Networking without feeling pushy, operations analyst here

I sent 7 messages on a professional network and got two replies. Thank you in advance. I want advice, not a job directly. What did you ask?

Follow up with a thank-you and a short update. One of my chats led to a referral a month later.

I wrote three short lines: who I am, why them and a small ask for fifteen minutes. About one in four said yes.