While you might carry on a conversation and follow-up via email, phone or social media - it's always good to meet up for a longer conversation.
You'll be able to find out more about what they do away from the noise and distractions of a busy network meeting and perhaps discover something you didn't know.
As part of the follow-up process, after each networking meeting, arrange to meet up with at least one or two of the people you've met. Either a new contact or perhaps even someone you already know but haven't had a longer chat over coffee.
Remember, the intention is to find out more about them, their challenges and how you might be able to help. Don't see it as an opportunity to do a sales pitch.
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