CN114418228A - Air-rail combined transport double-layer weighted network modeling method based on multilayer network - Google Patents
Air-rail combined transport double-layer weighted network modeling method based on multilayer network Download PDFInfo
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Abstract
The invention discloses an air-railway combined transport double-layer weighted network modeling method based on a multilayer network, wherein the combined transport double-layer weighted network comprises an airport network layer for constructing a network of an aviation trip section between airports, a high-speed railway network layer for constructing a network of a high-speed railway trip section between high-speed railway stations, and interlayer connection edges of transfer nodes for constructing a network of transfer connection sections which are generated in the same city and simultaneously construct an airport and a high-speed railway station; the intermodal double-layer weighting network takes the frequency number of flights or high-speed rails between two nodes in unit time as the intra-layer side weight, and takes the transfer frequency between an airport and a high-speed rail station in the same city in unit time as the inter-layer side weight. The invention improves the problem that a single-layer network and an unweighted network cannot effectively depict the complex structure of the air-railway combined transportation system by simultaneously bringing the heterogeneity of nodes, connecting edges and edge weights into the air-railway combined transportation network and taking the structural characteristic indexes of the multilayer weighted network as entry points so as to improve the matching degree of an airport and a high-speed rail station.
Description
Technical Field
The invention relates to the technical field of air-rail combined transport double-layer weighted network modeling, in particular to an air-rail combined transport double-layer weighted network modeling method based on a multilayer network.
Background
The air-iron combined transport is used as a main mode for the cooperation of two rapid transport systems of civil aviation and high-speed rail, and plays an important role in the construction of the modern comprehensive transportation system and the efficient travel of people. The complex and huge air-railway combined transport network structure is analyzed, and the method has important significance for predicting or optimizing the system behavior of the air-railway combined transport network.
The multilayer network is one of emerging hotspots of current network scientific research, and provides a method for constructing an air-railway combined transport double-layer weighting network model and analyzing characteristics based on the multilayer network by taking the heterogeneity of nodes, connecting edges and edge weights into consideration aiming at the problem that a single-layer network and an unweighted network cannot effectively describe the complex structure of an air-railway combined transport system.
Disclosure of Invention
1. Technical problem to be solved
The invention aims to provide a modeling method of an air-rail transport double-layer weighting network based on a multilayer network, so as to solve the problems in the background technology.
2. Technical scheme
In order to solve the problems, the invention adopts the following technical scheme:
the intermodal double-layer weighting network modeling method based on the multilayer network comprises an airport network layer for constructing a network of an aviation trip section occurring between airports, a high-speed rail network layer for constructing a network of a high-speed rail trip section occurring between high-speed rails, and interlayer connection edges of transfer nodes for constructing a network of transfer connection sections which occur in the same city and are simultaneously constructed with an airport and the high-speed rail.
Further, the air-rail combined transport double-layer weighting network is represented as GmSaid airport network layer is denoted G[α]The high-speed rail network layer is represented as G[β]And the interlayer connecting edge is represented as G[α,β]The number of airport nodes in the airport network layer is represented as n[α]What is, what isThe number of high-speed rail station nodes in the high-speed rail network layer is represented as n[β]The total number of nodes in the intermodal double-layer weighting network is N ═ N[α]+n[β]。
Furthermore, the intermodal double-layer weighting network takes the frequency w of flights or high-speed rails between two nodes within 24 hours as the intra-layer side weight, and takes the transfer frequency M which can be realized between airports and high-speed rails in the same city through various traffic modes within 24 hours as the inter-layer side weight.
Furthermore, the airport network layer, the high-speed rail network layer and the intermodal double-layer weighting network are represented by adopting an adjacent matrix method. The adjacency matrix of the airport network layer is
The adjacency matrix of the high-speed rail network layer is
The adjacency matrix of the intermodal two-layer weighting network is
Further, the correlation coefficient between different network layers of the air-rail combined transport double-layer weighting network is defined as:
3. advantageous effects
1. The invention forms an air-railway combined transportation double-layer network on the basis of a multi-layer network, reflects the matching of nodes between different network layers and the connection tightness of the network by the interlayer correlation coefficient of the double-layer network, namely, the matching of the nodes between an airport layer and a high-speed rail layer and the tightness of the interlayer relation can be analyzed by the air-railway combined transportation double-layer network, thereby being beneficial to the optimization of the airport, the high-speed rail station and the network between the airport layer and the high-speed rail layer by people and the construction of an airport and high-speed rail integrated transfer hub.
