What Is Cyclic and Acyclic Graph in Data Structure?


Angela Bailey

A graph is a non-linear data structure that consists of a set of nodes (also known as vertices) and a set of edges that connect these nodes. Graphs are used to represent relationships between objects, such as web pages, social media connections, or network devices. In this article, we will explore the concepts of cyclic and acyclic graphs in data structures.

Cyclic Graph

A cyclic graph is a type of graph where at least one path exists that starts from a node and eventually leads back to the same node. In other words, it contains cycles or loops. These cycles can be of any length and can involve any number of nodes.


Consider the following graph:

   / \
  B - C
  • Node A is connected to nodes B and C.
  • Node B is connected to node C.
  • Node C is connected to nodes A and B.

This graph is cyclic because there exists a cycle: A → B → C → A.

Acyclic Graph

An acyclic graph, on the other hand, is a type of graph that does not contain any cycles. It is also referred to as a directed acyclic graph (DAG) when all edges have directions assigned to them.


Consider the following directed acyclic graph:

    A     D
   / \   / \
  B   C E   F
  • Node A is connected to nodes B and C.
  • Node D is connected to nodes E and F.
  • Nodes B, C, E, and F have no outgoing edges.

This graph is acyclic because there are no cycles. It is a directed graph that does not contain any paths leading back to any of its nodes.


The concepts of cyclic and acyclic graphs have various applications in computer science and real-world scenarios. Some common applications include:

  • Dependency resolution: Acyclic graphs are commonly used to represent dependencies between tasks or modules, where cycles would imply circular dependencies.
  • Topological sorting: Acyclic graphs can be sorted in a specific order called a topological order. This order is useful for scheduling tasks or determining the sequence of events.
  • Graph algorithms: The presence of cycles can affect the behavior and efficiency of graph algorithms. Detecting and handling cycles is crucial in many graph-related problems.


In summary, cyclic graphs contain at least one cycle or loop, while acyclic graphs do not contain any cycles. Understanding these concepts is essential when working with graph data structures and solving related problems. The applications of cyclic and acyclic graphs extend beyond the realm of data structures and find relevance in various areas of computer science.

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