Python Program for Detect Cycle in a Directed Graph

In this article, we will learn about the solution to the problem statement given below.

Problem statement − We are given a directed graph, we need to check whether the graph contains a cycle or not. The output should be true if the given graph contains at least one cycle, otherwise false.

Now let’s observe the solution in the implementation below −

Example

# collections module
from collections import defaultdict
# class for creation of graphs
class Graph():
   # constructor
   def __init__(self, vertices):
      self.graph = defaultdict(list)
      self.V = vertices
   def addEdge(self, u, v):
      self.graph[u].append(v)
   def isCyclicUtil(self, v, visited, recStack):
      # Marking current node visited and addition to recursion stack
      visited[v] = True
      recStack[v] = True
      # if any neighbour is visited and in recStack then graph is cyclic in nature
      for neighbour in self.graph[v]:
         if visited[neighbour] == False:
            if self.isCyclicUtil(neighbour, visited, recStack) == True:
               return True
         elif recStack[neighbour] == True:
            return True
      # pop the node after the end of recursion
      recStack[v] = False
      return False
   # Returns true if graph is cyclic
   def isCyclic(self):
      visited = [False] * self.V
      recStack = [False] * self.V
      for node in range(self.V):
         if visited[node] == False:
            if self.isCyclicUtil(node, visited, recStack) == True:
               return True
      return False
g = Graph(4)
g.addEdge(0, 3)
g.addEdge(0, 2)
g.addEdge(3, 2)
g.addEdge(2, 0)
g.addEdge(1, 3)
g.addEdge(2, 1)
if g.isCyclic() == 1:
   print ("Graph is cyclic in nature")
else:
   print ("Graph is non-cyclic in nature")

Output

Graph is cyclic in nature

All the variables are declared in the local scope and their references are seen in the figure above.

Conclusion

In this article, we have learned about how we can make a Python Program to Detect Cycle in a Directed Graph