2. According to the method, heterogeneity of nodes, connecting edges and edge weights is considered at the same time, an air-railway combined transportation double-layer weighting network is finally formed on the basis of the air-railway combined transportation double-layer network, and the model in the air-railway combined transportation double-layer weighting network can depict the air-railway combined transportation network closer to reality by considering the mass connecting edge weights, so that the problem that partial key information (such as traffic flow, flight frequency, high-speed rail shift and the like between the nodes) of the reality network is omitted and network characteristics can not be accurately described due to the fact that the edge weights are not considered in the past model is solved; in other words, in the invention, the frequency number of flights or high-speed rails between two nodes within 24 hours is taken as the weight of the connection edge in the layer, and the transfer connection of any frequency can be realized between the airport and the high-speed rail in the same city at any time through various traffic modes within 24 hours, and finally the weight of the connection edge between the layers is set as M.
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FIG. 1 is a graph of node degree distribution and cumulative degree distribution, point intensity distribution, and cumulative point intensity distribution in an example;
FIG. 2 is a graph of log-log cumulative intensity distribution and log-log cumulative dot intensity distribution in the example.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
In the invention, the representation method of the multilayer network comprises the following steps: multilayer network GmDenotes a multilayer network G with m layersmThe network layer connection method is characterized by comprising a set g of each network layer and a set C of connection edges between layers. If the alpha-layer network is G[α]＝(V[α]，E[α])，V[α]And E[α]Respectively, node set and layer-in edge set of the alpha-th layer network, and then the network layer set G of the multilayer network is { G ═ G[α]Is due to {1, 2, ·, m }. Interlayer edge set C ═ E[αβ]∈V[α]×V[β]The method comprises the following steps that (1) the method is a set of connecting edges among nodes of different network layers, wherein alpha and beta belong to {1, 2.., m }, and alpha is not equal to beta;
multi-layer networkMay be represented by an adjacency matrix. If the alpha-layer network G[α]Has a node number of n[α]Then G is[α]Adjacent matrix A of[α]Is n[α]×n[α]Order square matrix of elements therein
The assignment rule is:
wherein i, j ∈ (1, 2.. n.)[α]) And i ≠ j. If the layer G of the beta network[β]Has a node number of n[β]Layer n of the alpha-th network[α]S nodes in each node and the beta-layer network n[β]If t nodes in each node have interlayer connection edges, the interlayer adjacency matrix A[α，β]Is an s x t order matrix, in which the elements
The assignment rule is:
wherein i belongs to (1, 2,. eta., s), j belongs to (1, 2,. eta., t), alpha, beta belongs to {1, 2,. eta., m }, and alpha is not equal to beta;
in the invention, the intermodal double-layer weighting network comprises an airport network layer for constructing the network of an aviation trip section between airports, a high-speed rail network layer for constructing the network of a high-speed rail trip section between high-speed rail stations, and interlayer connection edges of transfer nodes for constructing the network of transfer connection sections which are generated in the same city and are simultaneously provided with an airport and the high-speed rail stations;
in addition, the basic elements for constructing the network are nodes and edges, and the edge weight of the heterogeneous connected edges is considered, so for the convenience of research, the construction description of the air-railway combined transportation double-layer weighting network is described as follows:
(1) a node; the method specifically comprises the following steps: the network comprises two types of heterogeneous nodes of an airport and a high-speed rail station, and the same type of nodes in the same city are merged. For example, Shanghai Hongqiao and Pudong airports are merged into Shanghai airport, and the high-iron Nanjing station and Nanjing station are merged into Nanjing high-iron station.
(2) An edge; the method specifically comprises the following steps: the network includes a layer interconnect and a layer interconnect. In the airport network layer, two airport nodes of the straight flight are connected; in the high-speed rail network layer, two high-speed rail stations which can be reached by a high-speed rail train number are connected; airport nodes in the same city are connected with high-speed rail stations and are connected with edges between layers.
