"But Why would density lead to higher murder rate?"
It's about opportunity. A kleptomaniac is going to find they steal left often when they're in the middle of a 100 acre property that they own than in a dense apartment complex.
One of the most significant criteria for committing murder (as opposed to suicide) is other people. You can have all the murderous intent in the world, but if there is no one else around, you're unlikely to pull it off. On the other hand, even if you don't generally have murderous intent, if a place is packed with other people, that increases the chances that for one reason or another you'll develop murderous intent towards one of them.