Types of Graphs

Types of graphs

There are two common types of graphs:

1. Undirected
2. Directed

Undirected graph

In an undirected graph, the edges are by default, bidirectional by default. For a pair (2, 3), there exists an edge between vertex 2 and 3 without any specific direction. You can go from vertex 2 to 3 or vice versa (from 3 to 2).

Calculate the maximum possible edges for an undirected graph. You 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 you $\frac{n(n-1)}{2}$; hence, there are $\frac{n(n-1)}{2}$ maximum possible edges in an undirected graph.

You can see an example of an undirected graph below: