A graph is a structure containing (V, E) set of objects. Here V represents the vertices or node and E represents the edges or arcs. Say V= {v1, v2, v3, v4, v5} and E = {e1, e2, e3, e4}. Each edge Ek is identified with an unordered pair (Vi, Vj) of vertices. The vertices Vi, Vj associated with edge Ek are called the end vertices of Ek. You can see the graph below.

An edge which has same vertices as both of its end vertices is called self-loop. Edge e1 is the self-loop in Fig1 above. And if more than one edges are associated with one set of end vertices then vertices are referred to as parallel edges. Edges e4 and e5 in the above figure are parallel edges.

## Types of Graph:

On the basis of vertices order and edges, connections graph is also classified into a various category.

### Undirected Graph:

A graph is called undirected graph if there is the same edge say Ek identified with a different pair of vertices say (Vi, Vj) and (Vj, Vi).

Let’s understand this with a more simple explanation. When we go from V1 to V2 and V2 to V1 in both the case we get same edge e1 as the resulting edge.

Set of vertices V= {v1, v2, v3, v4}

Set of edges E = {e1, e2, e3, e4}

In this graph pair (v1, v2) and (v2, v1) represent the same edge.

### Directed Graph:

In a directed graph, every edge of the graph is identified by an ordered pair of vertices. it is also known as a digraph, so don’t be confused with this other name of a directed graph.

In this graph, there exists some mapping, that maps each edge of a graph onto some ordered pair of vertices(Vi, Vj). The first element of an ordered pair of vertices is referred to as the start vertex and the second element is known as end vertex. Fig3 shows the directed graph.

Vertex pair (Vi, Vj) reads as Vi-Vj an edge is directed from Vi to Vj.

### Complete Graph:

A simple graph In which there exists an edge between every pair of vertices is called a complete graph. A complete graph is also known as a universal graph or a clique. Fig 4 shows complete graphs of two, three, four and five vertices.

### Connected Graph:

A graph G is known as a connected graph if there is at least one path between every pair of vertices in G. Otherwise, G is disconnected. See the below image for a connected graph.

### Multi Graph:

A graph which contains a pair of nodes joined by more than one edge is called a multigraph and such edges are called parallel edges. See the image below for the multigraph.

## Conclusion:

In this above blog post, you have learned about the graph and types of graph in the data structure. A graph is a shape which is built with the help of vertices or node and edges. and on the basis of their property, they are further classified into different types like a simple graph, undirected graph, directed graph, connected graph, complete graph, and multigraph. With a change in the order of vertices and edges connection a graph nature changes and it is known by some other name. A graph is used for solving many mathematical problems and it is used to get an optimal solution for a problem.

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