What Is a Simple Graph?

This video explains what a simple graph is and shows why this type of graph is so widely used.
The video contains an example and exercises to practice this.

DEFINITION
Most definitions describe a simple graph as a graph without multiple edges and self-loops. Multiple edges are also called parallel edges. An edge from a vertex to itself is a self-loop. So, in a simple graph each edge connects two distinct vertices and no two edges connects the same pair of vertices.

Implicitly, these definitions assume four other constraints:
- edges between an unordered pair of vertices;
- undirected graph;
- unweighted graph;
- finite graph.

WHY SIMPEL?
These constraints simplify a graph, which is why it is called a simple graph.

CAN A SIMPLE GRAPH BE DISCONNECTED?
If we add or remove edges or vertices, this graph still remains a simple graph. So, a simple graph can be connected or disconnected.

EXAMPLE SIMPLE GRAPH
A friend network on Facebook is an example of a simple graph.

EXERCISES
The video contains two exercises:
- Can you draw a simple graph with 4 vertices and 7 edges?
- Name at least 3 real networks that are not simple graphs.

MULTIGRAPH AND PSEUDOGRAPH
The opposite of a simple graph is called a multigraph or pseudograph. However, these definitions are not unambiguous, some authors use these terms as synonyms while others use them to distinguish the combination of self-loops and multiple edges.

CONCLUSION
When we simplify a graph as much as possible, we get a simple graph. This simple graph is well suited for explaining the core of a graph concept; this is why a simple graph is so popular with many authors. But as we saw in the last exercise, real networks are often more complicated.

ℹ️ 🔗 Definition simple graph https://symbio6.nl/en/blog/theory/def...

TIMESTAMPS
00:00 Introduction
00:12 Definition simple graph
00:49 Why simple?
01:05 Example simple graph
01:33 Opposite: multigraph/pseudograph
01:53 Exercise: name real networks that are not simple graphs
02:22 Conclusion

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CONTRIBUTIONS
Music: Nico Staf - Walking in the Sky