We'll be blunt: the people you're trying to network with don't need more work on their plate, so don't be more work on their plate. Try these easy swaps to ensure you're not cutting yourself off at the knees before you even begin networking: 
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‍Instead of aimless reach outs, get to the point. ‍

• Don't say: "Hey Shelby, how are you doing? It's been a minute!"
• Do say: "Hey Shelby, hope you're well. I'm working on XYZ and you came to mind as someone who might have some helpful perspectives. Do you have 10 minutes in the next week or so to quickly connect?"
  
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Instead of aimless conversations, you need to drive.

• Don't get on a networking call and expect the other person to lead the conversation.  
• Do come up with a few core goals/questions you want to ask that can guide the conversation. Don't be afraid to end a meeting early if you feel like the conversation is floundering. No one wins if people feel like they're wasting time.

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Instead of asking for just what they can do for you, offer up something you can do for them.

• Don't say: "Could you introduce me to so and so?"  
• Do try: "Would be open to introducing me to so and so? I want to keep it easy for you, so I'd be happy to draft a quick intro note with all the right context that you could send to them!"

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In a world where everyone is some degree of exhausted, don't be more work for someone than you need to be.