# Terms I

We will discuss some of the basic terminology associated with graphs. Some of this vocabulary should feel familiar from the trees section; trees are a specific type of graph!

`Nodes`

: Node is the general term for a structure which contains an item.`Size`

: The size of a graph is the number of nodes.`Capacity`

: The capacity of a graph is the maximum number of nodes.

**Nodes** can be, but are not limited to the following examples:
- physical locations (IE Manhattan, Topeka, Salina),
- computer components (IE CPU, GPU, RAM), or
- people (IE Kevin Bacon, Laurence Fishburne, Emma Stone)

`Edges`

: Edges are the connection between two nodes. Depending on the data, edges can represent physical distance, films, cost, and much more.`Adjacent`

: Node A and node B are said to be adjacent if there is an edge from node A to node B.`Neighbors`

: The neighbors of a node are nodes which are adjacent to the node.

**Edges** can be, but are not limited to:
- physical distances, like the distance between cities or wiring between computer components,
- cost, like bus fares, and
- films, like the Six Degrees of Kevin Bacon example

`Cycles`

: A cycle is a path where the first and last node are the only repeated nodes. More explicitly, this means that we start at node A and are able to end up back at node A.

## Example

For example, we can translate the Amtrak Train Station Connections into a graph where the edges represent direct train station connections.

^[Generated using the Amtrak system map from 2018. This graph does not include all stations or connections.]

Within this context, we could say that Little Rock and Fort Worth are `adjacent`

. The `neighbors`

of San Antonio are Fort Worth, Los Angeles, and New Orleans. The Amtrak Train Graph has multiple `cycles`

. One of these is `Kansas City -> St. Louis -> Chicago -> Kansas City`

.