Statistical Characteristics and Community Analysis of Urban Road Networks

Table 2

Six indices used for analysing urban road networks.

Indices	Equations	Interpretation
Degree		is the connection between node i and node j; if i and j are connected, is 1; otherwise, it is 0. The mean degree of a network, denoted as , is the average of the degree of all its nodes [32]. The degree distribution of the network is a ratio of the number of nodes with degree to the number of all nodes and represents the cumulative degree distribution.
Clustering coefficient		is the actual number of edges among the neighbours of node i (nodes connected with node i are called its neighbours); is the number of the neighbours of node i, namely degree of node i [3].
Closeness centrality		is the set of nodes, , and n is the number of nodes. is the length of the shortest path between i and j. For unweighted networks (i.e., every link has an equal length of 1), is the number of links of the shortest path between i and j, while for weighted networks, assuming that the weight is simply physical distance, is the physical distance of the shortest path from node i to j.
Betweenness centrality		is the total number of shortest paths between nodes and , and is the number of shortest paths passing through node i. Weighted betweenness centrality (WBC) takes the actual distance of the link as the edge weight.
Average path length		is the length of the shortest path between i and j. For unweighted networks (i.e., every link has an equal length of 1), is the number of links of the shortest path between i and j.
Efficiency		This index was first proposed by Crucitti et al. [33] to explore the global efficiency of complex networks and looked very similar to APL; in this study, actual distance is assigned to the weight of a link. The greater , the better the efficiency.