Implementation of Graph in JavaScript

Difficulty Level : Medium
Last Updated : 18 Sep, 2020

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

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 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 Lets see an example of Graph class-

Java

// 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 variable i.e noOfVertices to store the number of vertices in the graph and AdjList, which stores a adjacency list of a particular vertex. We used a Map Object provided by ES6 in order to implement Adjacency list. Where key of a map holds a vertex and values holds 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 initialize its values with an array.

Java

// 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.

Java

// 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 its adjacency list.

Java

// 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);
    }
}

Lets see an example of a graph

Graph Example

Now we will use the graph class to implement the graph shown above:

Java

// 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

Java

// 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 element
    while (!q.isEmpty()) {
        // get the element from the queue
        var getQueueElement = q.dequeue();
 
        // passing the current vertex to callback funtion
        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
Lets use the above method and traverse along the graph

Java

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

The Diagram below shows the BFS on the example graph:

BFS on Graph

dfs(startingNode) – It performs the Depth first traversal on a graph

Java

// 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
Lets use the above method to traverse along the graph

Java

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

The Diagram below shows the DFS on the example graph

DFS on Graph

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