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Types of Graphs with Examples

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  • Difficulty Level : Medium
  • Last Updated : 09 Sep, 2022
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A Graph is a non-linear data structure consisting of nodes and edges. The nodes are sometimes also referred to as vertices and the edges are lines or arcs that connect any two nodes in the graph. More formally a Graph can be defined as, A Graph consisting of a finite set of vertices(or nodes) and a set of edges that connect a pair of nodes.

Types of Graphs:

1. Finite Graphs

 A graph is said to be finite if it has a finite number of vertices and a finite number of edges. 

2. Infinite Graph: 

A graph is said to be infinite if it has an infinite number of vertices as well as an infinite number of edges. 

3. Trivial Graph: 

A graph is said to be trivial if a finite graph contains only one vertex and no edge. 

4. Simple Graph:

A simple graph is a graph that does not contain more than one edge between the pair of vertices. A simple railway track connecting different cities is an example of a simple graph. 

 

5. Multi Graph:

Any graph which contains some parallel edges but doesn’t contain any self-loop is called a multigraph. For example a Road Map. 

  • Parallel Edges: If two vertices are connected with more than one edge then such edges are called parallel edges that are many routes but one destination.
  • Loop: An edge of a graph that starts from a vertex and ends at the same vertex is called a loop or a self-loop.

6. Null Graph:

A graph of order n and size zero is a graph where there are only isolated vertices with no edges connecting any pair of vertices.

7. Complete Graph:

A simple graph with n vertices is called a complete graph if the degree of each vertex is n-1, that is, one vertex is attached with n-1 edges or the rest of the vertices in the graph. A complete graph is also called Full Graph. 

 

8. Pseudo Graph:

A graph G with a self-loop and some multiple edges is called a pseudo graph. 

9. Regular Graph:

A simple graph is said to be regular if all vertices of graph G are of equal degree. All complete graphs are regular but vice versa is not possible. 

10. Bipartite Graph:

A graph G = (V, E) is said to be a bipartite graph if its vertex set V(G) can be partitioned into two non-empty disjoint subsets. V1(G) and V2(G) in such a way that each edge e of E(G) has one end in V1(G) and another end in V2(G). The partition V1 U V2 = V is called Bipartite of G. Here in the figure: V1(G)={V5, V4, V3} and V2(G)={V1, V2} 

11. Labeled Graph:

If the vertices and edges of a graph are labeled with name, date, or weight then it is called a labeled graph. It is also called Weighted Graph. 

12. Digraph Graph:

A graph G = (V, E) with a mapping f such that every edge maps onto some ordered pair of vertices (Vi, Vj) are called a Digraph. It is also called Directed Graph. The ordered pair (Vi, Vj) means an edge between Vi and Vj with an arrow directed from Vi to Vj. Here in the figure: e1 = (V1, V2) e2 = (V2, V3) e4 = (V2, V4) 

13. Subgraph:

A graph G1 = (V1, E1) is called a subgraph of a graph G(V, E) if V1(G) is a subset of V(G) and E1(G) is a subset of E(G) such that each edge of G1 has same end vertices as in G. 

 

14. Connected or Disconnected Graph:

Graph G is said to be connected if any pair of vertices (Vi, Vj) of a graph G is reachable from one another. Or a graph is said to be connected if there exists at least one path between each and every pair of vertices in graph G, otherwise, it is disconnected. A null graph with n vertices is a disconnected graph consisting of n components. Each component consists of one vertex and no edge. 

15. Cyclic Graph:

A graph G consisting of n vertices and n> = 3 that is V1, V2, V3- – – – Vn and edges (V1, V2), (V2, V3), (V3, V4)- – – – (Vn, V1) are called cyclic graph. 

16. Types of Subgraphs:

  • Vertex disjoint subgraph: Any two graph G1 = (V1, E1) and G2 = (V2, E2) are said to be vertex disjoint of a graph G = (V, E) if V1(G1) intersection V2(G2) = null. In the figure, there is no common vertex between G1 and G2.
  • Edge disjoint subgraph: A subgraph is said to be edge-disjoint if E1(G1) intersection E2(G2) = null. In the figure, there is no common edge between G1 and G2.

Note: Edge disjoint subgraph may have vertices in common but a vertex disjoint graph cannot have a common edge, so the vertex disjoint subgraph will always be an edge-disjoint subgraph.

Related article: Applications, Advantages and Disadvantages of Graph

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