Spatio-temporal evolution of population mobility differentiation patterns in a pandemic context: based on a network perspective

Figures & data

Figure 1. Flowchart of the full study. Note: WA is the abbreviation of weighted average.

Figure 2. Study area.

Table 1. Description of the calculation methods of network characteristics.

Network indicators	Indicator meaning	Formulas
Vertex strength	It is described as the total of each node’s edge weights (Barrat et al. 2004).	$S_i=\sum _{j\in {\mathit{N}}_{\mathit{i}}}{\omega }_{ij}=\sum _{j\in {\mathit{N}}_{\mathit{i}}}(R_{ij}+R_{ji})$ (5) ωij is the weight of the edge between node i and node j; Ni denotes the set of neighboring nodes of node i.
Weighted average degree (D value)	Higher values indicate larger average weights of node connections and larger scale of population mobility.	$D=\frac{1}{2N}\sum _{i=1}^{\mathit{N}}{S}_i$ (6)
Weighted average clustering coefficient (C value)	Used to measure the degree of node clustering, higher values prove that nodes tend to create groups with tight connections. In weighted networks, the edges with higher weights form more tightly groups (Onnela et al. 2005).	$C_i=\frac{2}{k_i(k_i-1)}\sum _{j,k}(\widetilde{{\omega }_{ij}}+\widetilde{{\omega }_{jk}}+\widetilde{{\omega }_{ki}}{)}^{\frac{1}{3}}$ (7) $\widetilde{{\omega }_{ij}}={\omega }_{ij}/\max {\omega }_{\mathit{all}}$ (8) $C=\frac{1}{N}\sum _{i=1}^N{C}_i$ (9) ki is the degree of node i; j, k are the nodes connected to i.
Weighted average path length (L value)	It measures the average distance between two nodes in the network, the smaller the value the better the accessibility of the network. In weighted networks, the similarity and dissimilarity weights influence the definition of L. In population mobility networks, the weights are often considered the similarity weights, which are inversely proportional to the distances (Opsahl et al. 2010).	$l(i,j)=\min (\frac{1}{\widetilde{{\omega }_{ih}}}+\cdots +\frac{1}{\widetilde{{\omega }_{ih}}})$ (10) $L=\frac{1}{N(N-1)}\sum _{i\ne j\in G}l(i,j)$ (11) h is the possible intermediate node between nodes i, j.

Figure 3. Total migration scale of the population in 2019.

Figure 4. Net migration scale of the population in 2019.

Figure 5. Topology of population mobility network in 2020 (pre-epidemic).

Figure 6. Comparison of total migration in 2019, 2020, and 2021.

Figure 7. Topology of population mobility network in 2021 (post-epidemic).

Table 2. Comparison of network characteristics between 2020 and 2021.

	First stage		Second stage		Third stage		Fourth stage
	2020	2021	2020	2021	2020	2021	2020	2021
D	84.209	25.020	33.355	33.283	16.468	45.750	13.312	51.180
C	0.126	0.094	0.162	0.150	0.098	0.106	0.084	0.114
L	1.646	1.688	1.712	1.802	1.870	1.958	1.880	2.010

Figure 8. Community structure division.

Figure 9. Two-dimensional distribution of MAC and MAP: (a) general view; (b) close-up view.

Table 3. The MAC and MAP of each node.

Rank	City	MAC	MAP
1	Beijing	27.78	17.74
2	Tianjin	14.92	4.38
3	Tangshan	3.74	0.03
4	Langfang	3.40	2.00
5	Shijiazhuang	0.54	−1.86
6	Qinhuangdao	−0.67	−0.88
7	Zhangjiakou	−0.81	−1.76
8	Baoding	−1.38	−0.88
9	Cangzhou	−2.39	−0.80
10	Hengshui	−2.96	−1.00
11	Chengde	−6.16	−1.29
12	Xingtai	−11.79	−2.58
13	Handan	−49.58	−6.79

Figure 10. Comparison of net migration scale in three central cities in 2019 and 2021.

Figure 11. Spatial grading characteristics: (a) MAC; (b) MAP.

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Data availability statement

The data that support the findings of this study are available from the corresponding author upon request.