diff --git a/graphs/depth_first_search_2.py b/graphs/depth_first_search_2.py
index c932e7629..3072d527c 100644
--- a/graphs/depth_first_search_2.py
+++ b/graphs/depth_first_search_2.py
@@ -8,58 +8,58 @@ class Graph:
         self.vertex = {}
 
     # for printing the Graph vertices
-    def printGraph(self):
+    def print_graph(self) -> None:
         print(self.vertex)
-        for i in self.vertex.keys():
+        for i in self.vertex:
             print(i, " -> ", " -> ".join([str(j) for j in self.vertex[i]]))
 
     # for adding the edge between two vertices
-    def addEdge(self, fromVertex, toVertex):
+    def add_edge(self, from_vertex: int, to_vertex: int) -> None:
         # check if vertex is already present,
-        if fromVertex in self.vertex.keys():
-            self.vertex[fromVertex].append(toVertex)
+        if from_vertex in self.vertex:
+            self.vertex[from_vertex].append(to_vertex)
         else:
             # else make a new vertex
-            self.vertex[fromVertex] = [toVertex]
+            self.vertex[from_vertex] = [to_vertex]
 
-    def DFS(self):
+    def dfs(self) -> None:
         # visited array for storing already visited nodes
         visited = [False] * len(self.vertex)
 
         # call the recursive helper function
         for i in range(len(self.vertex)):
-            if visited[i] is False:
-                self.DFSRec(i, visited)
+            if not visited[i]:
+                self.dfs_recursive(i, visited)
 
-    def DFSRec(self, startVertex, visited):
+    def dfs_recursive(self, start_vertex: int, visited: list) -> None:
         # mark start vertex as visited
-        visited[startVertex] = True
+        visited[start_vertex] = True
 
-        print(startVertex, end=" ")
+        print(start_vertex, end=" ")
 
         # Recur for all the vertices that are adjacent to this node
-        for i in self.vertex.keys():
-            if visited[i] is False:
-                self.DFSRec(i, visited)
+        for i in self.vertex:
+            if not visited[i]:
+                self.dfs_recursive(i, visited)
 
 
 if __name__ == "__main__":
     g = Graph()
-    g.addEdge(0, 1)
-    g.addEdge(0, 2)
-    g.addEdge(1, 2)
-    g.addEdge(2, 0)
-    g.addEdge(2, 3)
-    g.addEdge(3, 3)
+    g.add_edge(0, 1)
+    g.add_edge(0, 2)
+    g.add_edge(1, 2)
+    g.add_edge(2, 0)
+    g.add_edge(2, 3)
+    g.add_edge(3, 3)
 
-    g.printGraph()
+    g.print_graph()
     print("DFS:")
-    g.DFS()
+    g.dfs()
 
     # OUTPUT:
-    # 0  ->  1 -> 2
-    # 1  ->  2
-    # 2  ->  0 -> 3
-    # 3  ->  3
+    # 0  ->  1 -> 2
+    # 1  ->  2
+    # 2  ->  0 -> 3
+    # 3  ->  3
     # DFS:
-    #  0 1 2 3
+    #  0 1 2 3