Graph Theroy 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.