Characteristics and prediction of urban interaction networks from the perspective of traffic flow and text information flow

Abstract

The degree of urban development depends on the degree of closeness between cities, which is reflected in the strength of interactions between cities, such as traffic and information flows. In this research, we compare and analyze the characteristics of urban interaction networks (UINs) at two spatial scales in Shandong Province and the whole country from two different perspectives of traffic flow and information flow and validate the spatial interaction characteristics reflected in the material space traffic flow from the perspective of textual spatial information flow. The UIN is constructed based on Tencent migration big data, and the assortative coefficient method is introduced to explore the assortative and interaction characteristics between core cities and edge cities in the traffic flow network. Introducing deep learning methods on a larger scale, the GCN_CD model is proposed for semi-supervised classification of nodes to realize community discovery for both traffic flow and information flow networks. The spatial interaction intensity prediction model $GAT_d^{β}$ is constructed taking into account geographic features, which improves the prediction accuracy. The results show that from the perspectives of traffic flow and text information flow, the urban interactive network in Shandong Province has the characteristics of Scale-Free and Small-World, showing certain homogeneity and strong spatial interaction. Shandong Province’s UIN formed Jinan, Qingdao, and other cities as the core, satellite cities around, the east and west ends of the remote echo structure. From the perspective of traffic flow, the national urban interactive network presents a jumping distribution, with a single core city as the dominant distribution structure. From the perspective of information flow, the dividing line between the eastern and western communities is obvious, and the internal aggregation of the community is strong. Distance attenuation effects have an impact on the strength of spatial interactions.

Keywords

Spatial interaction traffic flow network toponym co-occurrence network graph convolutional neural network interaction intensity prediction

Introduction

With the decrease in transportation costs and the development of internet technology, the functional connections between cities in the region have changed from a vertical hierarchical relationship to a network structural relationship (Sun and Hou, 2020). The urban interaction network (UIN) is a horizontal and non-hierarchical linkage of large, medium, and small cities with a mobility network structure (Capello, 2004). Understanding the characteristics of the spatial structure of the UIN as a theoretical foundation and scientific basis for the construction of new urbanization in the future is of great significance in alleviating the deepening urban problems, as well as in guiding the planning for the growth of the urban economy and the development of urbanization.

The study of urban interaction has always been a hot topic. Jia et al. mainly discussed dynamic community detection and spatio-temporal analysis in multi-layer spatial interaction networks based on trajectory data and proposed a new method to deal with multi-layer spatial interaction networks, which can provide valuable references and decision-making support for practical transportation planning and urban management (Jia et al., 2022). Gong et al. used social media data and high-speed rail network data to build an econometric model to study the impact between city interactions and social media use, and the results show that high-speed rail provides a new impetus for inter-city social media interactions while facilitating inter-city population mobility, and that the enhancement of inter-city social media interactions makes city interactions more frequent and closer (Gong et al., 2021). Li et al. used a method based on Baidu search data and microblogging data to analyze online information interactions in different cities and found that the intensity of city interactions is closely related to the size of the city’s population, the level of economic development, and the geographic distance between cities (Li and Duan, 2020). Michal et al. used complex network theory and spatial analysis methods to explore the characteristics and influencing factors of urban interaction space, and the results showed that the attractiveness of the area around the city not only depends on the size and geographic location of the city but is also affected by factors such as the competitive relationship between cities, transportation network, and economic development (Michal et al., 2021).

As cities are more and more closely connected to each other, research on the characteristics of UIN has gradually become a hot topic (Liu et al., 2020a; Yao et al., 2022). Cao used the complex network theory and spatial analysis methods to analyze the impact of urban spatial structure on the travel behavior of cab users and put forward targeted management recommendations, which are of great significance for urban planning and traffic management departments to formulate efficient traffic management policies (Cao, 2021). Lin et al. revealed the spatio-temporal asymmetry of population mobility based on the complex network analysis method of Spring Festival population migration big data (Lin et al., 2021). Wei et al. combined the data on population movement in China during the Spring Festival in 2015 to establish a network and conducted a structural analysis for the phenomenon of rich people’s clubs and found that the network was characterized by typical oligarchy (Wei et al., 2018).

Community discovery algorithms help researchers to extract useful information from UIN data in a way that aims to divide the graph into small-scale clusters (Gupta and Singh, 2020). Many community discovery algorithms have emerged in the last decade. Tang et al. proposed a new node influence measure based on local and global attributes to assess the importance of overlapping nodes (Tang et al., 2019). Xing et al. proposed a node influence-based label propagation community detection algorithm to improve the performance of Label Propagation Algorithm (LPA) by improving the node order of label update and the label selection mechanism when the maximum number of nodes contains multiple labels (Xing et al., 2014). Xie et al. proposed LabelRank, an efficient algorithm for detecting communities through label propagation, which solves the problem of randomness in the traditional LPA and stabilizes the discovery of communities in the same network (Xie and Szymanski, 2013). Sun et al. applied the ideas and concepts of game theory to the clustering of graphs and proposed a new community discovery algorithm, the game clustering approach (Sun et al., 2021). Newman proposed and studied a set of algorithms for discovering the structure of network communities the natural division of network nodes into densely connected subgroups (Newman and Girvan, 2004).

