If you really want your Facebook community to be active, then you need to make sure that it is connected to your other relevant online profiles and social media activity.
There are two main reasons for this:
One of the first things you need to do when you set up your profile, page, and community is to link it to your other online properties, such as a blog or business website. You can also mention your activity on these sites in your Facebook status updates.
But, there is another way to make dynamic connections to your other online social media activity...
How to Connect Social Media Accounts to Facebook
Pinterest: To connect your Facebook profile with Pinterest just go to the "Settings" menu which is located under the profile page on the top right-hand of your Pinterest account. Just scroll down to the bottom of the Settings page and move the slider over to the right so it is marked ON.
Twitter: According to the Twitter Help Center to connect your Twitter account to your Facebook profile:
Google+: Currently, Google+ doesn't make it easy to share posts from other networks on its platform. There are a few workarounds, though, that allow you to send your Google+ posts over to Facebook. Here are instructions on how to post on Facebook via Google+, and here is another method that automates the process.