Branches of Mathematics

Graph Theory

Citation Formats

General Reference

Mathematics Atlas. "Graph Theory." Accessed August 30, 2026. https://mathematics.interactiveatlas.org/branches/graph-theory.

APA Style

Mathematics Atlas. (n.d.). Graph Theory. Retrieved August 30, 2026, from https://mathematics.interactiveatlas.org/branches/graph-theory

BibTeX

@misc{mathematicsatlas-graph-theory,
  author = {Mathematics Atlas},
  title = {Graph Theory},
  year = {2026},
  url = {https://mathematics.interactiveatlas.org/branches/graph-theory},
  note = {Accessed August 30, 2026}
}

Graph theory is the study of graphs, mathematical structures of vertices connected by edges, used to model pairwise relations between objects. It originated with Leonhard Euler's 1736 solution to the Seven Bridges of Konigsberg problem, and has grown from a branch of combinatorics into a stand-alone field with applications throughout computer science and network science.

Facts

Central Question

Which structural properties of a network of vertices and edges, connectivity, colorability, the existence of an optimal path or cycle, can be established from its combinatorial structure alone, independent of what the vertices and edges are taken to represent? 1

Key Debate

Whether graph theory is best understood as a subfield of combinatorics or as a stand-alone branch in its own right; its rapid post-1950s growth, driven by applications in computer science, operations research and network science, gave it a body of problems distinct enough that most mathematicians now treat it as independent. 1

Cross-Tradition Connections