Example: The First Betti Number in Graph Theory
In topological graph theory the first Betti number of a graph G with n vertices, m edges and k connected components equals
This may be proved straightforwardly by mathematical induction on the number of edges. A new edge either increments the number of 1-cycles or decrements the number of connected components.
See cyclomatic complexity for an application of the first Betti number in software engineering.
Read more about this topic: Betti Number
Famous quotes containing the words number, graph and/or theory:
“The basis of successful relief in national distress is to mobilize and organize the infinite number of agencies of self help in the community. That has been the American way.”
—Herbert Hoover (1874–1964)
“When producers want to know what the public wants, they graph it as curves. When they want to tell the public what to get, they say it in curves.”
—Marshall McLuhan (1911–1980)
“every subjective phenomenon is essentially connected with a single point of view, and it seems inevitable that an objective, physical theory will abandon that point of view.”
—Thomas Nagel (b. 1938)