Graph is basically divided into two broad categories :
- Directed Graph (Di- graph) – Where edges have direction.
- Undirected Graph – Where edges do not represent any directed
There are various ways to represent a Graph:-
- Adjacency Matrix
- Adjacency List
There are several other ways like incidence matrix, etc. but these two are most commonly used. Refer to Graph and its representations for the explanation of the Adjacency matrix and list.
In this article, we would be using Adjacency List to represent a graph because in most cases it has a certain advantage over the other representation.
Now Let’s see an example of Graph class-
The above example shows a framework of Graph class. We define two private variables i.e noOfVertices to store the number of vertices in the graph and AdjList, which stores an adjacency list of a particular vertex. We used a Map Object provided by ES6 in order to implement the Adjacency list. Where the key of a map holds a vertex and values hold an array of an adjacent node.
Now let’s implement functions to perform basic operations on the graph:
- addVertex(v) – It adds the vertex v as key to adjList and initializes its values with an array.
- addEdge(src, dest) – It adds an edge between the src and dest.
- In order to add edge, we get the adjacency list of the corresponding src vertex and add the dest to the adjacency list.
- printGraph() – It prints vertices and their adjacency list.
- Let’s see an example of a graph
Now we will use the graph class to implement the graph shown above:
We will implement the most common graph traversal algorithm:
Implementation of BFS and DFS:
- bfs(startingNode) – It performs Breadth First Search from the given startingNode
- In the above method, we have implemented the BFS algorithm. A Queue is used to keep the unvisited nodes
Let’s use the above method and traverse along with the graph
- The Diagram below shows the BFS on the example graph:
- Time Complexity: O(V+E), where V is the number of nodes and E is the number of edges.
- Auxiliary Space: O(V)
- dfs(startingNode) – It performs the Depth-first traversal on a graph
- In the above example, dfs(startingNode) is used to initialize a visited array, and DFSutil(vert, visited)
contains the implementation of DFS algorithm
Let’s use the above method to traverse along with the graph
- The Diagram below shows the DFS on the example graph
Time Complexity: O(V + E), where V is the number of vertices and E is the number of edges in the graph.
Auxiliary Space: O(V), since an extra visited array of size V is required.
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