Research interests in the studies of complex systems have been booming in many disciplines for the last decade. As the nature of geographic environment is a complex system, researches in this field are anticipated. In particular, the urban street networks in the Geographic Information System (GIS) as complex networks are brought forth for the thesis study. Meanwhile, identifying the scale-free property, which is represented as the power law distribution from a mathematical perspective, is a hot topic in the studies of complex systems. Many previous studies estimated the power law distributions with graphic method, which used linear regression method to identify the exponent value and estimate the quality that the power law fits to the empirical data. However, such strategy is considered to cause inaccurate results and lead to biased judgments. Whereas, the Maximum Likelihood Estimation (MLE) and the Goodness of fit test based on Kolmogorov-Smironv (KS) statistics will provide more solid and trustable results for the estimations. Therefore, this thesis addresses these updated methods exploring the topological patterns of urban street networks from an analytical perspective, which is estimating the power law distributions for the connectivity degree and length of the urban streets. Simultaneously, this thesis explores the street networks from a visual perspective as well. The visual perspective adopts the large network visualization tool (LaNet-vi), which is developed based on the k-core decomposition algorithm, to analyze the cores of the urban street networks. By retrieving the spatial information of the networks from GIS, it actually enables us to see how the urban street networks decomposed topologically and spatially. In particular, the 40 US urban street networks are reformed as natural street networks by using three "natural street" models.

The results from analytical perspective show that the 80/20 principle still exists for both the street connectivity degree and length qualitatively, which means around 20% natural streets in each network have a connectivity degree or length value above the average level, while the 80% ones are below the average. Moreover, the quantitative analysis revealed the fact that most of the distributions from the street connectivity degree or length of the 40 natural street networks follow a power law distribution with an exponential cut-off. Some of the rest cases are verified to have power law distributions and some extreme cases are still unclear for identifying which distribution form to fit. The comparisons are made to the power law statement from previous study which used the linear regression method. Moreover, the visual perspective not only provides us the chance to see the inner structures about the hierarchies and cores of the natural street networks topologically and spatially, but also serves as a reflection for the analytical perspective. Such relationships are discussed and the possibility of combining these two aspects are pointed out. In addition, the future work is also proposed for making better studies in this field.