(3) An edge right; the method specifically comprises the following steps: since travelers often change their travel decisions based on the day's experience, the change in traffic flow pattern occurs on a day-to-day scale, taking the frequency of flights or high-speed rails between two nodes over a 24 hour period as the weight of the intra-layer edges. The boundary weight of the interlayer connection is special, and because the transfer connection with any frequency can be realized between the airport and the high-speed rail station in the same city at any time in 24 hours through various traffic modes, the weight of the interlayer connection is set to be M, and the M is a relatively large positive value.
(4) A unidirectional network; the method specifically comprises the following steps: air-iron intermodal transportation can generally achieve two-way intermodal transportation. Therefore, regardless of the direction of the intermodal route, the airport network layer, the high-speed rail network layer or the air-rail intermodal double-layer weighted network is abstracted to a undirected network.
In the invention, the air-rail combined transport double-layer weighting network is represented as GmSaid airport network layer is denoted G[α]The high-speed rail network layer is represented as G[β]And the interlayer connecting edge is represented as G[α,β]The number of airport nodes in the airport network layer is represented as n[α]The number of high-speed rail station nodes in the high-speed rail network layer is represented as n[β]The total number of nodes in the intermodal double-layer weighting network is N ═ N[α]+n[β]The airport network layer, the high-speed rail network layer and the combined transportation double-layer weighting network are all represented by an adjacent matrix method;
the adjacency matrix of the airport network layer is:
if there are w straight flights between airport node i and airport node j in 24 hours, the corresponding element a in the matrixijW; if no straight flight exists between the airport node i and the airport node j within 24 hours, aij0; element a on the diagonal of the matrixii＝0；
The adjacency matrix of the high-speed rail network layer is as follows:
if u rows of high-speed railway trains can be reached between nodes i and j of two high-speed railway stations within 24 hours, the corresponding element b in the matrixijU; element b on the diagonal of the matrixii＝0；
In the air-rail transport double-layer network, if an airport node i and a high-speed rail station node j are built in the same city and air-rail transfer in the same city can be realized, the airport node i and the high-speed rail station node j carry out interlayer connection edges, and a matrix formed by the nodes and the interlayer connection edges is connected with each other
Corresponding element c inijOr else, c ij0. The projection network adjacency matrix of the air-rail transport double-layer weighting network is
Wherein A is[C]TIs A[C]The transposed matrix of (2);
in the invention, the measurement index of the multilayer weighting network structure is similar to but different from the index of a single-layer complex network, and each index has unique and specific practical meaning in the air-railway combined transportation double-layer weighting network;
(1) node degree and point intensity, degree k of node iiIs defined as the number of nodes immediately adjacent to it, generally denoted
Point strength s of node iiDefined as the sum of the weights of all edges connecting the node, commonly denotedIs composed of
In the air-rail combined transport double-layer weighting network, the greater the degree of a certain node is, the higher the importance of the airport node or the high-speed rail station in the network is; the higher the strength of a certain node is, the higher the actual navigation route density or the high-speed railway route passing density of the node is, and the stronger the bearing and transportation capacity of the node is;
(2) the average path length, L, of the network is the average of the shortest distances between all node pairs. If the edge weight is not considered, the shortest distance d between the node pairijThe minimum number of edges which need to be passed from the node i to the node j is defined; if the side weight is considered, dijWhich is the minimum sum of the weights that connecting nodes i and j need to pass through each edge. Because the weight of the edge is the flight frequency or the high-speed rail train number, in the air-railway combined transportation double-layer network, the average path length without considering the edge weight reflects the average times of air-railway transfer in the traveling process from any departure place to a destination, and can be used for judging whether the network has the small-world characteristic or not; considering the average path length of the edge weights reflects the average number of combined flights and high-speed rail intermodal transportation that can reach the destination from the origin by empty rail transfer. If the total number of nodes of the network is N, the calculation expression of the average path length is as follows:
(3) and the clustering coefficient describes the proportion of adjacent points of the nodes in the network to each other. To distinguish from the edge connecting set symbol C between layers of the multi-layer network, the cluster coefficient is represented by a character C'. In the weighted network, the cluster coefficient of the node i is defined as:
wherein wijAnd wikThe edge weights, s, for the edges between node pairs (i, j) and (i, k), respectivelyiIs the point strength of node i. If the total number of nodes in the network is N, the clustering coefficient of the network is
In the air-railway combined transport network, the clustering coefficient can reflect the aggregation degree of the combined transport small group formed by the cooperation of the airport nodes and the high-speed rail nodes;
