Understanding Simple Graphs | A Fundamental Concept in Mathematics and Beyond

Simple graph

In mathematics, a simple graph is a mathematical structure that represents a set of objects called vertices (or nodes) and a set of connections between them called edges

In mathematics, a simple graph is a mathematical structure that represents a set of objects called vertices (or nodes) and a set of connections between them called edges. A simple graph is called “simple” because it does not allow multiple edges between the same pair of vertices or loops (edges connecting a vertex to itself).

Formally, a simple graph G is represented as G = (V, E), where V is a finite set of vertices and E is a set of unordered pairs of distinct vertices, known as edges. Each edge in E connects two distinct vertices in V.

A simple graph can be visually represented by dots (vertices) and lines (edges) connecting the vertices. The dots represent the objects or entities, while the lines represent the relationships or connections between them.

For example, consider a simple graph representing a social network. The vertices could represent individuals, while the edges could represent friendships or connections between individuals. In this graph, each individual is represented by a vertex, and if two individuals are friends, there will be an edge connecting their corresponding vertices.

It is important to note that in a simple graph, the edges have no inherent direction or weight associated with them. If direction or weights are assigned to the edges, the graph becomes a directed graph or a weighted graph, respectively.

Simple graphs play a fundamental role in various areas of mathematics, computer science, and real-world applications such as social networks, transportation networks, and computer networks.

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