This note explains the fundamental terminology and basic concepts of Graph Theory.

Vertex, Vertices

Vertex and Vertices, also known as node and nodes, originate from Graph Theory. I still remember when I was confused by these words—it’s actually simple but, my brain tend to overcomplicated things. In simple terms, Vertex is a single point or node in graph. Think of it as a dot representing an object such as a car, city, computer or person, while Vertices refers to more than one node in a graph.

In Short...

  • Vertex: Single dot, node or object in a graph.
  • Vertices: More than one dots, nodes, or object in a graph.
  • Vertices is the plural form (multiple dots or nodes) of “vertex”.

Edges are the lines that represent connection between vertices, you can imagine it this way. A vertex is an island, while vertices are multiple islands, and edges are the bridges connecting the island.

Multiple Edges

Multiple edges (or parallel edges) mean that a single pair of vertices can have more than one edge (or connection) between them. These kinds of graphs are referred to as multigraphs.

Loops

A loop is a special type of edge that connects a vertex to itself. In other words, it’s an edge that starts and ends at the same vertex.


🔗 Sources

  1. Fundamentals of Graph Theory - GeeksforGeeks