Because graph convolutional neural networks have shown excellent ability in processing non-Euclidean data, scholars have gradually applied them to urban computing. Zhang et al. investigated the Seasonal Prediction Recurrent Network (SPRNN) for seasonal spatio-temporal data and its application in urban computing, proposed a novel SPRNN model that can efficiently deal with spatio-temporal data while taking seasonal changes into account, and realized various applications in urban computing (Zhang et al., 2020a). Guo et al. proposed a spatio-temporal recurrent convolutional network model aimed at modeling the short-term patterns of population flow for the purpose of predicting traffic flow in urban areas (Guo et al., 2019). Ling et al. combined the ideas of Graph Convolutional Neural Network (GCN) and Gate Recurrent Unit (GRU) to propose a time-map convolutional neural network-based approach aimed at capturing the spatial and temporal dependencies of traffic data that are used to predict traffic flow (Ling et al., 2019).

Scholars’ research methods for UIN mostly adopt the traditional complex network theory (Peng et al., 2021; Wang and Xu, 2009; Zou et al., 2013; Wang et al., 2021). However, the matchability method for central cities and edge cities is relatively rare, resulting in the inability to better analyse the connectivity trend of the nodes of urban agglomerations, which is not conducive to the study of the diversification and specialisation of urban development. Modularity optimization, LPA, etc., are generally used in community discovery in existing studies (Akbarzadeh et al., 2019; Liu et al., 2020b). Deep learning method belong to the frontier in the field, and it is a promising approach to fully utilize the advantages of graph neural networks in processing network data for UIN community discovery and interaction intensity prediction (Jiang, 2022; Tian et al., 2023; Yang, 2023). Meanwhile, most of the existing studies study urban interaction from a single perspective of material space, such as traffic flow, and the comparative analysis of the material flow UIN from the perspective of text space information flow is a new perspective, which helps to explore the different characteristics of urban interaction from two perspectives and deepen the understanding of the characteristics and structure of the UIN.

To address the above issues, this study constructs two types of UINs based on Tencent migration big data and place name co-occurrence data from two perspectives: material space traffic flow and text space information flow, respectively, and compares and analyzes the structural characteristics of the networks under different perspectives. Matching coefficients are introduced, and the matching coefficient method is used to explore the matching and interaction characteristics between core cities and edge cities in the two types of networks. Deep learning methods in the field of artificial intelligence are introduced into community discovery, and a graph neural network-based community discovery GCN-based Community (GCN_CD) Detection algorithm is proposed to classify city nodes and to validate the city interaction features and community agglomeration reflected by the traffic flow in the material space from the perspective of information flow in the text space. Based on a graph neural network, the spatial interaction intensity prediction model $GAT_d^{β}$ is constructed taking into account the distance feature, which improves the model prediction accuracy and is conducive to the formulation of rational urban development planning.

Data sources and preprocessing

The traffic flow data in this study comes from the Tencent Migration Big Data positioning platform (https://heat.qq.com/qianxi.php) (Lai and Pan, 2019), which provides migration data for many different modes of transportation (Zhang et al., 2020b), helping to solve the current problem of not being able to coordinate traffic travel data from multiple sources.

The traffic flow data is divided into two scales. The Shandong Province scale data are the top 10 in-migration and out-migration data in terms of people flow under the two modes of transportation, highway and railroad, and contain a total of 90,586 records. The national-scale data uses air flow data from 329 cities across China for a total of 31 days from 1 January to 31 January, 2018, with a spatial resolution of 1 km and a temporal resolution of 1 day. There are a total of 599,550 records. After data cleaning, the city interaction data was finally integrated to get the city interaction data.

The information flow data are characterized by toponymic co-occurrence in text space. Toponym co-occurrence data were obtained from China News (https://sou.chinanews.com/advSearch.do). The toponymic co-occurrence data of Shandong Province for a total of 31 days from 1 January to 31 January, 2018, and the national toponymic co-occurrence data were obtained. The national place name co-occurrence data includes 328 cities, compared to the Tencent migration data lacking Laiwu, as the keyword place name co-occurrence data, totaling 54,765 records.

Method

Characterizing urban interactive network from two perspectives

According to the principle of graph theory (Liu et al., 2014), two kinds of traffic flows between cities in Shandong Province are abstracted into a complex network, and an interaction-weighted directed network $G = (V, E, W)$ is established for cities in Shandong Province (Figures 1 and 2). Where $V = {v_{1}, v_{2}, \dots, v_{n}}$ is the set of 17 cities in Shandong province as nodes, $E = {e_{1}, e_{2}, \dots, e_{n}}$ is the set of inter-city migration routes as edges, and the total number of population migrations on each migration route is used as weights $W = {w_{12}, w_{23}, \dots, w_{i j}}$ .

From a statistical point of view, when two place names co-occur in a document, it represents that there is some kind of connection and interaction between the geographic entities referred to by these two place names. That is to say, place name co-occurrence can be used as the information flow mapping of city interaction in material space in text space. The information flow UIN $M = (X, Y, W)$ is constructed in Shandong Province based on the toponymic co-occurrence data (Figure 3), with cities as the network nodes $X = {x_{1}, x_{2}, \dots, x_{n}}$ and the co-occurrence relationship of cities in the news as the edges $Y = {y_{12}, y_{23}, \dots, y_{i j}}$ , and the value of the association strength is the weight of the edges $W_{i j}$ .

