Fix: Unable to reconnect after deleting the connection between begin and parser #13868 (#13869)

### What problem does this PR solve?

Fix: Unable to reconnect after deleting the connection between begin and
parser #13868
### Type of change

- [x] Bug Fix (non-breaking change which fixes an issue)

web/src/pages/agent/canvas/node/handle.tsx

@@ -18,10 +18,20 @@ export function CommonHandle({
   const { visible, hideModal, showModal } = useSetModalState();
   const { canShowDropdown, setActiveDropdown, clearActiveDropdown } =
     useDropdownManager();
-  const { hasChildNode } = useGraphStore((state) => state);
+  const { hasDownstreamNode, hasUpstreamNode } = useGraphStore(
+    (state) => state,
+  );
   const isPipeline = useIsPipeline();
 
-  const isConnectable = !(isPipeline && hasChildNode(nodeId)); // Using useMemo will cause isConnectable to not be updated when the subsequent connection line is deleted
+  let isConnectable = true;
+
+  if (isPipeline) {
+    if (props.type === 'source') {
+      isConnectable = !hasDownstreamNode(nodeId);
+    } else if (props.type === 'target') {
+      isConnectable = !hasUpstreamNode(nodeId);
+    }
+  }
 
   const value = useMemo(
     () => ({

web/src/pages/agent/constant/index.tsx

@@ -692,6 +692,7 @@ export const RestrictedUpstreamMap = {
   [Operator.Loop]: [Operator.Begin],
   [Operator.LoopStart]: [Operator.Begin],
   [Operator.ExitLoop]: [Operator.Begin],
+  [Operator.PDFGenerator]: [Operator.Begin],
 };
 
 export const NodeMap = {

web/src/pages/agent/store.ts

@@ -115,7 +115,8 @@ export type RFState = {
   ) => void; // Deleting a condition of a classification operator will delete the related edge
   findAgentToolNodeById: (id: string | null) => string | undefined;
   selectNodeIds: (nodeIds: string[]) => void;
-  hasChildNode: (nodeId: string) => boolean;
+  hasDownstreamNode: (nodeId: string) => boolean;
+  hasUpstreamNode: (nodeId: string) => boolean;
 };
 
 // this is our useStore hook that we can use in our components to get parts of the store and call actions
@@ -469,7 +470,7 @@ const useGraphStore = create<RFState>()(
         const { updateNodeForm, edges, getOperatorTypeFromId } = get();
         if (sourceHandle) {
           // A handle will connect to multiple downstream nodes
-          let currentHandleTargets = edges
+          const currentHandleTargets = edges
             .filter(
               (x) =>
                 x.source === source &&
@@ -647,10 +648,14 @@ const useGraphStore = create<RFState>()(
           })),
         );
       },
-      hasChildNode: (nodeId) => {
+      hasDownstreamNode: (nodeId) => {
         const { edges } = get();
         return edges.some((edge) => edge.source === nodeId);
       },
+      hasUpstreamNode: (nodeId) => {
+        const { edges } = get();
+        return edges.some((edge) => edge.target === nodeId);
+      },
     })),
     { name: 'graph', trace: true },
   ),