The measure of map information has been one of the key issues in assessing cartographic quality and map generalization algorithms. It is also important for developing efficient approaches to transfer geospatial information. Road network is the most common linear object in real world. Approximately describe road network information will benefit road map generalization, navigation map production and urban planning. Most of current approaches focused on node diversities and supposed that all the edges are the same, which is inconsistent to real-life condition, and thus show limitations in measuring network information. As real-life traffic flow are directed and of different quantities, the original undirected vector road map was first converted to a directed topographic connectivity map. Then in consideration of preferential attachment in complex network study and rich-club phenomenon in social network, the from and to weights of each edge are assigned. The from weight of a given edge is defined as the connectivity of its end node to the sum of the connectivities of all the neighbors of the from nodes of the edge. After getting the from and to weights of each edge, edge information, node information and the whole network structure information entropies could be obtained based on information theory. The approach has been applied to several 1 square mile road network samples. Results show that information entropies based on edge diversities could successfully describe the structural differences of road networks. This approach is a complementarity to current map information measurements, and can be extended to measure other kinds of geographical objects.
Hierarchical structure of road network has received intensive attention either in urban planning or multi-scale representation. On the one hand, high-efficiency traffic flow counts on a reasonable hierarchical structure. On the other hand, it is a guide-line for cartographic generalization of road network. The paper attempts to investigate the hierarchical structure of a road network from two perspectives, a) the ht-index in terms of the degree connectivity, which was proposed to quantify the scaling and hierarchical structure of the network, b) the renormalization process, originated from complex network analysis, which is able to uncover the self-similarity of a network and reveal its hierarchical structure. We argue that the first point exhibits a big picture of the whole network, revealing the depth of the hierarchy, while the second point further illustrates how the nodes are organized to form a hierarchical structure at different scales. The hierarchical structures of 6 road networks in reality are examined accordingly. Results show that both indices are able to reveal the complexity of the hierarchy of a network. These conclusions can be beneficial to the road network generalization.
As one of the most important indexes for describing spatial complexity of urban road networks, radius fractal dimension has been proved to be useful in single-central cities. The method needs to choose a traffic hub as the center of measurement, but if the city has more than one traffic center, it will be difficult to choose a proper center and portray spatial complexity of the whole road network. The modified method proposed in this paper regards all the nodes of a network as centers of measurement and considers the whole effect of traffic centers in a polycentric city, so the modified radius fractal dimension describes the spatial complexity of a road network from an overall perspective and overcomes the problem that the traditional method relies on only one center. The experimental results show the modified radius fractal dimension is reliable, which can describe urban road networks in a new perspective.