Last I checked, node Title was a
required field, and by default, the node title on a home page displays
with a link to that piece of content. So how are you suppressing them
for the two paragraphs. Are you using panels? Are you supressing the the
titles via custom tpl's for specific node types (e.g. story.tpl)? Are
these blocks with custom text? Have you customized node.tpl, story.tpl
or another .tpl file to remove titles?
As one person has suggested,
adding the edit link at the theming layer with tests on which "role" a
user is in, is one way to add specific links to editing a node on the
page. Could you include more info about how your paragraphs are
constructed?
Dave