graph theory

Noun

graph theory (countable and uncountable, plural graph theories)

1. (uncountable) The branch of mathematics dealing with the properties of graphs (networks of vertices and edges).
   • The type of graph studied in graph theory is formally described as an ordered pair G#61;(V,E) comprising a set V of vertices, or nodes, and a set E of pairs (either ordered or unordered) of vertices, each representing an (directed or undirected) edge; if desired, the vertices and/or edges can be...
   • In graph theory there are two concepts of "sameness" whereby graphs are judged to be "the same", namely equality and isomorphism.[…]An indication of the pervasive role isomorphism has in graph theory is the fact that isomorphism has virtually captured the word "is".1993, Richard J. Trudeau, Introduction to Graph Theory, Dover, page 47
2. (countable, applied mathematics) A theory developed by applying graph theory to a particular problem or application.
   • The entity-level approaches build an internal representation for text units and their relationships, and use graph theories to determine the significance of units.2009, Fu Lee Wang, Christopher C. Yang, Chapter XI: Extracting the Essence: Automatic Text Summarization, Yin-Leng Theng, Schubert Foo, Dion Goh, Jin-Cheon Na (editors), Handbook of Research on...
   • Galloway and Thacker's own dissatisfaction with the graph theories of network science, for example, point to a tendency to attribute unfettered and apolitical naturalness to what are in effect asymmetrical topological spaces.2013, Tony D. Sampson, “6: Contagion Theory: Beyond the Microbe”, in Arthur Kroker, Marilouise Kroker, editors, Critical Digital Studies: A Reader, 2nd edition, University of Toronto Press, page 131