  Understanding human mobility patterns is important in applications as diverse
as urban planning, public health, and political organizing. One rich source of
data on human mobility is taxi ride data. Using the city of Chicago as a case
study, we examine data from taxi rides in 2016 with the goal of understanding
how neighborhoods are interconnected. This analysis will provide a sense of
which neighborhoods individuals are using taxis to travel between, suggesting
regions to focus new public transit development efforts. Additionally, this
analysis will map traffic circulation patterns and provide an understanding of
where in the city people are traveling from and where they are heading to -
perhaps informing traffic or road pollution mitigation efforts. For the first
application, representing the data as an undirected graph will suffice. Transit
lines run in both directions so simply a knowledge of which neighborhoods have
high rates of taxi travel between them provides an argument for placing public
transit along those routes. However, in order to understand the flow of people
throughout a city, we must make a distinction between the neighborhood from
which people are departing and the areas to which they are arriving - this
requires methods that can deal with directed graphs. All developed codes can be
found at https://github.com/Nikunj-Gupta/Spectral-Clustering-Directed-Graphs.
