(definition)
Definition: A graph in which the number of edges is close to the possible number of edges.
Generalization (I am a kind of ...)
graph.
Specialization (... is a kind of me.)
complete graph.
See also sparse graph, adjacency-matrix representation.
Note: A directed graph can have at most n(n-1) edges, where n is the number of vertices. An undirected graph can have at most n(n-1)/2 edges.
There is no strict distinction between sparse and dense graphs. Bruno Preiss' definition of sparse and dense graphs has problems, but may help. First, for one graph, one can always choose a k. Second a class of graphs might be considered sparse if |E| = O(|V|k) and 2 > k > 1. |E| is the number of edges, and |V| is the number of vertices.
Preiss reference from Andreas Leiser <andreas.leiser@bluewin.ch> 22 December 2003
Author: PEB
If you have suggestions, corrections, or comments, please get in touch with Paul Black.
Entry modified 14 August 2008.
HTML page formatted Mon Feb 2 13:10:39 2015.
Cite this as:
Paul E. Black, "dense graph", in
Dictionary of Algorithms and Data Structures [online], Vreda Pieterse and Paul E. Black, eds. 14 August 2008. (accessed TODAY)
Available from: http://www.nist.gov/dads/HTML/densegraph.html