CPP

Detect cycle in an undirected graph

//function snippet using DFS
bool dfs(int node,int parent, vector<int> adj[], vector<bool> &check)
    {
        check[node] = true;
        for(auto n1 :adj[node])
        {
            if(!check[n1])
                if(dfs(n1, node, adj, check)) return true;
            else if(n1 != parent) return true;
        }
        return false;
    }
    
    bool isCycle(int V, vector<int> adj[]) {
        vector<bool>check(V, 0);
        //for all the commponents 
        for(int i =0; i < V; i++)
        {
            if(!check[i])
                if (dfs(i, -1, adj, check)) return true;// if a component has a cycle then graph has a cycle 
        }
        return false;
    }

Detect cycle in an undirected graph

// A Java Program to detect cycle in an undirected graph
import java.io.*;
import java.util.*;
// This class represents a
// directed graph using adjacency list
// representation
class Graph {
 
    // No. of vertices
    private int V;
 
    // Adjacency List Representation
    private LinkedList<Integer> adj[];
 
    // Constructor
    Graph(int v)
    {
        V = v;
        adj = new LinkedList[v];
        for (int i = 0; i < v; ++i)
            adj[i] = new LinkedList();
    }
 
    // Function to add an edge
    // into the graph
    void addEdge(int v, int w)
    {
        adj[v].add(w);
        adj[w].add(v);
    }
 
    // A recursive function that
    // uses visited[] and parent to detect
    // cycle in subgraph reachable
    // from vertex v.
    Boolean isCyclicUtil(int v, Boolean visited[],
                         int parent)
    {
        // Mark the current node as visited
        visited[v] = true;
        Integer i;
 
        // Recur for all the vertices
        // adjacent to this vertex
        Iterator<Integer> it = adj[v].iterator();
        while (it.hasNext()) {
            i = it.next();
 
            // If an adjacent is not
            // visited, then recur for that
            // adjacent
            if (!visited[i]) {
                if (isCyclicUtil(i, visited, v))
                    return true;
            }
 
            // If an adjacent is visited
            // and not parent of current
            // vertex, then there is a cycle.
            else if (i != parent)
                return true;
        }
        return false;
    }
 
    // Returns true if the graph
    // contains a cycle, else false.
    Boolean isCyclic()
    {
 
        // Mark all the vertices as
        // not visited and not part of
        // recursion stack
        Boolean visited[] = new Boolean[V];
        for (int i = 0; i < V; i++)
            visited[i] = false;
 
        // Call the recursive helper
        // function to detect cycle in
        // different DFS trees
        for (int u = 0; u < V; u++) {
 
            // Don't recur for u if already visited
            if (!visited[u])
                if (isCyclicUtil(u, visited, -1))
                    return true;
        }
 
        return false;
    }
 
    // Driver method to test above methods
    public static void main(String args[])
    {
 
        // Create a graph given
        // in the above diagram
        Graph g1 = new Graph(5);
        g1.addEdge(1, 0);
        g1.addEdge(0, 2);
        g1.addEdge(2, 1);
        g1.addEdge(0, 3);
        g1.addEdge(3, 4);
        if (g1.isCyclic())
            System.out.println("Graph
                             contains cycle");
        else
            System.out.println("Graph
                        doesn't contains cycle");
 
        Graph g2 = new Graph(3);
        g2.addEdge(0, 1);
        g2.addEdge(1, 2);
        if (g2.isCyclic())
            System.out.println("Graph
                             contains cycle");
        else
            System.out.println("Graph
                        doesn't contains cycle");
    }
}
// This code is contributed by Aakash Hasija

Detect cycle in an undirected graph python

# Python Program to detect cycle in an undirected graph
from collections import defaultdict
 
# This class represents a undirected
# graph using adjacency list representation
 
 
class Graph:
 
    def __init__(self, vertices):
 
        # No. of vertices
        self.V = vertices  # No. of vertices
 
        # Default dictionary to store graph
        self.graph = defaultdict(list)
 
    # Function to add an edge to graph
    def addEdge(self, v, w):
 
        # Add w to v_s list
        self.graph[v].append(w)
 
        # Add v to w_s list
        self.graph[w].append(v)
 
    # A recursive function that uses
    # visited[] and parent to detect
    # cycle in subgraph reachable from vertex v.
    def isCyclicUtil(self, v, visited, parent):
 
        # Mark the current node as visited
        visited[v] = True
 
        # Recur for all the vertices
        # adjacent to this vertex
        for i in self.graph[v]:
 
            # If the node is not
            # visited then recurse on it
            if visited[i] == False:
                if(self.isCyclicUtil(i, visited, v)):
                    return True
            # If an adjacent vertex is
            # visited and not parent
            # of current vertex,
            # then there is a cycle
            elif parent != i:
                return True
 
        return False
 
    # Returns true if the graph
    # contains a cycle, else false.
 
    def isCyclic(self):
 
        # Mark all the vertices
        # as not visited
        visited = [False]*(self.V)
 
        # Call the recursive helper
        # function to detect cycle in different
        # DFS trees
        for i in range(self.V):
 
            # Don't recur for u if it
            # is already visited
            if visited[i] == False:
                if(self.isCyclicUtil
                   (i, visited, -1)) == True:
                    return True
 
        return False
 
 
# Create a graph given in the above diagram
g = Graph(5)
g.addEdge(1, 0)
g.addEdge(1, 2)
g.addEdge(2, 0)
g.addEdge(0, 3)
g.addEdge(3, 4)
 
if g.isCyclic():
    print("Graph contains cycle")
else:
    print("Graph does not contain cycle ")
g1 = Graph(3)
g1.addEdge(0, 1)
g1.addEdge(1, 2)
 
 
if g1.isCyclic():
    print("Graph contains cycle")
else:
    print("Graph does not contain cycle ")
 
# This code is contributed by Neelam Yadav