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
- Adjacency Matrix
- Adjacency List
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.