Implementation of Graph in JavaScript

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:- 

• 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- 

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);
}

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

// 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)
{
        // get 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);
    }
}

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

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();

• 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

// 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);
            }
        }
    }
}

• Let’s see an example of a graph
  

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

JavaScript

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

Graph Traversal

We will implement the most common graph traversal algorithm: 

• Breadth First Traversal for a Graph
• Depth First Traversal for a Graph

Implementation of BFS and DFS: 

• bfs(startingNode) – It performs Breadth First Search from the given startingNode

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

• 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.