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 2 September 2014.
HTML page formatted Fri Feb 23 10:06:07 2018.
Cite this as:
Alen Lovrencic, "connected components", in Dictionary of Algorithms and Data Structures [online], Vreda Pieterse and Paul E. Black, eds. 2 September 2014. (accessed TODAY) Available from: https://www.nist.gov/dads/HTML/connectedComponents.html