Graphs: Modeling Relationships

In the previous chapter we explored trees.

Trees are powerful, but they enforce a strict parent-child hierarchy.

Many real systems need more flexible relationships.

That is where graphs come in.

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What Is a Graph?

A graph consists of:

• nodes (entities)
• edges (relationships between entities)

graph LR
  A[Node A] --- B[Node B]
  B --- C[Node C]
  A --- C

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Directed vs Undirected

• Undirected graph: relationships go both ways.
• Directed graph: edges have direction.

Examples:

• friendship networks are often modeled as undirected
• follower relationships are naturally directed

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Why Graphs Matter

Graphs model systems where connectivity is central.

Common examples:

• social networks
• road maps and navigation
• dependency systems
• internet/network routing

When relationship paths matter, graph algorithms become essential.

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Typical Graph Questions

• Is there a path from A to B?
• What is the shortest path?
• Which nodes are most connected?
• Are there cycles?

These are core practical problems in many products.

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Key Ideas to Remember

• Graphs model arbitrary relationships using nodes and edges.
• Directed and undirected forms serve different domains.
• Many real systems are naturally graph-shaped.
• Path and connectivity questions are central graph tasks.
• Graph structures unlock powerful algorithmic solutions.

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What Comes Next

After exploring major structures, we now shift to algorithm design patterns.

Next chapter:

common techniques used to build algorithms.