When you need to pick a way to search through a graph, you might wonder whether to use Depth-First Search (DFS) or Breadth-First Search (BFS). Your choice can change how well the algorithm works. Sometimes, DFS can be the better option. Let’s look at a few reasons why.

Better Space Use
One big reason to choose DFS is that it uses less memory in some graphs. DFS uses a stack to keep track of nodes. This stack can be smaller, needing only space for the deepest part of the graph, which we call $O(h)$.

On the other hand, BFS uses a queue and needs to remember all the nodes at the same level, which takes more space—$O(w)$, where $w$ is the widest part of the graph. If your graph has many branches but is not very deep, DFS can save a lot of memory.

Searching Deep Solutions
If you're dealing with large graphs where the answers are deep down, DFS can be better. For example, in puzzles or video games, if you know the solution is deeper, DFS quickly finds it without checking all the easier options first.

Imagine you are in a maze where the exit is far down. With DFS, you can dive straight into the maze, finding paths to the exit more quickly.

Good for Finding Connections or Cycles
When you only want to check one branch of the graph at a time, DFS is great. If you need to find all connected parts or look for cycles (loops) in a graph, DFS is pretty simple to use. Each time you go down a path, you can mark nodes as "visited," which helps you avoid checking them again. While BFS works too, it requires more complicated tracking.

Backtracking Problems
DFS is super helpful when you need to try different options, like solving puzzles such as Sudoku or arranging queens on a chessboard. DFS explores one option fully before going back and trying another. This way, building the algorithm is simpler, letting you focus on solving the problem rather than the details of using a queue.

Natural Fit for Recursive Problems
Some problems fit well with a recursive approach, just like DFS. Many tree and graph problems show nested relationships, similar to how DFS works. If your problem has these recursive traits, using DFS can make designing the solution easier. For instance, when navigating through files or understanding tree structures, DFS helps you explore everything in one branch before going back up.

Easier to Understand and Implement
Finally, DFS can be simpler to use and understand. With its straightforward nature, the code for recursive DFS is often cleaner and clearer. This is especially true when compared to the more complicated approach of BFS. So, if you’re in a hurry or aren’t familiar with a certain way to search, using DFS can make your life easier.

Summary
Here's a quick list of when DFS is the better choice over BFS:

• When saving memory is important and you're working with big or deep graphs.
• When the answers lie deep within the graph, like in mazes.
• When you want to check for cycles or find connected parts of a graph.
• When the problem itself has a tree-like structure that matches well with recursion.
• When backtracking is a key part of solving the problem.
• When you want simple code that is easy to read and understand.

In conclusion, knowing the specific needs of your problem is essential to choosing the right way to explore a graph. DFS works well in many situations, especially when you need depth, save memory, and keep things simple.