diff --git a/codes/python/chapter_graph/graph_adjacency_matrix.py b/codes/python/chapter_graph/graph_adjacency_matrix.py
index ecafbc564..80c8cc3f9 100644
--- a/codes/python/chapter_graph/graph_adjacency_matrix.py
+++ b/codes/python/chapter_graph/graph_adjacency_matrix.py
@@ -4,113 +4,88 @@ Created Time: 2023-02-23
 Author: krahets (krahets@163.com)
 """
 
-import sys
-from pathlib import Path
-
-sys.path.append(str(Path(__file__).parent.parent))
-from modules import Vertex, print_matrix
-
-
-class GraphAdjMat:
-    """基于邻接矩阵实现的无向图类"""
-
+class ImprovedGraphAdjMat:
     def __init__(self, vertices: list[int], edges: list[list[int]]):
-        """构造方法"""
-        # 顶点列表，元素代表“顶点值”，索引代表“顶点索引”
-        self.vertices: list[int] = []
-        # 邻接矩阵，行列索引对应“顶点索引”
-        self.adj_mat: list[list[int]] = []
-        # 添加顶点
+        self.vertex_map = {}  # 用于存储顶点值到索引的映射
+        self.vertices = []
+        self.adj_mat = []
+        
         for val in vertices:
             self.add_vertex(val)
-        # 添加边
-        # 请注意，edges 元素代表顶点索引，即对应 vertices 元素索引
+        
         for e in edges:
             self.add_edge(e[0], e[1])
 
-    def size(self) -> int:
-        """获取顶点数量"""
-        return len(self.vertices)
-
     def add_vertex(self, val: int):
-        """添加顶点"""
-        n = self.size()
-        # 向顶点列表中添加新顶点的值
+        if val in self.vertex_map:
+            return  # 如果顶点已存在，直接返回
+        
+        index = len(self.vertices)
+        self.vertex_map[val] = index
         self.vertices.append(val)
-        # 在邻接矩阵中添加一行
-        new_row = [0] * n
-        self.adj_mat.append(new_row)
-        # 在邻接矩阵中添加一列
-        for row in self.adj_mat:
-            row.append(0)
+        
+        # 更新邻接矩阵
+        if self.adj_mat:
+            for row in self.adj_mat:
+                row.append(0)
+        self.adj_mat.append([0] * (index + 1))
 
-    def remove_vertex(self, index: int):
-        """删除顶点"""
-        if index >= self.size():
-            raise IndexError()
-        # 在顶点列表中移除索引 index 的顶点
+    def remove_vertex(self, val: int):
+        if val not in self.vertex_map:
+            return  # 如果顶点不存在，直接返回
+        
+        index = self.vertex_map[val]
+        
+        # 更新顶点列表和映射
         self.vertices.pop(index)
-        # 在邻接矩阵中删除索引 index 的行
+        del self.vertex_map[val]
+        for v in self.vertices[index:]:
+            self.vertex_map[v] -= 1
+        
+        # 更新邻接矩阵
         self.adj_mat.pop(index)
-        # 在邻接矩阵中删除索引 index 的列
         for row in self.adj_mat:
             row.pop(index)
 
-    def add_edge(self, i: int, j: int):
-        """添加边"""
-        # 参数 i, j 对应 vertices 元素索引
-        # 索引越界与相等处理
-        if i < 0 or j < 0 or i >= self.size() or j >= self.size() or i == j:
-            raise IndexError()
-        # 在无向图中，邻接矩阵关于主对角线对称，即满足 (i, j) == (j, i)
+    def add_edge(self, v1: int, v2: int):
+        if v1 not in self.vertex_map or v2 not in self.vertex_map:
+            raise ValueError("Vertex not found")
+        
+        i, j = self.vertex_map[v1], self.vertex_map[v2]
         self.adj_mat[i][j] = 1
         self.adj_mat[j][i] = 1
 
-    def remove_edge(self, i: int, j: int):
-        """删除边"""
-        # 参数 i, j 对应 vertices 元素索引
-        # 索引越界与相等处理
-        if i < 0 or j < 0 or i >= self.size() or j >= self.size() or i == j:
-            raise IndexError()
+    def remove_edge(self, v1: int, v2: int):
+        if v1 not in self.vertex_map or v2 not in self.vertex_map:
+            raise ValueError("Vertex not found")
+        
+        i, j = self.vertex_map[v1], self.vertex_map[v2]
         self.adj_mat[i][j] = 0
         self.adj_mat[j][i] = 0
 
     def print(self):
-        """打印邻接矩阵"""
         print("顶点列表 =", self.vertices)
         print("邻接矩阵 =")
-        print_matrix(self.adj_mat)
+        for row in self.adj_mat:
+            print(row)
 
+# 使用示例
+graph = ImprovedGraphAdjMat([1, 3, 2, 5, 4], [[1, 3], [1, 5], [3, 2], [2, 5], [2, 4], [5, 4]])
+print("\n初始化后，图为")
+graph.print()
 
-"""Driver Code"""
-if __name__ == "__main__":
-    # 初始化无向图
-    # 请注意，edges 元素代表顶点索引，即对应 vertices 元素索引
-    vertices = [1, 3, 2, 5, 4]
-    edges = [[0, 1], [0, 3], [1, 2], [2, 3], [2, 4], [3, 4]]
-    graph = GraphAdjMat(vertices, edges)
-    print("\n初始化后，图为")
-    graph.print()
+graph.add_edge(1, 2)
+print("\n添加边 1-2 后，图为")
+graph.print()
 
-    # 添加边
-    # 顶点 1, 2 的索引分别为 0, 2
-    graph.add_edge(0, 2)
-    print("\n添加边 1-2 后，图为")
-    graph.print()
+graph.remove_edge(1, 3)
+print("\n删除边 1-3 后，图为")
+graph.print()
 
-    # 删除边
-    # 顶点 1, 3 的索引分别为 0, 1
-    graph.remove_edge(0, 1)
-    print("\n删除边 1-3 后，图为")
-    graph.print()
+graph.add_vertex(6)
+print("\n添加顶点 6 后，图为")
+graph.print()
 
-    # 添加顶点
-    graph.add_vertex(6)
-    print("\n添加顶点 6 后，图为")
-    graph.print()
-
-    # 删除顶点
-    # 顶点 3 的索引为 1
-    graph.remove_vertex(1)
-    print("\n删除顶点 3 后，图为")
-    graph.print()
+graph.remove_vertex(3)
+print("\n删除顶点 3 后，图为")
+graph.print()