refactor: Extend shared graph workspace for undirected/weighted reuse

- Move weightedAdjacency/edgeList into graph.js as core helpers
  (shortestPath.js re-exports them; its imports are unchanged).
- floating-edge: draw the mid-edge travel arrow only when a direction
  is set (travelTo), so undirected uses get no arrow; add a 'reject'
  edge color.
- graph-menu: add a hideDirected prop to omit the Directed toggle.

Author: TamimEhsan

src/components/graph/floating-edge.jsx

@@ -16,6 +16,7 @@ const STROKE = {
     tree: '#f59e0b',
     path: '#10b981',
     negcycle: '#f43f5e',
+    reject: '#cbd5e1',
     normal: '#64748b',
 };
 
@@ -64,7 +65,9 @@ export default function FloatingEdge({ id, source, target, markerEnd, data }) {
     // doesn't grow during traversal; state is conveyed by color + the mid arrow.
     const strokeWidth = 2;
 
-    const showTravelArrow = state === 'tree' || state === 'path';
+    // only show the direction arrow when a travel direction was set (BFS/DFS/SSSP);
+    // undirected uses like MST leave travelTo null -> no arrow
+    const showTravelArrow = (state === 'tree' || state === 'path') && travelTo != null;
     const mx = (sx + ex) / 2;
     const my = (sy + ey) / 2;
     const deg = (Math.atan2(uy, ux) * 180) / Math.PI;

src/components/graph/graph-menu.jsx

@@ -22,6 +22,7 @@ export default function GraphMenu({
     algorithms,
     presets,
     weighted = false,
+    hideDirected = false,
     disabled,
     onDirectedChange,
     onAlgorithmChange,
@@ -44,7 +45,9 @@ export default function GraphMenu({
                     <span className="text-xs font-medium text-gray-500 uppercase tracking-wider">Config</span>
                     <div className="h-px flex-1 bg-gray-300" />
                 </div>
-                <CustomToggle title="Directed" onCheckedChange={onDirectedChange} disabled={disabled} />
+                {!hideDirected && (
+                    <CustomToggle title="Directed" onCheckedChange={onDirectedChange} disabled={disabled} />
+                )}
                 <CustomSelect
                     title="Algorithm"
                     options={algorithms}

src/lib/algorithms/graph.js

@@ -90,6 +90,32 @@ export function adjacency(edges, directed) {
     return adj;
 }
 
+// Weighted adjacency: id -> [{ node, edge, weight }] (used by shortest-path / MST).
+export function weightedAdjacency(edges, directed) {
+    const adj = {};
+    const add = (a, b, id, w) => { (adj[a] = adj[a] || []).push({ node: b, edge: id, weight: w }); };
+    for (const e of edges) {
+        const w = e.data?.weight ?? 1;
+        add(e.source, e.target, e.id, w);
+        if (!directed) add(e.target, e.source, e.id, w);
+    }
+    for (const k of Object.keys(adj)) {
+        adj[k].sort((x, y) => (x.node < y.node ? -1 : x.node > y.node ? 1 : 0));
+    }
+    return adj;
+}
+
+// Flat weighted edge list: [{ u, v, w, id }] — both directions when undirected.
+export function edgeList(edges, directed) {
+    const list = [];
+    for (const e of edges) {
+        const w = e.data?.weight ?? 1;
+        list.push({ u: e.source, v: e.target, w, id: e.id });
+        if (!directed) list.push({ u: e.target, v: e.source, w, id: e.id });
+    }
+    return list;
+}
+
 // Reconstruct start->finish path actions from parent maps.
 function pathActions(parent, parentEdge, startId, endId) {
     const nodes = [];

src/lib/algorithms/shortestPath.js

@@ -6,9 +6,10 @@
 //   { type: 'status', text }       -> overlay status text
 // plus edge states 'relax' | 'tree' | 'path' | 'negcycle'.
 
-import { toFlow } from './graph';
+import { toFlow, weightedAdjacency, edgeList } from './graph';
 
-export { toFlow };
+// re-exported for back-compat with existing imports from this module
+export { toFlow, weightedAdjacency, edgeList };
 
 export const SP_PRESETS = [
     {
@@ -50,32 +51,6 @@ export const SP_PRESETS = [
     },
 ];
 
-// id -> [{ node, edge, weight }]
-export function weightedAdjacency(edges, directed) {
-    const adj = {};
-    const add = (a, b, id, w) => { (adj[a] = adj[a] || []).push({ node: b, edge: id, weight: w }); };
-    for (const e of edges) {
-        const w = e.data?.weight ?? 1;
-        add(e.source, e.target, e.id, w);
-        if (!directed) add(e.target, e.source, e.id, w);
-    }
-    for (const k of Object.keys(adj)) {
-        adj[k].sort((x, y) => (x.node < y.node ? -1 : x.node > y.node ? 1 : 0));
-    }
-    return adj;
-}
-
-// [{ u, v, w, id }] — both directions when undirected (for Bellman-Ford)
-export function edgeList(edges, directed) {
-    const list = [];
-    for (const e of edges) {
-        const w = e.data?.weight ?? 1;
-        list.push({ u: e.source, v: e.target, w, id: e.id });
-        if (!directed) list.push({ u: e.target, v: e.source, w, id: e.id });
-    }
-    return list;
-}
-
 function pathActions(parent, parentEdge, startId, endId) {
     const nodes = [];
     const edgeSteps = [];