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# Fundamental Concepts

Some of the basic fundamental concepts of **graph theory** are:

## 1. Point

A **point** is a particular position that is located in a space. Space can be one-dimensional, two-dimensional or three-dimensional space. A dot is used to represent a point in graph and it is labeled by alphabet, numbers or alphanumeric values.

### Example

Here, dot is a point labeled by ‘p’.

## 2. Line

Two points are connected to each other through a **line**. A **line** is a connection between two points. It is represented by a solid line.

### Example

Here, ‘A’ and ‘B’ are the points and links between two points is called a line.

## 3. Vertex

A **vertex** is a synonym of point in graph i.e. one of the points on which the graph is defined and which may be connected by lines/edges is called a vertex.

Vertex is also called “node”, “point” or “junction”. A vertex is denoted by alphabets, numbers or alphanumeric value.

### Example

Here, point is the vertex labeled with an alphabet ‘v’.

## 4. Edge

**Edge** is the connection between two vertices. Each edge connects one vertex to another vertex in the graph. Without a vertex, an edge cannot be formed. It is also called line, branch, link or arc.

Edge can either be **directed** or **undirected**. A directed edge is the edge which points from one vertex to another, and an undirected edge has no direction.

If there is a directed edge from vertex A to B, and a directed edge from B to A, this would essentially be equivalent to an undirected edge connecting A and B.

### Example

Here, **‘A’ and ‘B’** are the **vertices** and the link ‘AB’ between them is called an **edge**.

## Graph

**Graph** specifies to a “function graph” or “graph of a function” i.e. a **plot**.

In mathematics terminology, a graph is a collection of points and lines connecting some (possibly empty) subset of them.

A graph G is defined as G = {V, E} where V is a set of all vertices or points and E is the set of all edges in the graph.

### Example 1

In the above example, A, B, C, D and E are the vertices of the graph and AB, BC, CA and AD are the edges of the graph.

### Example 2

In the above example, G1, G2 and G3 are graphs.