(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

(C++, C, Pascal, Mathematica, and Fortran)

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Entry modified 2 September 2014.

HTML page formatted Fri Feb 23 10:06:08 2018.

Cite this as:

Alen Lovrencic, "maximally connected component", 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/maximallyConnectedComponent.html