Given an undirected graph, the task is to check if the given graph is connected or not using DFS.

A connected graph is a graph that is connected in the sense of a topological space, i.e., there is always a path from any node to any other node in the graph. A graph that is not connected is said to be disconnected.

**Examples:**

Input:

Output:Graph is connected

Input:

Output:Graph is disconnected

**Approach:**

- Take a boolean visited [] array.
- Start DFS(Depth First Search) from any of the vertexes and mark the visited vertices as True in the visited[] array.
- After completion of DFS check if all the vertices in the visited [] array is marked as True.
- If yes then the graph is connected, or else the graph is not connected or disconnected.

**Code:**

## Java

`// Java Program to check if ` `// an undirected graph is connected or not` `// using DFS` ` ` `import` `java.util.*; ` ` ` `public` `class` `checkConnectivity {` ` ` ` ` `// Graph class` ` ` `static` `class` `Graph{` ` ` ` ` `int` `vertices;` ` ` `// Linked list for adjacency list of a vertex` ` ` `LinkedList<Integer> adjacencyList [];` ` ` ` ` `@SuppressWarnings` `(` `"unchecked"` `)` ` ` `public` `Graph(` `int` `vertices)` ` ` `{` ` ` `this` `.vertices = vertices;` ` ` `adjacencyList = ` `new` `LinkedList[vertices];` ` ` ` ` `for` `(` `int` `i = ` `0` `; i<vertices ; i++) ` ` ` `{` ` ` `adjacencyList[i] = ` `new` `LinkedList<>();` ` ` `}` ` ` `}` ` ` ` ` `// Function for adding edges` ` ` `public` `void` `addEdge(` `int` `source, ` `int` `dest)` ` ` `{` ` ` `adjacencyList.addFirst(dest);` ` ` `adjacencyList[dest].addFirst(source);` ` ` `}` ` ` `}` ` ` ` ` `// Function to check if the graph is connected or not` ` ` `public` `void` `isConnected(Graph graph){` ` ` ` ` `int` `vertices = graph.vertices;` ` ` `LinkedList<Integer> adjacencyList [] = graph.adjacencyList;` ` ` ` ` `// Take a boolean visited array` ` ` `boolean` `[] visited = ` `new` `boolean` `[vertices];` ` ` ` ` `// Start the DFS from vertex 0` ` ` `DFS(` `0` `, adjacencyList, visited);` ` ` ` ` `// Check if all the vertices are visited` ` ` `// Set connected to False if one node is unvisited` ` ` `boolean` `connected = ` `true` `;` ` ` ` ` `for` `(` `int` `i = ` `0` `; i <visited.length ; i++) {` ` ` `if` `(!visited[i]){` ` ` `connected = ` `false` `;` ` ` `break` `;` ` ` `}` ` ` `}` ` ` ` ` `if` `(connected){` ` ` `System.out.println(` `"Graph is connected"` `);` ` ` `}` `else` `{` ` ` `System.out.println(` `"Graph is disconnected"` `);` ` ` `}` ` ` `}` ` ` ` ` `public` `void` `DFS(` `int` `source, LinkedList<Integer> adjacencyList [], ` `boolean` `[] visited){` ` ` ` ` `// Mark the vertex visited as True` ` ` `visited = ` `true` `;` ` ` ` ` `// Travel the adjacent neighbours` ` ` `for` `(` `int` `i = ` `0` `; i <adjacencyList.size() ; i++) {` ` ` ` ` `int` `neighbour = adjacencyList.get(i);` ` ` ` ` `if` `(visited[neighbour]==` `false` `){` ` ` ` ` `// Call DFS from neighbour` ` ` `DFS(neighbour, adjacencyList, visited);` ` ` `}` ` ` `}` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `main(String[] args) {` ` ` ` ` `// Given graph 1` ` ` `Graph graph = ` `new` `Graph(` `5` `);` ` ` `graph.addEdge(` `0` `,` `1` `);` ` ` `graph.addEdge(` `0` `,` `4` `);` ` ` `graph.addEdge(` `1` `,` `4` `);` ` ` `graph.addEdge(` `1` `,` `3` `);` ` ` `graph.addEdge(` `3` `,` `4` `);` ` ` `graph.addEdge(` `2` `,` `1` `);` ` ` `graph.addEdge(` `2` `,` `3` `);` ` ` ` ` `// Check if it's connected` ` ` `System.out.print(` `"Graph 1:- "` `);` ` ` ` ` `checkConnectivity c = ` `new` `checkConnectivity();` ` ` `c.isConnected(graph);` ` ` ` ` `// Given graph 2` ` ` `graph = ` `new` `Graph(` `5` `);` ` ` `graph.addEdge(` `0` `,` `1` `);` ` ` `graph.addEdge(` `0` `,` `4` `);` ` ` `graph.addEdge(` `1` `,` `4` `);` ` ` `graph.addEdge(` `1` `,` `3` `);` ` ` `graph.addEdge(` `3` `,` `4` `);` ` ` ` ` `// Check if it's connected` ` ` `System.out.print(` `"Graph 2:- "` `);` ` ` ` ` `c = ` `new` `checkConnectivity();` ` ` `c.isConnected(graph);` ` ` `}` `}` |

**Output**

Graph 1:- Graph is connected Graph 2:- Graph is disconnected

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