What are the Islamic tenets regarding cemeteries?

I am visiting a village in a Muslim nation. There is a mosque here. Right next to the mosque is a cemetery with many graves, some very old and some relatively new. The cemetery is unmaintained, it seems. The grass is high, graves are crumbling over, and things are generally in bad condition. Given that it's right next to a mosque I was surprised to see this, as I assumed (apparently incorrectly?) that it would be the duty of the mosque to maintain it. Hence the question in the title: what should be done (according to Islam) about this cemetery, especially considering that it's right next to (adjoined to) a mosque>