What Is Complete Graph in Data Structure?


Scott Campbell

A complete graph is a type of graph in data structure that is characterized by having every pair of vertices connected by an edge. In other words, it is a graph in which there is a direct link between every pair of nodes or vertices.

Properties of Complete Graphs

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

  • Fully Connected: A complete graph is fully connected, meaning that there is an edge between every pair of vertices. This property makes complete graphs useful for modeling scenarios where all nodes are directly connected.
  • Number of Edges: The number of edges in a complete graph can be calculated using the formula E = n * (n-1) / 2, where E represents the number of edges and n represents the number of vertices.

    For example, a complete graph with 5 vertices will have (5 * (5-1)) / 2 = 10 edges.

  • Degree: The degree of each vertex in a complete graph is equal to the number of vertices minus one. This means that every vertex in a complete graph has the same degree.

Applications of Complete Graphs

Complete graphs find applications in various fields due to their unique properties:

  • Social Networks: Complete graphs can be used to model social networks where each person is directly connected to every other person. This can be helpful for analyzing patterns and relationships within the network.
  • Transportation Networks: Complete graphs can represent transportation networks where each location or node is directly connected to every other location.

    This can be useful for optimizing routes and planning efficient transportation systems.

  • Wireless Communication: Complete graphs can be used to model wireless communication networks, where each device is directly connected to every other device. This can aid in analyzing signal strength, interference, and network performance.


A complete graph is a powerful concept in data structures that represents a graph where every pair of nodes is directly connected. It has unique properties that make it useful for various applications such as social networks, transportation networks, and wireless communication. By understanding the properties and applications of complete graphs, you can leverage them to solve complex problems in different domains.

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