  Human mobility describes physical patterns of movement of people within a
spatial system. Many of these patterns, including daily commuting, are cyclic
and quantifiable. These patterns capture physical phenomena tied to processes
studied in epidemiology, and other social, behavioral, and economic sciences.
This paper advances human mobility research by proposing a statistical method
for identifying locations that individual move to and through at a rate
proportionally higher than other locations, using commuting data for the
country of New Zealand as a case study. These locations are termed mobility
loci and they capture a global property of communities in which people commute.
The method makes use of a directed-graph representation where vertices
correspond to locations and traffic between locations correspond to edge
weights. Following a normalization, the graph can be regarded as a Markov chain
whose stationary distribution can be calculated. The proposed permutation
procedure is then applied to determine which stationary distributions are
larger than what would be expected, given the structure of the directed graph
and traffic between locations. The results of this method are evaluated,
including a comparison to what is already known about commuting patterns in the
area as well as a comparison with similar features.

Applications;Methodology