Economic inequality is always presented as how economic metrics vary amongst individuals in a group, amongst groups in a population, or amongst some regions. Economic inequality can substantially impact the social environment, socioeconomics as well as human living standard. Since economic inequality always plays an important role in our social environment, its study has attracted much attention from scholars in various research fields, such as development economics, sociology and political science. On the other hand, economic inequality can result from many factors, phenomena, and complex procedures, including policy, ethnic, education, globalization and etc. However, the spatial dimension in economic inequality research did not draw much attention from scholars until early 2000s. Spatial dependency, perform key roles in economic inequality analysis. The spatial econometric methods do not merely convey a consequence of the characters of the data exclusively. More importantly, they also respect and quantify the spatial effects in the economic inequality. As aforementioned, although regional economic inequality starts to attract scholars' attention in both economy and regional science domains, corresponding methodologies to examine such regional inequality remain in their preliminary phase, which need substantial further exploration. My thesis aims at contributing to the body of knowledge in the method development to support economic inequality studies by exploring the feasibility of a set of new analytical methods in use of regional inequality analysis. These methods include Theil's T statistic, geographical rank Markov and new methods applying graph theory. The thesis will also leverage these methods to compare the inequality between China and US, two large economic entities in the world, because of the long history of economic development as well as the corresponding evolution of inequality in US; the rapid economic development and consequent high variation of economic inequality in China.