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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. 

The effects of gentrification are well studied, with varied findings. Studies debating and nuancing gentrification’s effects have subsequently entailed variation on how the phenomena should be defined. The variance in definitions can create different calculations and potentially muddy findings on its effects. Having a well-defined methodology for calculating gentrification is essential to ensuring a deeper understanding of the phenomena and its effects. This article seeks to establish such a methodology that relies exclusively on publicly available data. This article overviews the definitions used in several peerreviewed articles to identify 12 different methods for calculating gentrification. The authors created an interactive tool that classifies census tracts as gentrifying (https://ogilani.shinyapps.io/Gentrification/), nongentrifying, and nongentrifiable in metropolitan areas in the United States. Through a case study of Pittsburgh, the authors offer insights into which definition of gentrification best fits a qualitative understanding of the city. This article leaves readers with a methodology and tool for defining and mapping gentrification across the United States, making it easy to compare the results across different definitions. This tool and application offer a way for researchers, activists, and policymakers to compare various definitions in a particular geography to ensure consistent findings in studies across the United States.