Yes, it is widely known that population density increases the homicide rate. However your first comment in this thread asserted that it is illogical or improper to compare (the homicide rate in) the US to Germany or China on the grounds that the one has a much smaller total population than the US and that the other has a much larger total population, and you have added nothing that supports those 2 assertions.

If every country in the world had the same area as every other country, then you could draw a line from total population to population density, but of course that is not the case.

Now, do the same with similarly sized cities and regions in the developed world - the EU, for example.

You’ll find dramatically lower rates for comparable populations.