Degree and degree distribution

Scale-free characteristic is one of the important statistical features of complex networks. The research adopts node degree and degree distribution for the validation of scale-free characteristics of UIN from two perspectives. The degree $k_{i}$ of node $i$ in the network is calculated as follows:

k_{i} = \sum_{j} a_{i j} (i \neq j)

(1)

From the point of view of probability statistics, the degree distribution $P_{k}$ is the probability that any fixed node in the network has and only has $k$ edges, that is, the probability that the degree is $k$ .

Clustering coefficient and average path length

Small-world properties are another important statistical feature of complex networks. To analyze the small-world properties of UIN, the clustering coefficients and average path lengths are computed to obtain an overall indication of node clustering or clustering.

The clustering coefficient of node $i$ is the probability that the $k_{i}$ nodes connected to it are also connected to each other, and the formula for the clustering coefficient is as follows:

C_{i} = \frac{2 E_{i}}{k_{i} (k_{i} - 1)} i = 1, 2, \dots, N

(2)

In the formula, $E_{i}$ is the actual number of edges between the $k_{i}$ nodes. There may be at most $k_{i} (k_{i} - 1) / 2$ edges between these $k_{i}$ nodes, and the average clustering coefficient formula is as follows:

C = \frac{1}{N} \sum_{i = 1}^{N} C_{i}

(3)

In the formula, $N$ is the number of network nodes and $C$ is the average clustering coefficient.

Distance decay of spatial interaction

Distance decay is one of the main laws of geography. In order to study the difference between the two perspectives of urban interaction distance decay effect, the research uses the gravity model expressed in the following equation to calculate the distance number decay coefficient $β$ :

I_{i j} = K \frac{C_{i} C_{j}}{D_{i j}^{β}}

(4)

In the formula, $I_{i j}$ is the interaction strength between entities $i$ and $j$ , $K$ is a constant coefficient, $C_{i}$ and $C_{j}$ are the scales of the entities, and $D_{i j}$ is the distance between the entities.

Network local matchability methods

The research uses four types of centrality indicators, namely, degree centrality, median centrality, distance centrality, and eigenvector centrality, to analyze the centrality characteristics of UIN from two perspectives.

In the traffic flow UIN, the matching coefficient method is introduced to study the specific interaction characteristics of core cities and edge cities. For the traffic flow UIN in Shandong Province, the matching characteristics in four directions are measured separately, including in-degree-in-degree, in-degree-out-degree, out-degree-in-degree, and out-degree-out-degree, with the following formulas:

ρ (i n, i n) = \frac{\sum_{i = 1}^{M} [t_{i}^{j_{i n}} - (M + 1) / 2] [t_{i}^{k_{i n}} - (M + 1) / 2]}{\sqrt{\sum_{i = 1}^{M} {[t_{i}^{j_{i n}} - (M + 1) / 2]}^{2} \sum_{i = 1}^{M} {[t_{i}^{k_{i n}} - (M + 1) / 2]}^{2}}}

(5)

ρ (i n, o u t) = \frac{\sum_{i = 1}^{M} [t_{i}^{j_{i n}} - (M + 1) / 2] [t_{i}^{k_{o u t}} - (M + 1) / 2]}{\sqrt{\sum_{i = 1}^{M} {[t_{i}^{j_{i n}} - (M + 1) / 2]}^{2} \sum_{i = 1}^{M} {[t_{i}^{k_{o u t}} - (M + 1) / 2]}^{2}}}

(6)

ρ (o u t, i n) = \frac{\sum_{i = 1}^{M} [t_{i}^{j_{o u t}} - (M + 1) / 2] [t_{i}^{k_{i n}} - (M + 1) / 2]}{\sqrt{\sum_{i = 1}^{M} {[t_{i}^{j_{o u t}} - (M + 1) / 2]}^{2} \sum_{i = 1}^{M} {[t_{i}^{k_{i n}} - (M + 1) / 2]}^{2}}}

(7)

ρ (o u t, o u t) = \frac{\sum_{i = 1}^{M} [t_{i}^{j_{o u t}} - (M + 1) / 2] [t_{i}^{k_{o u t}} - (M + 1) / 2]}{\sqrt{\sum_{i = 1}^{M} {[t_{i}^{j_{o u t}} - (M + 1) / 2]}^{2} \sum_{i = 1}^{M} {[t_{i}^{k_{o u t}} - (M + 1) / 2]}^{2}}}

(8)

Among them, $t_{i}^{j_{i n}}$ and $t_{i}^{k_{i n}}$ are the sorted in-degree and in-degree levels of nodes at both ends of edge $i$ , $t_{i}^{j_{i n}}$ and $t_{i}^{k_{o u t}}$ are the in-degree and out-degree of nodes at both ends of edge $i$ degree-sorted grades, $t_{i}^{j_{o u t}}$ and $t_{i}^{k_{i n}}$ are the sorted out-degree and in-degree grades of the nodes at both ends of edge $i$ , $t_{i}^{j_{o u t}}$ and $t_{i}^{k_{o u t}}$ are the nodes at both ends of edge $i$ out-degree and out-degree sorted rank, and M is the total number of edges in the network.

