Figure 1.
Heat map of all check-in points and frequency distribution of check-ins in the 370 cities.
(A) The map, created using density estimation, clearly depicts the distributions of cities and transportation networks in China. Note that The South China Sea Islands are not shown for simplicity. (B) As shown by the CCDF (complementary cumulative distribution function), the frequency distribution exhibits a heavy tail characteristic. Shanghai and Beijing, the two biggest cities in China, have the most check-in records.
Figure 2.
Characteristics of check-ins from the perspective of users.
For each user, we compute the number check-ins, Nh, and the number of visited cities, Nc, so that the inter-urban movements can be extracted. Note that Nh and Nc are not well correlated, since a user may check in many times in the same city. (A) Complementary cumulative distribution of Nh. (B) complementary cumulative distribution of Nc. One user visited 83 cities, which is the maximum of all users. (C) Five anonymous example individuals’ trajectories.
Figure 3.
Comparison between trips extracted from check-in records, denoted by Tcij, and flight trips Tfij.
(A) Scatter plot of Tcij versus Tfij, indicating a weak positive correlation. (B) 50 city pairs with the top highest Tcij/Tfij.
Figure 4.
Characteristics of interaction strengths between the 370 cities.
(A) Interaction map of the 370 cities. The red lines indicate stronger interactions. The maximum value is 137,847, which is the number of trips between Shanghai and Suzhou, extracted from the check-in data set. The red dots represent capital cities of provinces in China. (B) Complementary cumulative distribution of edge weights (or interaction strengths) between cities.
Figure 5.
Plot of estimated versus observed interaction strengths when β = 0.8, indicating the observed inter-urban interactions can be well fitted using the gravity model.
The inset depicts the correlation in a log-log scale. Note that the estimated interaction strengths for some city pairs are less than 1 and thus negative values exist in the log-log plot.
Figure 6.
Different data sets represent different aspects of “the ground truth” of human movements and thus can be used for revealing different roles of the same city.
Given two known data sets for the same group of places, we can obtain two gravity models, denoted by and
. β1 and β2 represent the distance effect in the two interaction systems. Additionally,
and
indicate the importance of city i according to different data sets. For example, in the flight network, the attraction of Beijing is a bit greater than that of Shanghai, according to Ref. [11]. With regard to the check-in data, on the contrary, Shanghai is much more important than Beijing. Such a difference is caused by the fact that Beijing is China’s political center with more flight lines but Shanghai exceeds Beijing in both economy and ICT development. If we have a third inter-urban interaction data set for example collected from railway passenger flows, similar comparative investigation can also be conducted.
Figure 7.
Displacement distributions of observed and estimated trips.
The observed displacements follow an exponential distribution. We can find a small peak when Δd≈1200 km, since the distances between a number of big cities in China, such as Beijing-Shanghai, Beijing-Wuhan, Shanghai-Guangzhou, and Shanghai-Shenzhen, are all approximately 1200 km. There are a great number of trips for these city pairs (see Figure 4A). The closeness of two best fit lines indicates that the gravity model provides a reasonable explanation of the observed mobility pattern.
Figure 8.
Different individual level movement patterns may lead to the same collective statistics.
(A) The four persons’ movements are all influenced by the distance decay effect. (B) Distance decay effect is not clear for each person. However, the four persons’ movements collectively exhibit the distance decay effect.
Figure 9.
Communities detected from the interaction network G.
We run the multilevel algorithm 20 times, each of which yields a partition. By merging the Voronoi polygons of cities in the same community, a partition can be visualized. Regions with thicker borders indicate that they occur in more partitions.
Figure 10.
Log-log plot of estimated versus observed interaction strengths when β = 0.8.
The yellow rectangles and gray circles represent interactions between cities in one province and two different provinces, respectively. It is clear that the gravity model underestimates intra-province trips.