I am having trouble understanding the definition of components and connectivity. Here is the definition I have been given in my text:

Alright, I know that a subgraph is a subset of vertices and edges which itself forms a graph. I also know that a path is a subgraph in which no edge or vertex is repeated except for perhaps the first and last vertex.

Could someone perhaps reword the above definition of components and connectivity or provide a better definition of components and connectivity for me please? Thankyou.

I also have another question regarding paths. I know that perhaps the first and last vertex may be repeated, but does that mean that a subgraph is still a path if both the last and first vertex are repeated? Or that if a subgraph is still a path if either the first or last vertex is repeated? Or can both situations occur?