# Implementation of Graph in JavaScript

• Difficulty Level : Medium
• Last Updated : 22 Jun, 2022

In this article, we would be implementing the Graph data structure in JavaScript. The graph is a non-linear data structure. Graph G contains a set of vertices V and a set of Edges E. Graph has lots of applications in computer science.
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:-

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-

## JavaScript

 `// create a graph class``class Graph {``    ``// defining vertex array and``    ``// adjacent list``    ``constructor(noOfVertices)``    ``{``        ``this``.noOfVertices = noOfVertices;``        ``this``.AdjList = ``new` `Map();``    ``}` `    ``// functions to be implemented` `    ``// addVertex(v)``    ``// addEdge(v, w)``    ``// printGraph()` `    ``// bfs(v)``    ``// dfs(v)``}`

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.

## JavaScript

 `// add vertex to the graph``addVertex(v)``{``    ``// initialize the adjacent list with a``    ``// null array``    ``this``.AdjList.set(v, []);``}`

• addEdge(src, dest) – It adds an edge between the src and dest

## JavaScript

 `// add edge to the graph``addEdge(v, w)``{``    ``// get the list for vertex v and put the``    ``// vertex w denoting edge between v and w``    ``this``.AdjList.get(v).push(w);` `    ``// Since graph is undirected,``    ``// add an edge from w to v also``    ``this``.AdjList.get(w).push(v);``}`

• 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.

## JavaScript

 `// Prints the vertex and adjacency list``printGraph()``{``    ``// get all the vertices``    ``var` `get_keys = ``this``.AdjList.keys();` `    ``// iterate over the vertices``    ``for` `(``var` `i of get_keys)``{``        ``// great the corresponding adjacency list``        ``// for the vertex``        ``var` `get_values = ``this``.AdjList.get(i);``        ``var` `conc = ``""``;` `        ``// iterate over the adjacency list``        ``// concatenate the values into a string``        ``for` `(``var` `j of get_values)``            ``conc += j + ``" "``;` `        ``// print the vertex and its adjacency list``        ``console.log(i + ``" -> "` `+ conc);``    ``}``}`

• Let’s see an example of a graph Now we will use the graph class to implement the graph shown above:

## JavaScript

 `// Using the above implemented graph class``var` `g = ``new` `Graph(6);``var` `vertices = [ ``'A'``, ``'B'``, ``'C'``, ``'D'``, ``'E'``, ``'F'` `];` `// adding vertices``for` `(``var` `i = 0; i < vertices.length; i++) {``    ``g.addVertex(vertices[i]);``}` `// adding edges``g.addEdge(``'A'``, ``'B'``);``g.addEdge(``'A'``, ``'D'``);``g.addEdge(``'A'``, ``'E'``);``g.addEdge(``'B'``, ``'C'``);``g.addEdge(``'D'``, ``'E'``);``g.addEdge(``'E'``, ``'F'``);``g.addEdge(``'E'``, ``'C'``);``g.addEdge(``'C'``, ``'F'``);` `// prints all vertex and``// its adjacency list``// A -> B D E``// B -> A C``// C -> B E F``// D -> A E``// E -> A D F C``// F -> E C``g.printGraph();`

Graph Traversal

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

## JavaScript

 `// function to performs BFS``bfs(startingNode)``{` `    ``// create a visited object``    ``var` `visited = {};` `    ``// Create an object for queue``    ``var` `q = ``new` `Queue();` `    ``// add the starting node to the queue``    ``visited[startingNode] = ``true``;``    ``q.enqueue(startingNode);` `    ``// loop until queue is empty``    ``while` `(!q.isEmpty()) {``        ``// get the element from the queue``        ``var` `getQueueElement = q.dequeue();` `        ``// passing the current vertex to callback function``        ``console.log(getQueueElement);` `        ``// get the adjacent list for current vertex``        ``var` `get_List = ``this``.AdjList.get(getQueueElement);` `        ``// loop through the list and add the element to the``        ``// queue if it is not processed yet``        ``for` `(``var` `i ``in` `get_List) {``            ``var` `neigh = get_List[i];` `            ``if` `(!visited[neigh]) {``                ``visited[neigh] = ``true``;``                ``q.enqueue(neigh);``            ``}``        ``}``    ``}``}`

• 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

## JavaScript

 `// prints``// BFS``// A B D E C F``console.log(``"BFS"``);``g.bfs(``'A'``);`

• 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

## JavaScript

 `// Main DFS method``dfs(startingNode)``{` `    ``var` `visited = {};` `    ``this``.DFSUtil(startingNode, visited);``}` `// Recursive function which process and explore``// all the adjacent vertex of the vertex with which it is called``DFSUtil(vert, visited)``{``    ``visited[vert] = ``true``;``    ``console.log(vert);` `    ``var` `get_neighbours = ``this``.AdjList.get(vert);` `    ``for` `(``var` `i ``in` `get_neighbours) {``        ``var` `get_elem = get_neighbours[i];``        ``if` `(!visited[get_elem])``            ``this``.DFSUtil(get_elem, visited);``    ``}``}`

• 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

## JavaScript

 `// prints``// DFS``// A B C E D F``console.log(``"DFS"``);``g.dfs(``'A'``);`

• 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.

This article is contributed by Sumit Ghosh. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.