In order to study more deeply the contribution of individual city nodes to the overall assortative of the interaction network, the local assortativity method is introduced and its contribution value is expressed by $ρ_{i}$ . In the process of calculating the local assortativity of nodes in the network, not only the connectivity of the nodes themselves is considered but also the connectivity of the neighboring nodes is analyzed, so as to better reflect the degree of node’s contribution to the overall network assortativity, and the formula for the contribution value is as follows:

ρ_{i} = \frac{(j + 1) (j \bar{k} - μ_{q}^{2})}{M σ_{q}^{2}}

(9)

M

is the total number of edges in the network,

j

is the residual degree of the node,

\bar{k}

is the average residual degree of its neighbor nodes,

μ_{q}

is the expected value of the network residual degree distribution

q (j)

, and

σ_{q}^{2}

is the variance of the network residual degree distribution

q (j)

and

σ_{q}^{2} \neq 0

Community detection method based on GCN CD

The research is based on graph convolutional neural network (Figure 4), which uses semi-supervised node classification to classify the network nodes into communities.

The layer-by-layer propagation formula of a multilayer graph convolution neural network is as follows:

H^{(l + 1)} = σ ({\tilde{D}}^{- \frac{1}{2}} \tilde{A} {\tilde{D}}^{- \frac{1}{2}} H^{(l)} W^{(l)})

(10)

Among them, $\tilde{A} = A + I$ , I is the identity matrix; $\tilde{D}$ is the degree matrix of $\tilde{A}$ ; $H$ is the feature of each layer; for the input layer, $H_{0}$ is $X$ ; $σ$ is the nonlinear activation function.

The activation function adopts ReLU and Softmax, respectively, and then the overall forward propagation formula is as follows:

Z = f (X, A) = s o f t m a x (\hat{A} R e L U (\hat{A} X W^{(0)}) W^{1})

(11)

where

W^{(0)} \in R^{C \times H}

is the weight from the input layer to the hidden layer,

W^{1} \in R^{H \times F}

is the weight from the hidden layer to the output layer, and the Softmax function is to complete the Node classification task, predicting node labels.

Cross entropy is used as the cost function with the following formula:

L = - \sum_{l \in y_{L}} \sum_{f = 1}^{F} Y_{l f} \ln Z_{l f}

(12)

In this, $y_{L}$ is a collection of labeled nodes and node classification is achieved by updating the parameters of the network through gradient descent algorithm.

Interaction strength prediction method based on distance characteristics

Distance is a very critical factor in urban spatial interaction prediction research. In this research, on the basis of GAT model, urban interaction intensity prediction is carried out taking into account the distance characteristics.

The attention mechanism is a single-layer feed-forward neural network that is parameterized using a weight vector $a$ of size $\vec{a} \in R^{2 F^{'}}$ . The method uses LeakyReLU nonlinear operations to optimize the performance of the model, and the final attention coefficient formula is as follows, with $T$ denoting the transpose and || denoting the connect operation:

α_{i j} = \frac{\exp (L e a k y R e L U ({\vec{a}}^{T} [W {\vec{X}}_{i} ‖ W {\vec{X}}_{j}]))}{\sum_{k \in N_{i}} \exp (L e a k y R e L U ({\vec{a}}^{T} [W {\vec{X}}_{i} ‖ W {\vec{X}}_{K}]))}

(13)

{\vec{X}}_{i}^{'} = σ (\sum_{j ϵ N_{i}} α_{i j} W {\vec{X}}_{j})

(14)

The research uses a multi-head attention mechanism to aggregate node attribute features and connected edge weights with the following formula:

{\vec{X}}_{i}^{'} = ‖ \begin{array}{l} K \\ k = 1 \end{array} σ (\sum_{j ϵ N_{i}} α_{i j}^{k} W^{k} {\vec{X}}_{j})

(15)

Among them, $α_{i j}^{k}$ is calculated by the attention mechanism $a^{k}$ and $W^{k}$ represents the weight matrix of the linear transformation. The final output node $X^{'}$ contains $K F^{'}$ features over $F^{'}$ .

In this research, based on the principle of GAT model, the distance attenuation coefficient is introduced to calculate the weight of the edges to update the node features, so that the prediction results are more accurate. Among them, the formula for node weight calculation is as follows:

W_{i j} = d^{β}

(16)

Results and analysis

The two types of UINs of traffic flow and information flow constructed in part 2.1 are characterized in terms of network structure, and the differences in spatial interaction network characteristics between the two perspectives are compared and analyzed. Traffic flow UIN is divided into two types according to transportation modes, railroad transportation UIN and highway transportation UIN, so the network structure characterization is actually carried out for the three interaction networks.

