node_id, dep.dependency_id, dep.dependency_type))
                edges.extend(
                    [
                        {"u": f"dag:{dep.source}", "v": dep.node_id},
                        {"u": dep.node_id, "v": f"dag:{dep.target}"},
                    ]
                )
        self.nodes = nodes
        self.edges = edges
    @staticmethod
    def _node_dict(node_id, label, node_class):
        return {
            "id": node_id,
            "value": {"label": label, "rx": 5, "ry": 5, "class": node_class},
        }
class CustomPermissionModelView(PermissionModelView):