# Graph

A Graph is a collection of Vertices(V) and Edges(E).

Vertices also called as nodes. V is a finite set of nodes and it is a nonempty set.

Edge refers to the link between two vertices or nodes. So, E is a set of pairs of vertices.

In general,

#### G = (V,E).

where,

**G** - Graph

**V** - a set of nodes. Nonempty set.

**E** - a set of pairs of nodes. It can be an empty set.

## Undirected Graph

In Undirected Graph have **unordered pair** of edges.

Means edge E1 (x,y) and E2 (y,x) represent the **same** edge.

Edge can be traversed from **any direction**.

#### Example

**V** = {0, 1, 2, 3, 4}

**E** = {{0,1}, {0,2}, {0,3}, {1,0},{1,3},{1,4}, {2,0},{2,3}, {3,0},{3,1},{3,2},{3,4}, {4,1},{4,3}}

## Directed Graph(Digraph)

In the Directed Graph, each edge(E) will be associated with **directions**.

So, directed Graph have the **ordered pair** of edges.

Means edge E1 (x,y) and E2 (y,x) are two different edges.

Edge can only be traversed from the **specified direction**.

It is also called the **digraph**(**Di**rected **graph**).

#### Example

**V** = {0, 1, 2, 3, 4}

**E** = {<0,1>, <0,2>, <0,3>, <1,3>,<1,4>,<2,3>,<3,4>}