Concept: The graph component

Question

I have the following definition for a Component of a graph:

A subgraph $H$ of a graph $G$ is a component of $G$ if $H$ is a maximal connected subgraph of $G$, that is, there is no larger connected subgraph of $G$ having $H$ as a subgraph.

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Can someone give me some examples of this? I am having trouble understanding what this would be. Could I take for example $K_4$ and remove one of the vertices and have one component of four, or would there only be one component since removing any vertex the graph is isomorphic to removing any of the other three?

Thank you.

Answer 1

Note: I am the asker of this question. This is my attempt.

A component of a graph is a joint region, meaning: If a graph is not connected, each connected area is a component. So $K_4$ has $1$ component, which is itself and the following graph has $1$ component:

But if $V_3$ is removed, we have two components, both connected regions:

Answer 2

The components of a graph are often referred to in the literature as the connected components of a graph. It is intuitively clear what they are.