Graph Theory

Graph theory, a fundamental branch of mathematics with its ability to model relationships and connections which makes it a must know tool for developers.

What is a Graph ?

A graph is combination of

  • Nodes (vertices) - Represents entities or objects.
  • Edges - Represents relationships between nodes.

Types of Graphs

  • Directed and Undirected - In directed edges have a direction.
  • Weighted and Unweighted - Edges carry a value representing cost/time/priority etc.
  • Cyclic vs Acyclic - If a cycle exists within a graph or not.

Representing a Graph in memory

  1. Adjacency Matrix

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  1. Adjacency List

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Real-World Usage

1. Dependency Management

Package managers (npm, pip, cargo) build dependency graphs. Topological sorting ensures libraries are loaded in the correct order.

2. Routing Systems

Used in Path finding algorithms, traffic optimization and load balancing.

3. Algorithms

Often used to model our problems into a graph data structures help in easy thinking and solutions. Be it social network or cities on a map, it is used everywhere.


Conclusion

Graphs are probably the most key takeaway from discrete math that you will encounter in your day to day life as a software developer. Mastering them will not only help you in software engineering, but also emerging trends in machine learning and distributed systems.