Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures See more

A graph is an abstraction of relationships that emerge in nature; hence, it cannot be coupled to a certain representation. The way it is represented … See more

• Gallery of named graphs
• Glossary of graph theory
• List of graph theory topics
• List of unsolved problems in graph theory See more

1. ^ Bender & Williamson 2010, p. 148.
2. ^ See, for instance, Iyanaga and Kawada, 69 J, p. 234 or Biggs, p. 4.
3. ^ Bender & Williamson 2010, p. 149.
4. ^ See, for instance, Graham et al., p. 5. See more

Graphs can be used to model many types of relations and processes in physical, biological, social and information systems. Many practical problems can be represented by graphs. Emphasizing their application to real-world systems, the term network is … See more

The paper written by Leonhard Euler on the Seven Bridges of Königsberg and published in 1736 is regarded as the first paper in the history of graph theory. This paper, as well as … See more

Enumeration
There is a large literature on graphical enumeration: the problem of counting graphs meeting specified conditions. Some of this work is found in Harary and Palmer (1973).
Subgraphs, … See more