Employers need information to make good decisions about you. They can only act on the information you provide.
You have read the job description and discussed the position with your network. Having carefully considered it, you know why you are applying, and what experience you have to support your candidacy. Employers know what they know when you have shared information. Important, illuminating information must be shared in your resume and cover letter, and reflected in the recommendations that your network provides.
A primed network.
Once your network is primed and ready, you can deploy them to act on your behalf. Help your recommenders help you by telling them how the details of your mutual connection is relevant to the job you are seeking now. The information shared in your documents and reinforced by your recommenders will help prospective employers understand why you are the right candidate.
Employers need information to make good decisions, and telepathy is not a job search tool. Share information.