Graph Theory Techniques for Analyzing City Structure Regarding Socioeconomic Factors, Real Estate Market, and Climate Change

The primary purpose of this study is to present mathematical modeling methods inspired by graph theory operations and logic as a tool to structurally analyze the socio-economic composition of a city based on the geographical location of the investigated areas. We’ve incorporated graph theory concepts like connectivity, subgraph, degree, tree, complete graph, and dual graph as our model’s main components. We applied these methods to study the geographical distribution of food hardship in New York City, as well as housing prices in Boise, Idaho, and Miami, Florida. We conducted a structural analysis of our models and concluded several notable properties within the model results. We’ve also included the ocean’s current direction and location for the New York City model to speculate on the mechanism behind our results further. Graphs and quantitative data regarding each one of these factors are simulated and created through Gephi and R Studio, where the combination of these factors will be concluded and presented as the result of the study. In this way, the result of our model brings a step-by-step demonstration of how the graph theory and analysis techniques we’ve developed can be applied to any city with proper quantitative or qualitative data. The report in our prototype model focuses on population poverty and socio-economic conditions, emphasized and indicated through food hardship and the housing market within the area. We also discussed several plausible applications of our methods, including topics like climate change and the real estate market. Considering that our model is a skeletal position-based map exhibiting the functionality of the analysis techniques we’ve developed, the graph is a prototype for environmental science and mathematics researchers to examine, where they can further improve and optimize it for more accurate and informative results.