diff --git a/src/hooks/usePolygon.js b/src/hooks/usePolygon.js
index 988213f7..21429d66 100644
--- a/src/hooks/usePolygon.js
+++ b/src/hooks/usePolygon.js
@@ -1444,22 +1444,23 @@ export const usePolygon = () => {
     startLines.forEach((startLine) => {
       // 현재 남아있는 line들로 그래프 생성
       const graph = {}
-      const edges = remainingLines
-        .filter((line2) => line2 !== startLine)
-        .map((line) => {
-          return [line.startPoint, line.endPoint]
-        })
 
-      for (const [p1, p2] of edges) {
+      for (const line of remainingLines.filter((line2) => line2 !== startLine)) {
+        const p1 = line.startPoint
+        const p2 = line.endPoint
         const key1 = pointToKey(p1)
         const key2 = pointToKey(p2)
         const distance = calcDistance(p1, p2)
+        const isStartLine = line.attributes?.isStart === true
 
         if (!graph[key1]) graph[key1] = []
         if (!graph[key2]) graph[key2] = []
 
-        graph[key1].push({ point: p2, distance })
-        graph[key2].push({ point: p1, distance })
+        // isStart가 아닌 line을 우선하도록 distance 조정
+        const adjustedDistance = isStartLine ? distance + 1000 : distance
+
+        graph[key1].push({ point: p2, distance: adjustedDistance, line })
+        graph[key2].push({ point: p1, distance: adjustedDistance, line })
       }
 
       const startPoint = { ...startLine.startPoint } // 시작점