(4) the centrality is a measurement index which characterizes the central position degree of the network nodes. In general, the centrality of an unlicensed network includes a centrality CiDTight centrality CiCMedian center degree CiBThree kinds of the components are adopted. In the weighting network, the influence of the sum of all edge weights (i.e. point strength) connecting a certain node on the central position degree of the node is not negligible, so the point strength centrality C is considered for measuring the centrality of the weighting networkiS. As shown in table 1, the four centralities are respectively from the importance of the node elements in the network on different sides, and the network center can be more fully measured by combining the four centralities;
TABLE 1 four centrality node importance judgment bases and calculation formulas
(5) The more interlayer connections of the multilayer network, the tighter the interlayer relation. At present, the definition of the correlation between different network layers of a multi-layer network is not uniform. In the existing literature, a definition formula of a correlation coefficient between weighted multilayer network layers is more suitable for the situation that different network layers are all the same node, and the edge weight of an edge connecting between the layers is not taken into consideration, and the definition formula is improved on the basis of the definition formula, and the correlation coefficient between different network layers of the weighted multilayer network is defined as:
wherein R isαβRepresenting a correlation coefficient between the network layer alpha and the network layer beta; w[α]And W[β]Total weight of alpha and beta layers, respectively; w[C]Represents the total weight of all interlayer connecting edges between the alpha layer and the beta layer,
node pairs (i, j) and (i ', j') are node pairs in the alpha and beta layers, respectively,
and
respectively representing the edge weight between the alpha layer node pair (i, j) and the edge weight between the beta layer node pair (i ', j'); w is aii'The edge weight of the inter-layer connection between the node pairs (i, i'). The interlayer correlation coefficient of the air-rail combined transport double-layer weighting network can reflect the node matching of the airport network layer and the high-speed rail network layer and the closeness degree of the interlayer relation.
Examples
Carrying out empirical analysis on the structural characteristics of the east aviation air-iron transport network, and specifically as follows:
by investigation and statistics, the city of hong Kong and Macao station is not considered for the moment, and as the end of 7 months in 2021, the total number of east-navigation domestic navigable cities is 113, and 257 nationwide cities (including county-level cities) are opened and go to the bidirectional air-railway intermodal transportation of each east-navigation domestic navigable city through each transit hub. The east aviation air-railway combined transportation double-layer weighting network constructed by the method is composed of 370 heterogeneous nodes and 9598 heterogeneous connecting edges, and the weight of each connecting edge in each layer is the number of flights or high-speed railcars which can be passed by the edge. Wherein, the airport network layer is composed of 113 airport nodes and 1032 airport connecting edges; the high-speed rail network layer consists of 257 high-speed rail station nodes and 8521 high-speed rail connecting edges; in addition, 45 interlayer connecting edges are formed, and the interlayer connecting edge weight M is 500. All the heterogeneous nodes, connecting edges and edge weights are represented by adjacency matrixes. Analyzing the structural characteristics of the double-layer weighting network for the combined transport of the east aviation and the railway according to the structural measurement indexes of the multi-layer weighting network;
(1) scale-free property analysis based on degree and point intensity distribution; the distribution of the intensity of the degree and the intensity of the points reflects the bearing and the transportation capacity of the nodes in the air-railway combined transportation network, and can be used for judging whether the network has scale-free characteristics. Through the layered topology analysis, the degree distribution of an airport network layer and a high-speed rail network layer and the degree distribution and the cumulative degree distribution of an air-rail combined transportation double-layer network can be respectively obtained, as shown in fig. 1(a) and 1 (b); similarly, a spot intensity distribution and a cumulative spot intensity distribution can be obtained as shown in fig. 1(c) and 1 (d). As can be preliminarily judged from fig. 1, the airport layer, the high-speed rail layer, the network distribution and the point intensity distribution of the east aviation air-rail transport are subjected to power law distribution as a whole; further, a log-log distribution of the power and point intensity is plotted to more intuitively illustrate the power-law relationship, as shown in fig. 2. As can be seen from fig. 2, the bilogarithmic graph of the airport network hierarchy and the point intensity both show obvious linear relationship, which indicates that the eastern airport network has the typical characteristics of a scale-free network; the double logarithmic graphs of the east aviation air-rail transport network and the high-speed rail network layer are in a double-section power law relationship, on one hand, the network has a scale-free characteristic, on the other hand, the strength of the degree points of the nodes in the network is anisotropic, and the difference between the bearing capacity and the transport capacity of each node is large.
