Hospitality's relation to Community

We had our meeting this past Sunday night with our launch team. We talked about community and what it means. This week I've still been reflecting on it. I found myself thinking about hospitality in community. I kept coming back to certain questions. They weren't worded exactly like this but similar: Can you have community without hospitality at its core? If so, what would it look like? Can you have community without hospitality at all? I wonder if we were to "recover" a strong ethos or spirit of hospitality in our fellowships of Christ followers, how might that change the essence of each particular community of faith? A community could be hospitable and still closed off to those outside. But, I think that to do so would miss a major aspect of hospitality. What do you think?