Explanation of Complete Graph with Diagram and Example

A complete graph is a graph in which every vertex has an edge to all other vertices is called a complete graph, In other words, each pair of graph vertices is connected by an edge.

the complete graph with n vertices has calculated by formulas as edges. The complete graph with n graph vertices is denoted mn.

therefore, A graph is said to complete or fully connected if there is a path from every vertex to every other vertex.

Complete Graph defined as An undirected graph with an edge between every pair of vertices.

Defined Another way you can say, A complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge.

therefore, the complete digraph is a directed graph in which every pair of distinct vertices is connected by a pair of unique edges (one in each direction).

The complete graph on n vertices is denoted by Kn.
Kn has n(n−1)/2 edges and is a regular graph of degree n−1.

Undirected Graph

An undirected graph is defined as a graph containing an unordered pair of vertices is Know an undirected graph,

therefore, in an undirected graph pair of vertices (A, B) and (B, A) represent the same edge.
The set of vertices V(G) = {1, 2, 3, 4, 5}
The set of edges E(G) = {(1, 2), (1, 4), (1, 5), (2, 3), (3, 4), (3, 5), (1, 3)}

Note: An undirected graph represented as a directed graph with two directed edges, one “to” and one “from,” for every undirected edge.


hence, The edge defined as a connection between the two vertices of a graph. In a weighted graph, every edge has a number, it’s called “weight”.

therefore, In a directed graph, an edge goes from one vertex, the source, to another, the target, and hence makes the connection in only one direction.


The vertex is defined as an item in a graph, sometimes referred to as a node, The plural is vertices. Another plural is vertexes.

Example: Below is a complete graph with N = 7 vertices.

example of graph

As the above graph n=7
therefore, The total number of edges of complete graph = 21 = (7)*(7-1)/2.
To calculate total number of edges with N vertices used formula such as = ( n * ( n – 1 ) ) / 2