Comparative analysis of the structural characteristics of UIN

Scale-free characteristics

The degree distribution data of the constructed traffic flow and information flow UIN are calculated according to the degree and degree distribution formula (2). The degree distributions of the two networks present consistent characteristics, with a small number of nodes having a small number of connections and a large number of connections for most of the nodes, which is contrary to the case of the scale-free network where a small number of nodes have a large number of connections. In contrast, the majority of the nodes have a small number of connections. Both networks are calculated by two degree metrics, inbound and outbound, and the distributions of inbound and outbound degrees also show consistent characteristics. Further power law fitting is performed on the degree distributions of the traffic flow and the information flow UIN, and the fitting results are shown in Figures 5 and 6. It can be seen that the power indices of the power functions fitted to the three networks are not less than −1, indicating that none of them has scale-free characteristics.

Small-world property

According to the clustering coefficient and average path length formula (3), the results of the comparison between the traffic flow and information flow UIN and the random network characteristic indexes are obtained as shown in Figures 1 –3. It can be seen that the average clustering coefficients of the two networks are much higher than those of the random network with the same number of nodes, indicating that whether in the perspective of traffic flow or information flow, the inter-urban interaction network has small-world characteristics.

The assortative of UIN

Identification of core cities

The study analyzed UIN focusing on traffic and information flows. Centrality indices for each node were computed using specific metrics (refer to Figures 7 –9). Jinan, Jining, Linyi, and Qingdao exhibit a centrality of 1 in both traffic and information flow networks, indicating their core status. Notably, Dezhou, Tai’an, Weifang, Weihai, and Zibo also have a centrality of 1 in the railway traffic flow network, highlighting strong direct connections. However, in the information flow network based on toponym co-occurrence, only Qingdao and Jinan have a centrality of 1, suggesting a weaker inter-city information flow in Shandong Province than migration patterns.

The distance centrality of a city indicates its proximity to other cities, with highly central cities often situated centrally in space. Figures 7(b), 8(b), and 9(b) illustrate similar distributions of distance centrality and degree centrality in both traffic flow and information flow UIN. Meanwhile, the urban distance centrality of the three networks is generally high, which also fully supports the argument that the UIN in Shandong Province has small-world characteristics, as described in the previous section.

Betweenness centrality measures a city’s transit capability within the entire network. In the UIN for traffic and information flow, Jinan, Jining, and Qingdao exhibit high betweenness centrality, indicating their pivotal transit roles (see Figures 7(c) and 8(c)). Contrasting with physical traffic flow, the textual spatial information flow network, as depicted in Figure 9(c), shows reduced high betweenness centrality cities within Shandong Province’s hinterland. This suggests that textual spatial information flow in the province relies on the transmission and diffusion facilitated by the two city clusters of Qingdao and Jinan.

In the network, the importance of a city node depends on both the number of its neighboring city nodes and the importance of its neighboring city nodes themselves. The four cities of Jinan, Jining, Linyi, and Qingdao in the UIN of traffic flow have high eigenvector centrality, as shown in Figures 7(d) and 8(d). In the UIN of Shandong Province from the perspective of information flow, Qingdao and Jinan have high eigenvector centrality, as shown in Figure 9(d).

Through the centrality analysis, the cities with high centrality value of UIN in Shandong Province from the perspective of traffic flow are the core cities, which are Jinan, Jining, Linyi, and Qingdao, respectively, and the other 13 cities are the marginal cities. The core cities from the perspective of information flow are Jinan and Qingdao. The core city occupies a pivotal position in the entire UIN and is closely connected with the edge cities.

Network assortative characteristics

According to the assortative coefficient method formula and local assortativity method formulas (5)–(9), the assortative coefficient and contribution degree are calculated, and the assortative analysis is introduced for two networks with cities as nodes. From a global perspective, the UIN of Shandong Province as a whole reflects a heterogeneous network.

In the urban interaction network, there are many cities with the same degree value, but these cities are not connected to other cities in the same way, which leads to the fact that their contribution to the overall heterogeneity of the network is not always the same. In the urban assortative coefficient of highway traffic flow, the absolute value of in-degree-in-degree is larger, which is 0.112, as shown in Figure 4. Therefore, in this network, the interactive connection between city nodes is more dependent on the direction of in-migration. In the urban assortative coefficient of railway traffic flow, the absolute value of out-degree-out-degree is larger, which is 0.174, as shown in Figure 5, so the interactive connection between city nodes is more dependent on the direction of out-migration.

The contribution value of each city reflects the contribution of the city to the overall mismatch of the network and reflects the status of the city in the network. In the urban interactive network of highway traffic flow, the cities with high values of contribution values are Jinan, Jining, and Linyi, all of which are 0.3356, as shown in Figure 6. It indicates that the three city nodes are at the core of the network and contribute more to the overall heterogeneity of the network. In the network of railway traffic flow, five cities, namely, Dezhou, Qingdao, Jining, Tai’an, and Weifang, have the highest values of contribution values and excellent contributions, as shown in Figure 7.

