Murders are geographically highly concentrated.

You always have to be careful when mixing multiple dimensions of measurement.  From Murders in US Are Very Concentrated, and They Are Becoming Even More So by John R. Lott.  From the Abstract:

While murders and other violent crime in Los Angeles County and some other major urban areas have spread out to parts of those counties that didn’t previously experience much crime, nationwide murders appear to be coming even more concentrated in a small set of counties. When it comes to murder, there are three types of counties in the United States. Most counties experience no murders, a smaller set where there are a few murders, and then a tiny set of counties where murders are very common. In 2020, 52% of counties (with 10% of the population) had no murders. 68% of counties have no more than one murder, and about 18% of the population. These counties account for only 2.6% of all murders in the country. The worst 1% of counties (the worst 31 counties) have 21% of the population and 42% of the murders. The worst 2% of counties (62 counties) contain 31% of the population and 56% of the murders. The worst 5% of counties contain 47% of the population and account for 73% of murders. But even within those counties, the murders are very heavily concentrated in small areas.

The fact that 52% of counties (measurement of geographical dimension) have zero murders (murder dimension) is striking.  But it is sharply mitigated by the fact that they have only 10% of the population (population dimension).  "52% of counties (with 10% of the population) had no murders" catches your attention but it is not especially relevant.  Power Laws and the Pareto Distribution are prevalent in sociological research.  We would expect that 20% of the counties have 80% of the murders as a base line assumption because Pareto describes so many attributes.  20% of patients are 80% of the costs.  20% of the population earn 80% of the income.  

But the point isn't really that it is a Pareto Distribution but that it is a power law and Lott is pointing out useful information that in this instance, murders are a powerful power law.  "The worst 5% of counties contain 47% of the population and account for 73% of murders."  

Recognizing that, there are two obvious questions.  Is the concentration of murders in a small percentage of jurisdictions a function of density or of governance?

Both are valid assumptions.  Lott and others are leaning towards governance: that high murder rates are a function of public policies.  Presumably things like decarceration, depolicing, zero bond movement, deprosecution, etc.  

None-the-less, arguments could be made for the proposition that high murder rates are a function of density of population.   They can be made but likely won't hold water.  

I lean towards the argument that high murder rates are primarily a function of public policy in combination with local social norms/culture.  

In Why Do Democrats Think They Can ‘Win’ the Crime Issue? by Robert Stacy McCain tackles the argument that the murder rate follows gun ownership rates.  More guns owned, the higher the murder rate goes the argument.  McCain marries Lotts research with gun ownership data.

Among other things, Lott took into account rates of firearm ownership, and found an inverse relationship between the prevalence of murder and rates of gun ownership: “According to a 2021 Pew Research Center survey, the household gun ownership rate in rural areas was 79% higher than in urban areas. Suburban households are 37.9% more likely to own guns than urban households. Despite lower gun ownership, urban areas experience much higher murder rates.”

So much for the correlation between gun ownership and crime. What do we know about the correlation between politics and crime? The five U.S. cities with the highest per capita murder rates are St. Louis (69.4 per 100,000 population), Baltimore (51.1), New Orleans (40.6), Detroit (39.7), and Cleveland (33.7). In the 2020 presidential election, Joe Biden got 82 percent of the vote in St. Louis, 87 percent in Baltimore, 83 percent in New Orleans, 94 percent in Detroit and 80 percent in Cleveland. In other words, the most dangerous cities in America are all Democratic Party strongholds.

McCain's focus is more on partisanship than on policies per se.  I respectfully disagree, though there is an obvious connection.  I think his strongest point is the simple fact that the areas with the strictest gun control and the lowest gun ownership are also the areas with the highest murder rates.  It is generally true that these are also jurisdictions which are governed by Democrats but I would make a strong wager that the issue is much more aligned with public policy than it is partisan dominance.  A Democratic city with strong Second Amendment support and strong policing policies will almost certainly have lower than average murder rates.  

I think the county analysis is interesting but somewhat misleading But Lott's core point is an important one - murders are highly concentrated geographically, even below the county level.  Clearly gun control laws are only a weak explanatory variable, and where it is a strong variable, it is inversely related.  Fewer guns means higher murder rates, counter-intuitive as that might appear to some.

If we acknowledge that murders are highly concentrated, and if we acknowledge that gun control is at best a red herring, then we can begin the real worthwhile discussion.  Given the geographical concentration of murders, what are the public policies, particularly with regard to policing and the judicial system, which might be most conducive of lowering the murder rate.  And even more challengingly, what can City or County government do to change the cultural/social norms in a fashion conducive of lowering the murder rate.

Finally there is the unresolved issue of the connection between murder rates and urban density.  I have lived in very dense cities with extraordinarily low murder rates.  Just not in America.  This is part of why I think social and cultural norms are such a critical part of the equation.  Regardless, we need to know more.  Given high density, what are the public policies which might make a difference.  Particularly, perhaps, in terms of built environment considerations.  The possibility that urban design might have a direct influence on murder rates is a long standing argument.  I don't think it holds much water but we really don't know as far as I can tell.