High criminality rates within a neighborhood are directly related to the social gap there is between them and other higher status neighborhoods, within the same region.
It's not a coincidence that the ones where there is more crime, are usually in the peripheric area of a city. It's an inevitable structural consequence of the cities' growth process. Long ago, when the big cities were still being born, the best places to live were given to the nobles, the privileged part of the population, to settle, usually close to the commercial center (what grew to be nowadays' downtown).
While the rest of the population (the less privileged) were to occupy the surrounding areas. Evidently, this part of the population left to live at the margins would have lesser conditions to enjoy their basic social rights (access to education, health care, leisure, mobility to work, etc.), which back then were given very less importance to. And therefore, they would need more attention from the public authorities to secure those rights.
If you project this through the decades, with the natural exponential increase of the population, this disparity between regions only gets worse. And simultaneously, the transit of information and people became much easier with technology, so those in poorer conditions would have the means to know the lifestyle of those in better conditions, although unreachable for them.
At last, it's only natural for the underprivileged to desire at least a small fraction of what those with better social standards have, for themselves. And since the easiest way to achieve such, is through stealing, the crime rates rise where these people live.
