Small question about vertices in hypergraphs

Say we have a hypergraph $$H$$ and a (hyper)edge $$E$$. Does that mean that all vertices in $$E$$ are connected?

So if $$E= \{a,b,c\}$$ does that necessarily mean $$a$$ and $$b$$ are connected?

And does that mean that every vertex is connected to it self?