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Having a drawing (see image) of an undirected graph $G=(V,E)$ where

  • $V = \{A,B,C,D,E,F,G\}$ and $v \in V$

  • $E = \{\{A,B\},\{B,C\},\{C,D\},\{D,A\},\{D,E\},\{E,F\},\{F,G\},\{G,E\}\}$

  • each vertex $v$ has a position $\lambda$

    • $\lambda_v = \{x, y\}$

After removing edge $\{D,E\}$, two components $c_1$ and $c_2$ exists. Is there a term for the component $c_2 = \{\{E,F\},\{F,G\},\{G,E\}\}$ surrounded by $c_1$?

Drawing of Graph $G$

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The most common way to express this is that component $c_1$ is not simply connected (it has a hole). Of course, this doesn't help to give a term for $c_2$, but in analogy with political maps, we might call it an enclave.

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