(2) Small world property analysis based on mean path length and cluster coefficients; a network has little world-wide characteristics if it has a smaller average path length and a larger aggregation factor than a similarly sized random network. Comparing the calculated average path length with corresponding indexes of the random network with the same scale (the total number of nodes and the total number of connecting edges are the same) of the cluster coefficient, as shown in table 2;
TABLE 2 index comparison of Dong-aviation air-railway combined transport double-layer network and its sub-network with the same-scale random network
As can be seen from table 2, the east aviation air-rail transport double-layer network and the sub-network layer thereof have smaller average path length and larger clustering coefficient compared with the random network of the same scale, which indicates that the network has the characteristics of a small-world network. The average path length of the intermodal network is 2.0128, which indicates that in the current east aviation railway intermodal network, passengers can arrive at the destination from any departure place through 2 transfers on average, wherein the departure place and the destination are specifically to an airport or a high-speed railway station in a certain city. Compared with the prior art, the average path length of the intermodal network is smaller than that of the airport layer, and the network accessibility is enhanced by the currently continuously improved high-speed rail network after the air-railway intermodal is pushed; the cluster coefficient of the intermodal network is 0.4462, which is significantly higher than the airport layer, because the intermodal network includes a high-concentration high-speed rail network
(3) Based on centrality analysis of centrality, the centrality of the east aviation air-iron combined transportation network can be reflected by a centrality index. Respectively calculating degree centrality C of two-layer sub-networks of east aviation air railway combined transportiDPoint intensity centrality CiSTight centrality CiCMedian center degree CiBFor convenience of comparison, the four centrality index values are normalized and summed to be the comprehensive centrality. And sequencing the comprehensive centrality of the two-layer sub-network and the two-layer network projection network from large to small, wherein the first 20 nodes with the maximum comprehensive centrality index values are shown in table 3.
TABLE 3 ranking of the top 20 nodes with the greatest value of the composite centrality index
In the east aviation airport network, the maximum value of the comprehensive centrality is 4 (Shanghai airport), the minimum value is 0.0019 (Dereamha airport), and the average value is 0.4428; only 6 airports with comprehensive central value larger than 1 are available, namely Shanghai, Kunming, Beijing, Xian, Chengdu and Nanjing airports with the top six ranks. In the high-speed rail network layer, the maximum value of the comprehensive centrality is 3.4107 (Chongqing station), the minimum value is 0.3982 (near-high station), and the average value is 1.0770. In the air-iron combined transport double-layer network, the maximum value of the comprehensive centrality is 3.3737 (Shanghai station), the minimum value is 0.1376 (Qilian airport), and the average value is 0.8161. The data are integrated, so that the centrality of the east aviation airport network layer is outstanding, and airports with strong transportation capacity and transfer capacity are mainly concentrated in the first-line city and provincial meeting cities in the north; the centrality of the high-speed rail network layer is relatively low, and the reason is that the high-speed rail network layout is increasingly perfect, and high-speed rail stations with high-frequency train numbers are more and are scattered; the centrality distribution of the intermodal network is non-uniform, only 2 airport nodes of Shanghai and Kunming exist in nodes with 20 top centrality ranks, and the other nodes are high-speed rail station nodes
And based on the interlayer correlation analysis of the interlayer correlation coefficient, the interlayer correlation coefficient of the multilayer network reflects the matching of the nodes between different network layers and the connection tightness of the network. According to the formula (3), the interlayer correlation coefficient R is obtained by calculationαβ0.3589, the current east aviation combined transport double-layer network has weak correlation between layers, the matching degree of the nodes of the airport layer and the high-speed rail layer is not high, and the closeness of the relation between the layers is to be strengthened.
