# Spatio-Temporal Change Characteristics of Spatial-Interaction Networks: Case Study within the Sixth Ring Road of Beijing, China

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Data Description and Processing

#### 2.1. Study Area and Data Description

^{2}. Its spatial structure is relatively stable. We chose the area within Beijing’s Sixth Ring Road as the study area, which covers 2267 km

^{2}and accounts for 8% of the total area of Beijing (Figure 1). As the main urban area of Beijing, it is the core area of economic development in Beijing, comprising many financial institutions, large enterprises, scientific-research institutions, and medical institutions. The area within the Sixth Ring Road in Beijing with a large population has a well-developed street network. Even though the subway is the main mode of public transportation, taxis have been an important component of the urban transportation system in recent years. Taxi data are widely used in analyzing urban functions, urban structures, and human mobility patterns. This research applies a taxi dataset collected from Beijing, China, including more than 15,000 taxis from several anonymous taxi companies in consecutive weeks (6 June to 3 July 2016). The data contain each taxi’s ID, location, sampling time, velocity, and status (vacancy or occupancy of passengers). In this paper, we only extracted the taxi’s ID, the time when the passengers were picked up and dropped off, and the location where the passengers were picked up and dropped off. Usually, the locations of these activities are viewed as the OD of a trip. These extracted trips together reflect the spatial interaction between places. Table 1 shows an example of the processed taxi data.

#### 2.2. Extracting Place Footprints

#### 2.3. Construction of Spatial-Interaction Networks

#### 2.4. Framework Overview

## 3. Methods

#### 3.1. Jensen–Shannon Distance between Snapshots

^{th}eigenvalue of $\mathrm{p}$. Neumann entropy ${\mathrm{S}}_{\left(\mathrm{r}\right)}$ and ${\mathrm{S}}_{\left(\mathrm{q}\right)}$ corresponds to matrices $\mathrm{p}$ and r, respectively.

#### 3.2. Hierarchical-Clustering Method

#### 3.3. Weighted K-Core Decomposition Method

#### 3.4. Additional Methods

_{c}is the number of nodes of the core layer. Similarly, the link ratio of the node within the bridge layer and the periphery layer are quantified by ${\mathrm{r}}_{\mathrm{b}}={\mathrm{l}}_{\mathrm{b}}/{\mathrm{n}}_{\mathrm{b}}$ and ${\mathrm{r}}_{\mathrm{p}}={\mathrm{l}}_{\mathrm{p}}/{\mathrm{n}}_{\mathrm{p}}$, respectively. In addition, we considered the ratio of connections from every layer to its neighbors and defined ${\mathrm{r}}_{\mathrm{cb}}$ as the ratio between the core layer and the bridge layer, which is

## 4. Results

#### 4.1. SINB Layer Aggregation

#### 4.2. SINB Change Properties on Weekdays

#### 4.2.1. Properties of Each Layer

#### 4.2.2. Evolving Topological SINB Characteristics on Weekdays

#### 4.2.3. Connection Patterns between Layers and Their Neighbors on Weekdays

#### 4.3. SINB Change Properties on Weekends

#### 4.3.1. Properties of Each Layer

#### 4.3.2. Evolving SINB Topological Characteristics on Weekends

#### 4.3.3. Connections between Nodes and Their Neighbors

## 5. Summary and Discussion

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Overall research structure and data-preprocessing flowchart. (

**a**) Extracting place footprints; (

**b**) Jensen–Shannon distance between snapshots; (

**c**) hierarchical-clustering method; (

**d**) aggregating the layers; and (

**e**) weighted K-core decomposition method.

**Figure 5.**Layer aggregation of Spatial-Interaction Networks of Beijing (SINB). (

**a**) Ratio of within-cluster variance to total variance for each possible choice of k (number of clusters) on weekdays; (

**b**) ratio of within-cluster variance to total variance for each possible choice of k (number of clusters) on weekends; (

**c**) dissimilarity matrix between snapshots on weekdays; (

**d**) hierarchical clustering on weekdays; (

**e**) dissimilarity matrix between snapshots on weekends; and (

**f**) hierarchical clustering on weekends.

**Figure 6.**Distribution of all places in different periods in three layers on weekdays. (

**a**) Early morning; (

**b**) morning; (

**c**) afternoon; and (

**d**) evening.

**Figure 7.**Distribution connection ratio of the core layer, the bridge layer, and the periphery layer on weekdays.

**Figure 8.**Distribution of all places in different periods in three layers on weekends. (

**a**) Early morning; (

**b**) morning; (

**c**) afternoon; and (

**d**) evening.

**Figure 9.**Connection ratio of the core layer, the bridge layer, and the periphery layer on weekends.

Taxi ID | Pick-Up Time | Pick-Up Coordinates | Drop-Off Time | Drop-Off Coordinates |
---|---|---|---|---|

