maximally connected component

(definition)

Definition: A connected subgraph of a graph to which no vertex can be added and it still be connected.

Formal Definition: Given a graph G=(V, E), a subgraph S=(V', E') is a maximally connected component if

• S is connected, and
• for all vertices u such that u∈ V and u∉ V' there is no vertex v∈ V' for which (u, v)∈ E.

See also connected graph, connected components, biconnected component, strongly connected component.

Note: Informally, (one of) the biggest connected subgraph(s) of a graph. Also know as "connected component", with the "maximal" property understood.

Author: AL

More information

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Entry modified 17 December 2004.
HTML page formatted Tue Dec 6 16:16:32 2011.

Cite this as:
Alen Lovrencic, "maximally connected component", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology. 17 December 2004. (accessed TODAY) Available from: http://www.nist.gov/dads/HTML/maximallyConnectedComponent.html