**Graph traversals** are methods for visiting all the vertices and edges of a graph in a systematic way.

**There are two primary methods for graph traversal:**

- Depth-First Search (DFS)
- Breadth-First Search (BFS).

## Depth-first search (DFS)

**DFS **works by starting at the root node of a graph and exploring all of the nodes in the left subgraph of the root node before moving on to the right subgraph. This process is then repeated for each of the child nodes of the root node, and so on.

â€¢ **DFS **is a good algorithm for finding all of the paths between two nodes in a graph, or for finding all of the nodes in a graph that are reachable from a given node. It is also a good algorithm for finding the topological order of a directed acyclic graph (DAG).

## Breadth-first search (BFS)

**Breadth-First Search (BFS)** is a graph traversal algorithm that explores a graph level by level, visiting all the neighbors of a given vertex before moving on to the next level.

â€¢ It is commonly used to explore and analyze the structure of a graph.

â€¢ BFS is applicable to both directed and undirected graphs.

**Note:** BFS uses a **queue data structure** (**FIFO**) to keep track of the vertices to be visited next.

## Algorithm for BFS:

**Select a starting vertex and enqueue it into a queue. Mark the starting vertex as visited.**

**While the queue is not empty, repeat the following steps:**

- Dequeue a vertex from the front of the queue.
- Enqueue all the unvisited neighbors of the dequeued vertex.
- Mark each visited neighbor as visited.

**Continue until the queue is empty, indicating that all reachable vertices have been visited.**

**For example:**

**Step 1:** Select a starting vertex and enqueue it into a queue.

**Step 2:** Dequeue a vertex from the front of the queue.

## Applications of BFS and DFS

BFS and DFS are both powerful algorithms with a variety of applications

** Here are a few examples:**

**BFS:**

- Finding the shortest path between two nodes in a graph
- Finding all of the nodes in a graph that are within a certain distance of the root node
- Finding the minimum spanning tree of a graph
- Testing for bipartiteness in a graph

**DFS:**

- Finding all of the paths between two nodes in a graph
- Finding all of the nodes in a graph that are reachable from a given node
- Finding the topological order of a directed acyclic graph (DAG)
- Detecting cycles in a graph
- Finding strongly connected components in a graph