Identifying loci in mobility networks with applications in New Zealand work commutes: a statistical test for identifying extreme stationary distribution values in Markov transition matrices

Abstract 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 urban planning, 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. We term these locations 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 distribution values 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.