# 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

## Implementation

(C++, C, Java, and Mathematica)

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

If you have suggestions, corrections, or comments, please get in touch
with Paul Black.

Entry modified 2 November 2020.

HTML page formatted Mon Nov 2 12:36:42 2020.

Cite this as:

Alen Lovrencic, "maximally connected component", in
*Dictionary of Algorithms and Data Structures* [online], Paul E. Black, ed. 2 November 2020. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/maximallyConnectedComponent.html