I am a bit confused about the notion of connected component of a graph. I understand what is a subgraph and what means for a graph to be connected. But the definition we got in class is this: "A connected component of a graph is a maximal connected subgraph.". My question is, if the subgraph is connected but it is not maximal connected, it isn't considered anymore a connected component? For example if we have 4 nodes and 4 edges forming a square, and we pick 4 nodes and only 3 of the edges, this is still connected, but it is not maximal connected. So this isn't anymore a connected component?