158 | 6-6-2016 6:27:21 | 116.45806 E 39.98764 N | 2013-6-6 6:44:5 | 116.40218 E 39.94539 N |

2056 | 10-6-2016 0:2:44 | 116.58275 E 40.07931 N | 2013-6-10 0:31:47 | 116.28463 E 40.02774 N |

30024 | 29-6-2016 6:40:2 | 116.45534 E 39.94887 N | 2013-6-29 7:11:26 | 116.58095 E 40.07179 N |

Place Name | Business Name | Latitude | Longitude |
---|---|---|---|

Wudaokou | Yuye | 39.99102 N | 116.3353 E |

Wangjing | Bafu | 39.99644 N | 116.4815 E |

Sanlitun | Hema | 39.93144 N | 116.4535 E |

**Table 3.**The average cluster coefficient (C), average path length (S), and diameter (D) of SINB on weekdays.

C | S | D | |
---|---|---|---|

Early morning | 0.8259669 | 1.3944209 | 3 |

Morning | 0.7591855 | 1.5010729 | 3 |

Afternoon | 0.8049185 | 1.4240058 | 3 |

Evening | 0.8450749 | 1.3682659 | 3 |

**Table 4.**Top five places with the largest coreness values in the core layer, the bridge layer, and the periphery layer on weekdays. Value is the cluster coefficient of a place.

Early Morning | Morning | Afternoon | Evening | |
---|---|---|---|---|

Core layer | 0.000187 | 0.000221 | 0.000092 | 0.000059 |

0.000111 | 0.000521 | 0.000228 | 0.000657 | |

0.002032 | 0.000936 | |||

0.000513 | 0.000196 | |||

0.001762 | 0.000316 | |||

Bridge layer | 0.002022 | 0.001049 | 0.000689 | 0.000767 |

0.002474 | 0.001123 | 0.001070 | 0.000274 | |

0.005346 | 0.002169 | 0.001368 | 0.000447 | |

0.000386 | 0.004221 | 0.001873 | 0.000372 | |

0.002764 | 0.002141 | 0.000806 | 0.000179 | |

Periphery layer | 0.004975 | 0.004806 | 0.002203 | 0.001230 |

0.004348 | 0.007954 | 0.001953 | 0.001131 | |

0.004881 | 0.004186 | 0.002721 | 0.001210 | |

0.003932 | 0.007567 | 0.002327 | 0.001115 | |

0.004823 | 0.004240 | 0.002207 | 0.001146 |

**Table 5.**The average cluster coefficient (C), average path length (S), and diameter (D) of SINB on weekends.

C | S | D | |
---|---|---|---|

Early morning | 0.542549 | 1.837083 | 4 |

Morning | 0.576149 | 1.763341 | 4 |

Afternoon | 0.572588 | 1.800642 | 4 |

Evening | 0.581760 | 1.784302 | 4 |

**Table 6.**Top five places with the largest coreness in the core, bridge, and periphery layers on weekends. Value is the cluster coefficient of a place.

Early Morning | Morning | Afternoon | Evening | |
---|---|---|---|---|

Core layer | 0.000624 | 0.000480 | 0.000431 | 0.000445 |

0.000953 | 0.000330 | 0.002602 | 0.002483 | |

0.004744 | 0.000917 | 0.001010 | ||

0.000785 | 0.003006 | 0.002719 | ||

0.000937 | 0.001638 | 0.002119 | ||

Bridge layer | 0.009873 | 0.002981 | 0.003217 | 0.001839 |

0.003197 | 0.003591 | 0.008582 | 0.001667 | |

0.008192 | 0.001418 | 0.003176 | 0.003493 | |

0.009276 | 0.002487 | 0.004670 | 0.003904 | |

0.005565 | 0.001590 | 0.005999 | 0.004558 | |

Periphery layer | 0.012143 | 0.004031 | 0.006808 | 0.007372 |

0.019334 | 0.003653 | 0.008446 | 0.008036 | |

0.007584 | 0.005999 | 0.008629 | 0.006303 | |

0.008897 | 0.003227 | 0.017204 | 0.005884 | |

0.025682 | 0.004670 | 0.010522 | 0.009533 |

**Table 7.**Comparison of the number of different coreness values obtained by a previous method and our method. Spre and Sour, number of different coreness values obtained by the previous method and our method, respectively. Cpre and Cour, number of places in the core layer obtained by the previous method and our method, respectively.

Spre | Sour | Cpre | Cour | |
---|---|---|---|---|

Early morning | 91 | 133 | 57 | 3 |

Morning | 94 | 117 | 56 | 14 |

Afternoon | 90 | 120 | 60 | 34 |

Evening | 91 | 111 | 66 | 40 |

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**MDPI and ACS Style**

Yang, J.; Yi, D.; Qiao, B.; Zhang, J. Spatio-Temporal Change Characteristics of Spatial-Interaction Networks: Case Study within the Sixth Ring Road of Beijing, China. *ISPRS Int. J. Geo-Inf.* **2019**, *8*, 273.
https://doi.org/10.3390/ijgi8060273

**AMA Style**

Yang J, Yi D, Qiao B, Zhang J. Spatio-Temporal Change Characteristics of Spatial-Interaction Networks: Case Study within the Sixth Ring Road of Beijing, China. *ISPRS International Journal of Geo-Information*. 2019; 8(6):273.
https://doi.org/10.3390/ijgi8060273

**Chicago/Turabian Style**

Yang, Jing, Disheng Yi, Bowen Qiao, and Jing Zhang. 2019. "Spatio-Temporal Change Characteristics of Spatial-Interaction Networks: Case Study within the Sixth Ring Road of Beijing, China" *ISPRS International Journal of Geo-Information* 8, no. 6: 273.
https://doi.org/10.3390/ijgi8060273