Node

Definition

A node is an individual object in a graph.

It represents something that can be connected to other things.

Example:

Nodes: A, B, C

The nodes are the things being studied.

Node = object in a graph.

---

Node As Element

From the previous chapter, a set contains elements.

A graph starts with a set of nodes.

Example:

V = {A, B, C}

Here V is the set of nodes.

Each node is one element of that set.

Nodes are the elements that graph structure is built on.

---

What A Node Can Represent

A node can represent many kinds of things.

Examples:

• a person
• a city
• a web page
• a task
• a state
• a value in a computation

The graph does not care what the node means by itself.

The graph cares about how nodes are connected.

Meaning comes from interpretation; graph structure comes from connections.

---

Label vs Node

A node may have a label.

Example:

Node label: A

The label is a name used to refer to the node.

The node is the object inside the graph.

Two graphs can both have a node labeled A, but those nodes belong to different graph structures.

A label names a node; it is not the whole structure of the node.

---

Why Nodes Matter

Nodes let us separate objects from relationships.

Example:

Objects: A, B, C
Connections: A connected to B, B connected to C

Without nodes, there is nothing to connect.

Without connections, nodes are just isolated objects.

Graphs begin by identifying the objects that can participate in structure.

---

Final Summary

• A node is an object in a graph.
• A graph starts with a set of nodes.
• Nodes can represent many kinds of things.
• A label names a node.
• Nodes become useful when connections between them are defined.