Section: STEM · MathematicsDifficulty: Medium
Graph Theory
USUK
The study of graphs as mathematical structures representing pairwise relations between objects.
Definition
Graph theory is a branch of mathematics that studies graphs, which consist of vertices (nodes) connected by edges (links). Graphs can be directed or undirected, weighted or unweighted, and model a vast range of real-world networks. Key concepts include paths, cycles, connectivity, spanning trees, and graph coloring. Graph theory is foundational to computer science, logistics, social network analysis, and biology.
Example
“Shipping companies model their delivery networks as weighted graphs, where cities are vertices and routes are edges with weights representing distances or travel times, then apply shortest-path algorithms to minimize delivery costs.”
Synonyms
- network theory
- graph mathematics
- combinatorial graph theory
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Related Terms
- Algorithm
- Network Theory
- Discrete Mathematics
- Euler Path