A social network often has numerous interesting attributes. When an attribute is quantified, a social tomography would
arise from the underlying social network. One of the most interesting attributes is crime hotspots, whose existence has
been strongly supported by observations that serious crime…
A social network often has numerous interesting attributes. When an attribute is quantified, a social tomography would
arise from the underlying social network. One of the most interesting attributes is crime hotspots, whose existence has
been strongly supported by observations that serious crimes ranging from residential burglary to homicide are strongly
patterned in time and space, and by mathematical modeling. So far, however, the structures of hotspots, including their
size distributions, have not been adequately studied. Here, we focus on a special type of hotspots, the sex offender
clusters, in the United States, and show that their size distribution, where size is defined as the ratio between sex offender
population and total population in a 5-digit zip code area, follows a power-law distribution. In contrast, such local total
population, both general and sex offenders, do not quite follow power-laws. A heavy-tailed power-law distribution is
fundamentally different from a thin-tailed distribution such as a Poisson distribution, and can be used as an objective
criterion for defining sex offender clusters. More fundamentally, a power-law is a defining property of self-similarity or
fractal behavior. Therefore, our finding indicates that sex offender clusters, size-wise, self-organize into a fractal, due to
interplay of economic conditions of offenders, policies and public perceptions.