diff --git a/src/graph/directed_graph.rs b/src/graph/directed_graph.rs
index 8c76610..653e164 100644
--- a/src/graph/directed_graph.rs
+++ b/src/graph/directed_graph.rs
@@ -137,33 +137,26 @@ impl DirectedGraph {
     pub fn dfs_recursive(
         &self,
         start: VertexIndex,
-        visited_set: &mut HashSet<usize>,
-        dfs_order: &mut Vec<usize>,
+        visited: &mut HashSet<usize>,
+        order: &mut Vec<usize>,
     ) -> Result<Vec<VertexIndex>, GraphError> {
-        // Check if the starting vertex exists in the graph
-        if self.vertices.get(start).is_none() {
-            return Err(GraphError::VertexNotFound);
-        }
+        // Ensure the starting vertex exists
+        let vertex = self.vertices.get(start).ok_or(GraphError::VertexNotFound)?;
 
         // Mark the current vertex as visited
-        visited_set.insert(start);
+        visited.insert(start);
 
-        // Recurse for each unvisited neighbor
-        for neighbor in self
-            .vertices
-            .get(start)
-            .unwrap()
-            .borrow()
-            .outgoing_edges
-            .iter()
-        {
-            if !visited_set.contains(&neighbor.borrow().index) {
-                self.dfs_recursive(neighbor.borrow().index, visited_set, dfs_order)?;
+        // Recurse for unvisited neighbors
+        for neighbor in &vertex.borrow().outgoing_edges {
+            let neighbor_index = neighbor.borrow().index;
+            if !visited.contains(&neighbor_index) {
+                self.dfs_recursive(neighbor_index, visited, order)?;
             }
         }
 
-        dfs_order.push(start);
-        Ok(dfs_order.to_vec())
+        // Record the vertex in the DFS order
+        order.push(start);
+        Ok(order.clone())
     }
 
     // /// TopoSort Pseudocode
diff --git a/src/graph/undirected_graph.rs b/src/graph/undirected_graph.rs
index b1c2e98..74a8dfe 100644
--- a/src/graph/undirected_graph.rs
+++ b/src/graph/undirected_graph.rs
@@ -121,29 +121,31 @@ impl UndirectedGraph {
     ///             mark w as explored
     ///             add w to the end of Q
     pub fn shortest_path_bfs(&self, start: usize) -> Result<HashMap<usize, usize>, GraphError> {
+        // Ensure the starting vertex exists
         if !self.vertices.contains_key(&start) {
             return Err(GraphError::VertexNotFound);
         }
-        let mut dist = HashMap::new();
+
+        let mut distances = HashMap::new();
         let mut queue = VecDeque::new();
 
-        // Start by setting the distance to the start node as 0
-        dist.insert(start, 0);
+        // Initialize the BFS
+        distances.insert(start, 0);
         queue.push_back(start);
 
         while let Some(current) = queue.pop_front() {
-            let current_distance = dist[&current];
+            let current_distance = distances[&current];
 
             for neighbor in self.get_neighbors(current) {
-                // If the neighbor hasn't been visited (i.e., it has no distance assigned)
-                if let std::collections::hash_map::Entry::Vacant(e) = dist.entry(neighbor) {
-                    e.insert(current_distance + 1);
+                // Add unvisited neighbors to the queue
+                distances.entry(neighbor).or_insert_with(|| {
                     queue.push_back(neighbor);
-                }
+                    current_distance + 1
+                });
             }
         }
 
-        Ok(dist)
+        Ok(distances)
     }
 
     /// Pseudocode undirect connected components