What Is Circular Graph in Data Structure?

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Scott Campbell

A circular graph is a data structure that represents a collection of nodes or vertices connected in a circular manner. In this type of graph, each node is connected to its adjacent nodes, forming a closed loop or cycle. Circular graphs are often used to model relationships or connections between different entities.

Properties of Circular Graphs

Circular graphs have several unique properties that distinguish them from other types of graphs:

  • Cyclic Nature: As mentioned earlier, the nodes in a circular graph are arranged in a cyclic manner, forming a closed loop or cycle.
  • Connectivity: Every node in a circular graph is connected to two other nodes – the previous node and the next node in the cycle.
  • No Isolated Nodes: Unlike some other types of graphs, circular graphs do not have isolated nodes. Each node is part of the cycle and has connections with other nodes.

Applications of Circular Graphs

Circular graphs find applications in various fields, including computer science, mathematics, and social sciences. Some common applications include:

  • Network Topology: Circular graphs are used to represent network topologies where each device is connected to its adjacent devices. Examples include ring networks and token ring networks.
  • Scheduling Problems: Circular graphs can be used to model scheduling problems where tasks or events need to be scheduled in a cyclic manner.
  • Social Networks: Circular graphs can represent social networks where individuals are connected to their immediate neighbors or friends.

Implementation of Circular Graphs

In order to implement a circular graph, we typically use a combination of arrays and linked lists. Each node in the circular graph is represented by a data structure that contains a value and references to the previous and next nodes in the cycle.

Here is an example of a circular graph implementation using JavaScript:


class Node {
  constructor(value) {
    this.value = value;
    this.next = null;
    this.prev = null;
  }
}

class CircularGraph {
  constructor() {
    this.head = null;
  }

  addNode(value) {
    const newNode = new Node(value);

    if (!this.head) {
      this.head = newNode;
      newNode.next = newNode;
      newNode.prev = newNode;
    } else {
      const tailNode = this.head.prev;

      tailNode.prev = tailNode;

      this.prev = newNode;
      newNode.next = this.head;
    }
  }

  // Other methods like removeNode, traverse, etc. can be added here
}

// Usage example
const graph = new CircularGraph();
graph.addNode(1);
graph.addNode(2);
graph.addNode(3);

In the above code snippet, we define two classes – Node and CircularGraph. The addNode() method adds a new node to the circular graph by updating the appropriate references.

Conclusion

Circular graphs provide an efficient way to represent cyclic relationships or connections between entities. They have various applications in different domains, including computer science and social sciences. By using appropriate data structures and algorithms, circular graphs can be effectively implemented and utilized.

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