As I understand the difference between extroverts and introverts, extroverts draw energy from being around others while introverts draw energy from being alone. As a natural introvert, I am challenged both by my faith and my profession to be engaged with others: Christians and consultants both need to be out there, interacting with and learning from and influencing others. Naturally, I approach networking as an introvert (INTJ in the Myers-Briggs sense, to be more specific) would: systematically, picking my spots, intentionally working on it rather than it being a breezily easy thing to do.
Thank goodness for tools like Facebook and LinkedIn, which I use to "collect" contacts. I hope that doesn't sound too creepy or shallow, but it's nice to have lots of contacts, because you never know when you can be useful to someone or when someone can be useful to you. For example, after my mom's car accident, I searched my contact lists and found out that a friend of mine who I used to go to church with and who subsequently moved out of the US cared for people with spinal cord injuries for a living. Her occupation was not a piece of information I knew her well enough to know when we were actually living in the same city and going to the same church; but, months after she had moved away, we exchanged messages on Facebook and she was incredibly helpful to me as I was trying to make sense of my mom's new challenges. Indeed, studies have demonstrated "the strength of weak ties" - people with lots of weak ties tend to get more job and business offers, because their weak ties connect them to circles they don't otherwise have access to, versus those who just maintain strong ties end up only being able to access the same circles they're already established in.
Some may hold out for a higher bar for being linked. Meanwhile, others will "friend" or "follow" complete strangers in a frenzied effort to up their numbers. I tend to be somewhere in the middle: I have to at least know you well enough that I could actually have a non-generic conversation with you. And, in fact, I do try to have at least the occasional "touch" with every one I'm connected to, if only to say "happy holidays" or to announce some big thing going on in my life.
But real relationships aren't formed by sending generic end-of-year greetings or press releases. They take work; but they are worth the work, for ultimately, in business and for the Kingdom, relationships are all that matter. So I do try to make time to work on relationships, to make deposits in as many relationship banks as possible: emailing folks to congratulate them on a recent honor, forwarding them an article I think they might be interested in, calling them to see how they're doing, or taking them out for coffee to pick their brain about something.
It can seem there's hardly any time for this sort of work, between work and kids and church and house and life. But, when it comes to being a Christian and being a consultant, life is relationships. So this introvert will keep on working on it.