This is a list of graph theory topics, by Wikipedia page.

See glossary of graph theory terms for basic terminology

Examples and types of graphs

Graph coloring

Paths and cycles

Trees

Terminology

• Node
  • Child node
  • Parent node
  • Leaf node
  • Root node
  • Root (graph theory)

Operations

• Tree structure
• Tree data structure
• Cayley's formula
• Kőnig's lemma
• Tree (set theory) (need not be a tree in the graph-theory sense, because there may not be a unique path between two vertices)
• Tree (descriptive set theory)
• Euler tour technique

Graph limits

• Graphon

Graphs in logic

• Conceptual graph
• Entitative graph
• Existential graph
• Laws of Form
• Logical graph

Mazes and labyrinths

• Labyrinth
• Maze
• Maze generation algorithm

Algorithms

• Ant colony algorithm
• Breadth-first search
• Depth-first search
• Depth-limited search
• FKT algorithm
• Flood fill
• Graph exploration algorithm
• Matching (graph theory)
• Max flow min cut theorem
• Maximum-cardinality search
• Shortest path
  • Dijkstra's algorithm
  • Bellman–Ford algorithm
  • A* algorithm
  • Floyd–Warshall algorithm
• Topological sorting
  • Pre-topological order

Other topics

Networks, network theory

See list of network theory topics

Hypergraphs

• Helly family
• Intersection (Line) Graphs of hypergraphs