On Quantitative Measurements Of The Strucrural Complexity Of Road Networks

The urban road network is known as the basis of social economy development and human activities, which supports the transportation and communication. As the speeding up of urbanization, the urban road network is becoming increasingly complex no matter in shape but also in its structure. The complex network theory, arising in late 20s, has provided a new perspective for description of road network complexity. However, current research on road network based on complex network is limited to the complexity of pattern or testifying the common character of the structure, lacking quantitative measurements to describe their structure from the perspective of the connection relationship, e.g. the diversity, heterogeneity and etc. Entropy and Fractality theory are effective methods in complexity research. The topological entropy is able to describe the complexity of network structure, but current measurements are based on different model and not accurate enough. The structural fractality in the research of road network is limited to the box-counting dimension currently, which requires further investigation.Current index to quantify the topological entropy of map symbols only focus on the diversity or closeness of their connection relationship. They failed to characterize the space pattern and the structural feature of map symbols, especially when they did not take the compactness and heterogeneity into consideration. Therefore the measurements of compactness and heterogeneity entropy are proposed, and have been applied to three real-life road networks. Results indicated that the new developed compactness and heterogeneity entropy can accurately depict the topological properties of road networks.The thesis then examined the structural fractality of road network quantitatively according to the box-counting dimension, the volume dimension and the degree-volume dimension, taking road networks of different patterns and scales of examples. Results has shown that the road network is a typical structural fractal. The box-counting dimension decreased as the scales shrink. The volume dimension is closely related to the compactness and heterogeneity of the road network. The degree-volume dimension doesn’t relate to the scales. The thesis has further proved that the pattern has an influence on structure in its completeness, heterogeneity, accessibility, compactness and etc, while the three structural dimensions have described these influence from different perspectives.The conclusions of this thesis is benefit for understanding the relationship between structure and function, and it is able to provide theoretical ground for urban transportation planning, road selection and multi-scale representation in cartography. Further research effort will be devoted to building thorough measurement system to quantifying structural entropy of road network and applying the measurements in this thesis into cartographic generalization.