undirected graph

(data structure)

Definition: A graph whose edges are unordered pairs of vertices. That is, each edge connects two vertices.

Formal Definition: A graph G is a pair (V,E), where V is a set of vertices, and E is a set of edges between the vertices E ⊆ {{u,v} | u, v ∈ V}. If the graph does not allow self-loops, adjacency is irreflexive, that is E ⊆ {{u,v} | u, v ∈ V ∧ u ≠ v}.

See also directed graph, hypergraph, multigraph.

Note: An undirected graph may be represented as a directed graph with two directed edges, one "to" and one "from," for each undirected edge.

Author: PEB

Go to the Dictionary of Algorithms and Data Structures home page.

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Entry modified 18 October 2007.
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Cite this as:
Paul E. Black, "undirected graph", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 18 October 2007. (accessed TODAY) Available from: