Combining K-means method and complex network analysis to evaluate city mobility

Complex networks have been used to model public transportation systems (PTS) considering the relationship between bus lines and bus stops. Previous works focused on statistically characterize either the whole network or their individual bus stops and lines. The present work focused on statistically characterize different regions of a city (Curitiba, Brazil) assuming that a passenger could easily access different unconnected bus stops in a geographic area. K-means algorithm was used to partition the bus stops in (K =) 2 to 40 clusters with similar geographic area. Results showed strong inverse relationship (p < 2 × 10−16 and R2 = 0.74 for K = 40 in a log model) between the degree and the average path length of clustered bus stops. Regarding Curitiba, it revealed well and badly served regions (downtown area, and few suburbs in Southern and Western Curitiba, respectively). Some of these well served regions showed quantitative indication of potential bus congestion. By varying K, city planners could obtained zoomed view of the behavior of their PTS in terms of complex networks metrics.