How do I expand my network with people who are MORE influential than I am? I'm looking for tips and tricks to do this online (with LinkedIn, etc)

They say that when you reach out to someone online (over email, LinkedIn, etc), you should give value before you ask for something from them, and I understand that. How do you provide value to someone who you've never met before? If you consider yourself influential (someone that other professionals are likely to respond to and connect with), what do you look for when you decide which contact requests to accept? If you are not well known, what strategies have worked (or not worked) for you? Thanks..