Community detection results and validation

Community detection results

Selecting 31 provincial capital cities, municipalities, and autonomous regions as city nodes to build an UIN for both air and information flows (Figures 10 and 11). The proposed GCN_CD algorithm is used for community segmentation of two UINs. Using the natural breakpoint method to classify the degree centrality of the nodes in the UIN, it is determined that the central cities of the air traffic flow network are Beijing, Hangzhou, Jinan, Shijiazhuang, Guangzhou, and Lanzhou, and the central cities of the information flow network are Beijing, Hangzhou, Guangzhou, Jinan, Wuhan, and Xi’an. The central city node is used as the label node to community detection of the GCN_CD algorithm, and the loss function image is shown in Figure 12.

Figures 13 and 14 show the community detection results of the national air traffic flow urban interactive network and information flow urban interactive network obtained by using the GCN_CD algorithm. In two interactive networks, the national urban is divided into six communities. In the air traffic flow network, the results of community detection show that the geographical space is mostly distributed in jumps, and they are distributed in multiple independent spaces at the same time, but they are closely related to each other. The space-time distance in the traditional sense has been greatly compressed, and the high-intensity population flow across large-scale geographical spaces will inevitably become a future development trend. In the information flow network, the internal connections of the six major communities are relatively close, and the boundaries between the communities are obvious, reflecting that the urban interaction based on the toponym co-occurrence still has a distance attenuation effect, and the urban nodes in the network are more concentrated.

Community detection validation

Comparison verification based on the fast unfolding algorithm

To verify the community detection results of the GCN_CD method, the fast unfolding traditional community detection algorithm to identify the urban interactive network of traffic flow and information flow was used. The community detection results of the GCN_CD method used in this research are compared with fast unfolding algorithm, and the results are shown in Figures 15 and 16.

Both interaction networks divide the national cities into five community types, and the modularity is 0.063 and 0.034, respectively, so the community detection results can be considered to be of good quality. Compared with the results obtained by the GCN_CD algorithm, both of them also show a jump distribution in geographical space, but the number of communities and the cities contained in the communities are not the same. The members of the same community also have a large span, which is consistent with the results obtained by the GCN_CD algorithm, but the detection results obtained by the GCN_CD algorithm divide the community more finely, and the detection in southern Chinese cities is more accurate.

In the information flow network, the community detection results show that the urban compactness based on the toponym co-occurrence is still subject to the geospatial effect, and the cities in each community are relatively clustered.

Based on the above, comparing the community division results of the national air traffic flow urban interactive network and information flow urban interactive network obtained by the two algorithms, the community structure layout of the GCN_CD algorithm is more refined and the community distribution is obvious. At the same time, the GCN_CD algorithm has the advantages of strong learning ability, high data-driven upper limit, and good adaptability. It adopts the method based on neural network, which can deal with large-scale graph data effectively and has good scalability. And it uses a small amount of labeled data to learn the labels of a large number of unlabeled data and can identify communities quickly and effectively in the urban interactive network to better obtain cities. In the study of UIN, the result of community division by this method is more reasonable.

Validation based on interaction strength ranking

For the community structure identified by the community division algorithm based on GCN_CD, the interaction strength between city pairs is validated by calculating the interaction strength. The quotient of the total number of population movements between city pairs and the mean number of population is used as a measure of interaction strength, and the top 10 city pairs are taken, as shown in Figures 8 and 9.

By comparing and analyzing the top 10 city pairs in the national air traffic flow network and information flow network with the community structure detected by the GCN_CD algorithm, it is found that the interaction intensity between cities in a community is significantly higher than that the city pair in different communities. In the air traffic flow network, the interaction intensity of Beijing–Shanghai, Chengdu–Beijing, Shanghai–Guangzhou, and other city pairs in the same community ranks high; in the information flow network, Beijing–Shanghai, Chongqing–Beijing, Hangzhou–Nanjing, etc., are in the same community. The interaction intensity of the city pairs in the community ranks first, and the ranking order of the city pairs matches the results of the community detection, which verifies the feasibility and rationality of the method.

Results of spatial interaction strength prediction

Comparative analysis of model prediction results

In this research, we first compare and analyze three prediction models of GCN network: the GCN model, the ChebNet model, and the GAT model, to achieve the purpose of selecting the optimal model. In deep learning, the model accuracy can be evaluated by three indicators: MSE (mean square error), MAPE (mean absolute percentage error), and MAE (mean absolute error). The formula is as follows:

M S E = \frac{1}{n} \sum_{i = 1}^{n} {({\hat{y}}_{i} - y_{i})}^{2}

(17)

M A P E = \frac{100 %}{n} \sum_{i = 1}^{n} | \frac{{\hat{y}}_{i} - y_{i}}{y_{i}} |

(18)

M A E = \frac{1}{n} \sum_{i = 1}^{n} | {\hat{y}}_{i} - y_{i} |

(19)

Figure 17 shows the change curves of the loss function values of the three models during the training process, and Figure 10 demonstrates the comparison of the experimental results of the three models on the same dataset, from which it can be seen that the three accuracy indexes MAE, MAPE, and RMSE of the GAT model are 0.76, 0.06%, and 1.2, respectively, and the model has the highest prediction accuracy in comparison and predicts more exactly the future urban interaction intensity. Combining the experimental results of the three prediction models, the GCN model and ChebNet model have large fluctuations between the prediction curve and the target curve, while the GAT model has relatively small fluctuations and the fluctuations of the curves are similar, and the prediction values are more accurate. In summary, the GAT prediction model is the optimal model, so this research constructs a spatial interaction strength prediction model based on the GAT network, taking into account the distance characteristics.

