Types of Graphs

This lesson showcases the two main categories of graphs.

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Types of Graphs

There are two common types of graphs:

  1. Undirected
  2. Directed

Undirected Graph

In an undirected graph, the edges are bi-directional. For e.g., an ordered pair (2, 3) shows that there exists an edge between vertex 2 and 3 without any specific direction. You can go from vertex 2 to 3 or from 3 to 2.

Let’s calculate the maximum number of edges for an undirected graph. We are denoting an edge between vertex a and b as (a, b). So, the maximum possible edges of a graph with n vertices will be all possible pairs of vertices of that graph, assuming that there are no self-loops.

If a graph has n vertices, then there are C (n,2) possible pairs of vertices according to Combinatorics. Solving C (n,2) by binomial coefficients gives us n(n−1)2\frac{n(n-1)}{2}. Hence, there are n(n−1)2\frac{n(n-1)}{2} maximum possible edges in an undirected graph.

You can see an example of an undirected graph below:

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