Understanding Simple Graphs in Graph Theory | Definition and Examples

simple graph

In graph theory, a simple graph is a type of undirected graph that has no self-loops or multiple edges between the same pair of vertices

In graph theory, a simple graph is a type of undirected graph that has no self-loops or multiple edges between the same pair of vertices.

To understand this definition, let’s break it down:
1. Undirected graph: A graph consists of a set of vertices (also called nodes) and a set of edges. In an undirected graph, the edges do not have any specific direction associated with them. They simply connect two vertices.
2. Self-loops: A self-loop occurs when an edge connects a vertex to itself. In a simple graph, such self-loops are not allowed.
3. Multiple edges: Multiple edges are multiple connections between the same pair of vertices. In a simple graph, each pair of vertices can have at most one edge connecting them.

So, in essence, a simple graph is a type of undirected graph where there are no self-loops or multiple edges between any pair of vertices. It represents a more basic and straightforward form of a graph, without any additional complexities.

For example, let’s consider a simple graph with 3 vertices: A, B, and C. If there is only one edge connecting A and B, and no edges connecting A to itself or B to itself, then this graph is a simple graph.

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