# Graph (mathematics) facts for kids

In mathematics, a **graph** is used to show how things are connected. The things being connected are called **vertices**, and the connections among them are called **edges**. If vertices are connected by an edge, they are called **adjacent**. The **degree** of a vertex is the number of edges that connect to it. A graph's **size** is the number of edges in total. The number of vertices, written as , is called the **order** of a graph.

Edges may have weights, which show the costs associated with using each edge. In a graph of cities on a map, the cost may be the distance between two cities, or the amount of time it takes to travel between the two.

**Directed graphs** go in one direction, like water flowing through a bunch of pipes. **Undirected graphs** don't have a direction, like a mutual friendship. A graph where there is more than one edge between two vertices is called **multigraph.** One where there is at most one edge is called a **simple graph**. A simple graph, where every vertex is directly connected to every other is called **complete graph**. A **loop** is an edge that connects to its own vertex. Loops are only allowed in multigraphs.

A sequence of edges is called a **path**. A path which starts and ends at the same edge is called a **cycle**.

*Kiddle Encyclopedia.*