A genetic algorithm to partition weighted planar graphs in which the weight of nodes follows a power law

Abstract

This research makes use of evidence that the distribution of crime by census tracts in large cities follows a Power Law. This means that there are few places that concentrate many crimes and many places that concentrate few crimes. In this article we investigate how modeling complex networks and genetic algorithms can help to understand the behavior of samples representing views of part of the map of crimes of a large metropolis. The representation of the network is a planar graph where the nodes are the centroids of census tracts, the edges represent the adjacency between the tracts, and each node has a weight representing the number of crimes recorded in the census tract. The problem of this research lies in the context of the study of sampling distributions that have long tails (e.g. the weight of the nodes of the graph follows a Power Law). In particular, we describe a genetic algorithm to explore the space of possible samples of the initial distribution (plotted crimes throughout the city) so that the maximum number of samples holds features to follow a Power Law with an exponent close to the original distribution. © 2013 Springer-Verlag Berlin Heidelberg.