At present, in an east aviation and railway combined transport network, the number of cities in which airports and high-speed railway stations are built simultaneously is 45, and only 19 cities in which airports and high-speed railway stations are built into an integrated hub. With the rapid development of the high-speed rail network in China, the number of cities building airport and high-speed rail stations is increased continuously, and the integrated transfer hubs of the airport and the high-speed rail are expected to increase day by day, so that the interlayer correlation of the air-railway combined transportation double-layer network can be predicted to be enhanced continuously.
According to the contents, the heterogeneity of the nodes, the edges and the edge weights is taken into consideration simultaneously, and an air-railway combined transport double-layer weighting network model is constructed based on a multi-layer network; taking the structural characteristic index of the multilayer weighted network as an entry point, taking the current air-railway transport network of the oriental airliners of China as a research object, and analyzing the structural characteristic of the east air-railway transport network in an empirical mode from four aspects of scale-free characteristic, small-world characteristic, centrality and interlayer correlation; and the following conclusions were drawn:
1. the double-layer network and the sub-network layer of the east aviation air railway transport network have scale-free characteristics and small-world characteristics. Whether the airport layer or the high-speed rail layer, a few nodes often have a large number of connections; the non-scale characteristic of the airport layer is obviously stronger than that of a high-speed rail layer; with the east aviation air rail transport network, the destination can be reached from any origin on average through 2 transfers.
2. The centrality of the east navigation airport network layer is more outstanding, and the airports with strong comprehensive transportation functions are fewer and centralized; the centrality of the high-speed rail network layer is relatively low, and high-speed rails with strong transportation and transfer capabilities are distributed in many stations; the central distribution of the east aviation air-rail transport network is non-uniform, and the number of airport nodes in important central nodes is obviously less than that of high-speed rail stations.
3. The interlayer of the double-layer network for the east aviation air-iron combined transport has weak correlation. At present, the node matching degree of an east-navigation airport network and a high-speed rail network is not high, and the interlayer relation compactness of an airport layer and a high-speed rail layer needs to be strengthened.
In summary, the overall structure and the intermodal function of the east aviation air-railway intermodal double-layer weighting network are good, but the matching degree of the airport and the high-speed railway station needs to be improved.
It should be understood by those skilled in the art that the above embodiments are only for illustrating the present invention and are not to be used as a limitation of the present invention, and that changes and modifications to the above embodiments are within the scope of the claims of the present invention as long as they are within the spirit and scope of the present invention.
Claims (5)
1. The method is characterized in that the intermodal double-layer weighting network comprises an airport network layer for constructing a network of an aviation trip section between airports, a high-speed rail network layer for constructing a network of a high-speed rail trip section between high-speed rails, and interlayer connection edges of transfer nodes for constructing a network of transfer connection sections which are generated in the same city and are constructed with an airport and the high-speed rail at the same time.
2. The modeling method for air-rail transport double-layer weighting network based on multi-layer network as claimed in claim 1, wherein the airport network layer is represented as G[α]The number of airport nodes is represented as n[α](ii) a The high-speed rail network layer is represented as G[β]The number of nodes of the high-speed rail station is represented as n[β](ii) a The above-mentionedThe interlayer connecting edge is represented as G[α,β](ii) a The air-rail combined transport double-layer weighting network is represented as GmThe total number of nodes in the intermodal double-layer weighting network is N ═ N[α]+n[β]。
3. The modeling method of the air-railway combined transportation double-layer weighting network based on the multilayer network according to claim 1, wherein the combined transportation double-layer weighting network takes the frequency number w of flights or high-speed railways between two nodes within 24 hours as an intra-layer edge weight, and takes the transfer frequency M which can be realized by various traffic modes between an airport and a high-speed railway station in the same city within 24 hours as an inter-layer edge weight.
4. The modeling method of the air-rail transport double-layer weighting network based on the multilayer network is characterized in that the airport network layer, the high-speed rail network layer and the transport double-layer weighting network are represented by an adjacent matrix method; the adjacency matrix of the airport network layer is
The adjacency matrix of the high-speed rail network layer is
The adjacency matrix of the intermodal two-layer weighting network is
5. The modeling method for air-railway transport double-layer weighting network based on multilayer network according to claim 1, characterized in that correlation coefficients between different network layers of the air-railway transport double-layer weighting network are defined as follows:
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