Trees and Graphs - Programming for Machine Learning and Business

Modeling Hierarchies and Relationships¶

Trees and graphs extend node thinking from chains into branching relationships¶

Linked lists connected one node to the next in a line. Trees and graphs widen that idea: a node can connect to multiple other nodes, which lets you model hierarchies, routes, dependencies, recommendations, and many other relationship patterns.

Core Explanation¶

A tree is a special kind of graph with parent-child structure and no cycles.

A graph is more general and may represent many types of connections.

tree = {
    "A": ["B", "C"],
    "B": [],
    "C": ["D"],
    "D": []
}
print(tree["A"])

Worked Example: hierarchy versus network¶

The code cell above shows a tree-like structure: one node can have children, and the relationships form a clear hierarchy. That is different from a general graph, where nodes may connect in more flexible patterns such as routes, collaboration networks, or recommendation links.

Exercises¶

Describe one example of a hierarchy and one example of a network.
Explain why every tree is a graph, but not every graph is a tree.
Draw a tiny tree with a root and two children.
Give one example where a graph is a better model than a tree.

Practice Lab¶

This first example behaves like a tree: the top node branches into departments, and lower nodes continue the hierarchy.

This second example behaves like a graph: node D can be reached from more than one parent path, which already feels less tree-like and more network-oriented.

Reading Node Relationships¶

These short examples separate hierarchy thinking from general connectivity.

Read children in a tree¶

A tree node often points to the next level of the hierarchy.

Count nodes in a graph¶

An adjacency-list dictionary can show how many nodes are currently defined.

Check shared connections¶

Graphs often highlight that multiple nodes can connect to the same destination.

Guided Practice¶

What is a key difference between a tree and a general graph?¶

A tree stores only integersThe data type of node values is not the key difference.

A tree has a hierarchical parent-child structureCorrect. Trees emphasize hierarchy.

A graph cannot store nodesGraphs are made of nodes and edges.

A graph is always smaller than a treeSize is not the defining difference.

In the graph example, how many nodes are defined?¶

2There are more nodes than that.

4Correct. The nodes are A, B, C, and D.

3Check the dictionary keys again.

5There are not five nodes listed.

Key Takeaway¶

Trees and graphs both organize data through nodes and connections, but trees emphasize hierarchy while graphs emphasize general relationships. This overview prepares you for the next tree-specific notebooks on traversal and binary search trees.