Prediction accuracy analysis taking into account distance characterization models

In order to effectively verify the validity of the GCN prediction model with distance features, this research sets up three types of experiments for comparative verification, in which ${GAT_d}^{β}$ is the constructed GCN prediction model for urban interaction intensity with distance features, ${GAT_d}^{2}$ is the prediction model constructed based on the gravity model, and $GAT_d$ is the prediction model that adopts the actual distance as the edge’s weight $W_{i j}$ , and the models are shown in Figure 18.

As can be seen from the resulting graph, the predicted value curve and the target value curve change with the change of the model, among which the ${GAT_d}^{β}$ model has the best prediction effect, and the two curves change similarly and the difference in value is small. The second is the ${GAT_d}^{2}$ model, whose initial prediction effect is better, but with the increase of the prediction time, the two curves are gradually separated, and the prediction effect is obviously weakened. The worst prediction effect is the $GAT_d$ model, which uses the actual distance as the weight of the edges, resulting in a big difference between the predicted and target values.

The accuracy evaluation results of the models are shown in Figure 11. It can be observed that the evaluation indexes of the ${GAT_d}^{β}$ model increase by 3.02, 0.17%, and 19.23 compared with the ${GAT_d}^{2}$ model and by 6.28, 0.38%, and 36.83 compared with the $GAT_d$ model, which indicates that the spatial interaction prediction model proposed in this research can make effective use of geospatial laws and improve the prediction accuracy; the ${GAT_d}^{β}$ can effectively utilize geospatial laws and enhance the prediction accuracy; the ${GAT_d}^{β}$ model is the most ineffective one. The prediction accuracy of the ${GAT_d}^{β}$ model is better than that of ${GAT_d}^{2}$ , which means that under the same conditions, the structure of ${GAT_d}^{β}$ model is more reasonable and can adapt to the complex characteristics of urban population migration, so as to accurately predict the intensity of urban interaction.

Urban interactivity discussion

Driver analysis

In order to excavate the intrinsic driving factors behind the results of community delineation in a more detailed way, this research adopts the random forest model and the SHAP method to calculate the contribution values of the dimensions of urban interaction characteristics from four perspectives, namely, the resident population, the general public budget expenditure, the gross regional product, and the passenger flow, and the results are shown in Figures 19 and 20.

The SHAP contribution map of the city interaction characteristics of the air traffic flow and information flow network shows that the contribution value of general public budget expenditure is the largest. Public budget expenditure reflects the importance the government attaches to urban development. Government investment in infrastructure construction, education, health care, and other fields will affect the attractiveness and competitiveness of cities and then affect the interaction and cooperation between cities. These investments not only improve the quality of life of residents but also attract more business and talent inflows, thus promoting inter-city interactions.

The next three indicators in order of contribution value are Gross regional product (GRP), passenger flow, and resident population. Gross regional product is a measure of a city’s economic vitality and level of development. Higher Gross Domestic Product (GDP) usually reflects the strong economic growth and attractiveness of a city, and economic development and wealth creation will attract more enterprises and talents to flow into the city. Regional GDP is an important index to measure the level of regional economic development and has a direct impact on urban interaction. A high regional GDP tends to mean that economic activities and resources are more intensive, attracting more people, logistics, and capital flows, thus promoting the increase of city interactions. Passenger flow and resident population reflect the movement of people between cities and the demographic structure of cities, respectively, which are the bases of city development and interaction, and changes in both directly affect city interaction. The increase in passenger traffic and the number of permanent residents is often accompanied by the growth and expansion of economic activities. The passenger flow and population flow between cities will promote the exchange and circulation of goods, services, funds, and other factors and promote trade and economic development. Unlike the previous three indicators, larger resident population size has a negative impact on city interactions, implying that this type of city has poor population mobility and relatively few interactions with other cities. The increase in passenger traffic and the number of permanent residents is often accompanied by the growth and expansion of economic activities. The passenger flow and population flow between cities will promote the exchange and circulation of goods, services, funds, and other factors and promote trade and economic development.

Based on the GCN_CD algorithm, the results show that there are differences between the community boundaries of the air traffic flow network and the administrative divisions of the whole country, which are characterized by the large spatial span and scattered distribution among different communities. Cities with similar levels of economic development have high spatial interaction intensity and close ties, thus forming a unique community structure. At the same time, higher passenger flow means more tourism, business, and transportation activities, which also promotes the formation of stable partnerships between cities. In the information flow UIN, the community delineation results show that cities within each community are relatively clustered, with clear community delineation boundaries. This is due to the fact that the toponymic co-occurrence data comes from online news, and the frequent occurrence of neighboring cities in such news and the greater likelihood of emergencies lead to high-intensity city interactions existing in neighboring cities. Coastal cities in the southeast region have a higher level of economic development than inland cities in the northwest region, and the spatial interactions between coastal cities are strong, so there is a clear boundary between the east and west communities.

