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Modeling General Relationships

graph = {
    "A": ["B", "C", "D"],
    "B": ["E", "F"],
    "C": ["G"],
    "D": ["H"],
    "E": [],
    "F": [],
    "G": [],
    "H": [],
}
print(graph["A"])
print(graph["B"])

Graphs model networks where connections are more flexible than a tree

Binary search trees relied on strict ordering and parent-child structure. Graphs relax those rules: a node can connect to many others in patterns that look more like routes, dependencies, recommendations, or social links than a simple hierarchy.

Core Explanation

Graphs represent entities and the connections between them.

They are useful for transportation networks, dependency graphs, recommendation systems, and social relationships.

How to read this figure

  • A is a starting node with three direct neighbors

  • B, C, and D are branch points reached in one step

  • E, F, G, and H are outer nodes reached after following a branch

This same graph shape is reused in the BFS and DFS notebooks so the traversal order is easier to compare visually.

Continuity from binary search trees

BSTs used structure to narrow search by ordering. Graphs drop that left/right ordering and instead focus on which nodes are connected at all.

Worked Example and Practice Lab

Expected output
['B', 'C', 'D']
['E', 'F']

This example uses an adjacency list: each node maps to the nodes it can reach directly.

Expected output
3
True

Reading Graph Connectivity

These short examples focus on how adjacency lists describe a network.

Read outgoing neighbors

A node’s adjacency list shows where it can connect next.

Count outgoing edges

You can count how many direct connections a node has.

Check whether a node exists

Graph dictionaries also let you test whether a node is present in the structure.

Exercises

  1. Explain what a node and an edge represent in a graph.

  2. Describe one real-world system that is better modeled as a graph than as a tree.

  3. Explain what the adjacency list for node A means in the example.

  4. Give one reason graphs are a natural setup for BFS or DFS.

Hint

A graph is often the right model when one item can connect to several others without a strict hierarchy.

Guided Practice

What does an adjacency list represent in a graph?

Only the graph titleAn adjacency list stores connectivity, not a title.
Which nodes are connected to each nodeCorrect. Adjacency lists show neighbors.
A sorted list of weights onlyThis example tracks neighbors, not just sorted weights.
A tuple of all nodes and valuesThat is not the standard idea here.

How many outgoing neighbors does node `A` have in the example?

1A connects to more than one node.
3Correct. A connects to B, C, and D.
2That would miss one branch.
4Only three neighbors are listed for A.

Key Takeaway

Graphs describe general connectivity rather than strict hierarchy or ordered branching. That foundation prepares you for BFS and DFS, where the central question becomes how to explore a network systematically.

Programming for Machine Learning and Business
Binary Search Trees
Programming for Machine Learning and Business
Breadth First Search BFS