Definition: The set of maximally connected components of an undirected graph.
Generalization (I am a kind of ...)
See also connected graph, biconnected component, undirected graph, subgraph, clique, strongly connected components.
Note: If a graph is connected, it has only one connected component. Often the term "component" is used, with the "connected" property understood.
Let G=(V, E) be a graph and G1=(V1, E1)..., Gm=(Vm, Em) be its connected components. Every vertex is in exactly in one connected component, that is, the components partition(1) V. Formally, for all i ≠ j, Vi∩ Vj=ø. Further, V=V1∪...∪ Vm and E=E1∪...∪ Em.
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Entry modified 18 October 2007.
HTML page formatted Tue Dec 6 16:16:32 2011.
Cite this as:
Alen Lovrencic, "connected components", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology. 18 October 2007. (accessed TODAY) Available from: http://www.nist.gov/dads/HTML/connectedComponents.html