Distance attenuation effect

When the research carries out the spatial interaction intensity prediction, the distance attenuation effect is introduced to calculate the weights on the basis of the principle of GAT model, and more accurate prediction results are obtained. The distance attenuation coefficients under different transportation modes and their differences in different networks were calculated to verify the contribution of the introduced distance attenuation effect. According to 2.2.3 distance attenuation function formula, the relationship graph between the goodness of fit (GoF) and distance attenuation coefficient $β$ is calculated, as shown in Figure 21, and the distance attenuation coefficient $β$ is about 1.65 and 0.6 when the goodness of fit $R^{2}$ reaches the maximum value of 0.5733 and 0.8008 for the highway and railroad traffic, respectively. The distance attenuation coefficient of the network is larger than that of the railroad traffic because the distance has a greater effect on the road traffic flow than the railroad traffic flow. Compared with the distance attenuation coefficient $β$ = 0.3 for the co-occurrence of geographical names, the spatial interactions represented by the information flow have lower distance attenuation coefficients, and the effect of distance on non-spatial movement is not obvious, that is, the distance attenuation effect of Shandong Province in the view of information flow is far less significant than that of the view of traffic flow. This is also consistent with the reality because information flow is based on physical space, and the effect of pure spatial distance on information flow is generally weaker.

Conclusion

In this research, from two perspectives of material space traffic flow and text space information flow, respectively, using complex network method and GCN_CD community discovery method, we analyze the structural characteristics of UIN in Shandong Province and the structure of community division of UIN in China and carve out the roles and positions of cities in different networks, and the main conclusions are as follows:

(1) In terms of network structural features, the UINs of traffic and information flows have certain spatial homogeneity, are more evenly connected, are better connected between cities, and do not present scale-free characteristics. The UINs in both perspectives have small-world characteristics, leading to the conclusion of higher accessibility between cities and smaller separation between nodes as structural characteristics in Shandong Province.

(2) From the perspective of assortative, in the road traffic flow, the central cities are sparsely dispersed and relatively few in number, which is related to the flexibility of road transportation; in the railroad traffic flow, the core cities are closely distributed depending on the railroad network in Shandong Province, and the number of high and medium-centered cities is high. Through the segmentation study of the two kinds of transportation flow, it is found that the UIN architecture of Shandong Province in the overall network distribution is even, the cities are closely connected, and the network has been fully developed. Population migration serves as a spatial exchange carrier of factors between cities, conducive to the balanced development of production factors in the network.

(3) The results of community discovery of two types of UINs, traffic flow and information flow, show that the community structure of the national air traffic flow UIN jumps in distribution, revealing a tendency to overcome spatial friction, with a large span of cities between the same community, and at the same time showing the structural characteristics of a single city as the core unit. The national UIN under the perspective of information flow has clear demarcation between communities, strong aggregation, and still has the distance attenuation effect.

(4) To predict the intensity of urban interaction, the performance of GCN model, ChebNet model, and GAT model is tested, and the prediction results of the three models are compared and analyzed, and the results show that the GAT model has the best results. In this research, the distance feature is introduced into the GAT model, and a spatial interaction prediction ${GAT_d}^{β}$ model considering the distance feature is proposed. The experimental results show that compared with the above three models, the ${GAT_d}^{β}$ model achieves better prediction results at different prediction durations, and the values of the evaluation indexes of the ${GAT_d}^{β}$ model increase by 3.02, 0.17%, and 19.23 compared with that of the ${GAT_d}^{2}$ model, 6.28 and 0.38% compared with that of the $GAT_d$ model, and 36.83 compared with the $GAT_d$ model, which significantly improves the prediction accuracy, 36.83, and the prediction accuracy is obviously improved.

This research analyzes the structural characteristics of UIN in Shandong Province and the community aggregation characteristics of national UIN from the perspective of traffic flow and information flow and constructs a prediction model of UIN taking distance characteristics into account. By analyzing the structural features of UIN based on traffic flow and information flow, and finding the driving factors behind these features, we can provide decision-making basis for future urban planning and construction as well as resource allocation and deployment from different perspectives.

Further research will introduce multi-source information flow big data, such as search index, to compare and study the structural characteristics of different information flow spatial interaction networks. In the constructed urban interaction intensity prediction model ${GAT_d}^{β}$ , the influence of time sequence is not analyzed, and the Recurrent Neural Network (RNN) structure can be embedded in the framework of graph neural network in further research to analyze the spatial interactions with the characteristics of time sequence and improve the accuracy of prediction results.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was supported by Foundation support: Natural Science Foundation of Shandong Province (NO. ZR2019MD034).

Data availability statement

The datasets used and analyzed during the current study are available from the corresponding author upon reasonable request.*

Lin Liu is currently working as an associate professor and master’s tutor at Shandong University of Science and Technology, China. She holds a PhD degree in Shandong University of Science and Technology. Her current research interest includes LBS, mobile terminal navigation, and deep learning.

Yi Sun is with Ocean University of China, China. He holds a bachelor degree from Shandong University of Science and Technology. His current research interest includes GIS and LBS.

Wanwu Li is with Shandong University of Science and Technology, China. He holds a PhD degree from Shandong University of Science and Technology. His current research interest includes InSAR, LBS, and Marine Geographic Information System.

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