Spatiotemporal Change Characteristics of Nodes’ Heterogeneity in the Directed and Weighted Spatial Interaction Networks: Case Study within the Sixth Ring Road of Beijing, China

Yusi Liu,Jingjing Liu,Disheng Yi,Jing Yang,Jing Zhang

doi:10.3390/su11226359

Abstract

Spatial heterogeneity patterns in cities are an essential topic in geographic research and urban planning. This paper analyzes the spatial heterogeneity of places and reflects on the urban structure in cites based on spatial interaction networks. To begin with, we constructed 24 sequentially directed and weighted spatial interaction networks (DWNs) on the basis of points of interest (POIs) and taxi GPS data in Beijing. Then, we merged 24 sequential networks into four clusters: early morning, morning, afternoon, and evening. Next, we introduced the weighted D-core decomposition method in view of the complex network method and weighted distance in a geographic space in order to obtain the in-coreness/out-coreness of places. Finally, three indices (the entropy index, the node symmetry index, and the t-test) were used to measure the heterogeneity of places from both the strength dimension and the direction dimension. The results showed: (1) For the strength dimension, the spatiotemporal strength characteristics of the nodes in the DWN are uneven on weekdays or on the weekends, and the strength heterogeneity on weekdays is more obvious than on weekends; (2) for the direction dimension, out-flows and in-flows are different in the early morning and evening on weekends. In addition, the direction of the DWN is not obvious. The city networks present flat characteristics. This study used the weighted D-core method to identify the heterogeneity of nodes in the DWN, which has certain theoretical and practical value for the planning of urban and urban systems and the coordinated development of cities.

Highlights

Spatial heterogeneity is a basic concept of geography which mainly reflects the first-order distribution of geographic phenomena and the spatiotemporal change characteristics of the second-order interaction in places [1]
We analyzed the heterogeneity of nodes from both the strength dimension and the direction dimension with the help of the entropy index, the node symmetry index, and the t-test
It can be seen that the difference of weighted out-coreness gradually increased, and the weighted in-coreness tended to be more balanced in the four periods on weekdays

Summary

Introduction

Spatial heterogeneity is a basic concept of geography which mainly reflects the first-order distribution of geographic phenomena and the spatiotemporal change characteristics of the second-order interaction in places [1]. The wide application of spatiotemporal big data and improvements in the social sensing concept offer a new paradigm for exploring spatial heterogeneity [2]. Betweenness centrality [17] relies on the identification of the shortest paths and measures the number of them that pass through a node, which characterizes how influential a node is in communicating between node pairs. Another centrality measure is the eigenvector centrality [15], which is defined as the principal or dominant eigenvector of the adjacency matrix A, which represents the connected subgraph or component of the network. Giatsidis et al [21] capitalized on the concept of graph degeneracy and defined a novel D-core framework, extending the classic graph-theoretic notion of k-cores for undirected graphs to directed ones

Methods

Results

Conclusion