CN112270462B - Subway network fragile line identification method based on Rich curvature - Google Patents
Subway network fragile line identification method based on Rich curvature Download PDFInfo
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Abstract
The invention discloses a method for identifying a fragile line of a subway network based on a Rich curvature, which comprises the following steps of: establishing a subway network based on subway line data and station passenger flow volume data, and giving the passenger flow volume as weight to a station; calculating the Reed-Cookie value of the line in the subway network; and sequencing the lines according to the sequence from negative to positive of the Rich cookie values, removing the lines in the subway network in sequence, and calculating the relative size change of the maximum connected subgraphs so as to identify the fragile lines. The method provided by the invention is a method for extracting the fragile lines of the subway network from the perspective of traffic transmission by combining with actual passenger flow data, solves the problems that the existing method only analyzes the fragile lines from the topological structure of the subway network, and does not fully consider the actual passenger flow distribution condition of each station in the actual passenger flow transmission of the lines and the traffic transmission characteristics in the subway network, and has strong universality.
Description
Technical Field
The invention relates to the technical field of intelligent traffic, in particular to a method for identifying a fragile line of a subway network based on a Rich curvature.
Background
In a traffic system, a subway system becomes a key for solving the problem of urban traffic jam due to the characteristics of high speed, punctuality and large capacity. The subway system network is composed of a group of fixed lines with distributed stations, and passengers finish traveling through line interaction between the stations, so that the subway system network can be naturally used as a network for analysis.
At present, complexity research on subway systems is systematic, but research mainly focuses on statistical views, and mainly analyzes connection characteristics of stations in the subway systems, but ignores actual passenger flow transmission capacity among the stations. When studying the passenger flow transmission capability of a line in a subway network of a subway line, the current situation of the passenger flow of two stations forming the line cannot be considered, and the coming station of the current passenger flow of the line and the capability of the passenger flow on the line transmitted outwards through the stations need to be considered. At present, most of existing subway network fragile line identification methods only identify fragile lines from the topological structure of a subway network, and the problem of actual flow transmission capacity between stations is not fully considered.
Disclosure of Invention
In view of the above, the present invention provides a method for identifying a fragile line in a subway network based on a curie curvature, the method combines the curie curvature with a passenger flow weighted subway network, sorts the lines according to the curie curvature values from negative to positive by calculating weighted curie curvature values of the lines in the subway network, sequentially removes the lines in the network, calculates the relative size of the maximum connectivity subgraph of the network as the evaluation of network connectivity, and identifies the fragile line in the subway network by combining with real passenger flow information, so that the identification effect is more real, stable and reliable.
The invention aims to realize the method, which is based on the Ridge curvature, for identifying the fragile line of the subway network, and comprises the following steps:
step 1, establishing a subway network based on subway line data and station passenger flow volume data, and giving passenger flow volume to a station as weight;
step 2, calculating a Reed-Cookie value of a line in the subway network;
and 3, sequencing the lines according to the sequence from negative to positive of the Rich cookie values, sequentially removing the lines in the subway network, and calculating the relative size change of the maximum connected subgraphs so as to identify the fragile lines.
Specifically, the station passenger flow volume data is converted into passenger flow volume characteristics on the station according to inbound and outbound information of subway card swiping data; the step 1 comprises the following steps:
step 101: constructing a subway network by taking actual stations as nodes and lines connecting two adjacent stations as edges;
step 102: counting the occurrence frequency of each station in the subway card swiping data, namely counting the total passenger flow of each station;
step 103: and dividing the total passenger flow of the station by the node degree of the station to serve as the weight of the station.
Specifically, the formula for calculating the richness value of the line in step 2 is as follows:
indicating the line between adjacent site S and site T
Value of the cookie, mSRepresenting the distribution of the passenger traffic to be transmitted into the S site between the S site neighbors, mTIt indicates that the line is going to be passed
Distribution of passenger flow to other sites adjacent to the T site, W1(mS,mT) The optimal transmission distance between two passenger flow distributions of passenger flow distribution to be transmitted and passenger flow distribution to be transmitted is required to be calculated, d (S, T) represents the length of the shortest path between a station S and a station T in the subway network, d (S, T) between adjacent stations is 1, and the step 2 comprises the following steps:
step 201: normalizing the actual passenger flow distribution of each site adjacent to site S to order WSRepresents the sum of the weights of the other stations adjacent to station S, WSiRepresenting the weight value of site Si adjacent to site S, the normalization formula is WSi/WSThe obtained normalized actual passenger flow distribution is mS；
Step 202: normalizing the actual passenger flow distribution of each site adjacent to site T to order WTIs shown andsum of weights of other stations adjacent to station T, WTiThe weight value of a site Ti adjacent to the site T is represented, and the normalization formula is WTi/WTThe obtained normalized actual passenger flow distribution is mT；
Step 203: line in a computing network
Value of the cookie
Step 204: repeating the steps 201 to 203 to obtain the Rich cookie value Ric of each edge, namely each line e in the subway networkO(e)。
Specifically, the relative size of the maximum connected subgraph in step 3 is a ratio LCC of the number of nodes owned by the maximum connected subgraph in the network to the number of nodes in the original network, and step 3 includes the following steps:
step 301: sorting the lines according to the sequence from negative to positive of the Rich cookie values;
step 302: removing lines in the subway network in sequence, and calculating the relative size change LCC of the maximum connected subgraph;
step 303: and setting a threshold value delta, comparing the relative size LCC of the maximum connected subgraph with the threshold value delta, and extracting the removed line set if the relative size LCC is lower than the threshold value.
Compared with the prior art, the method has the advantages that: the invention provides a method for extracting a fragile line of a subway network from the perspective of traffic transmission by combining actual passenger flow data, which solves the problems that the existing method only analyzes the fragile line from the topological structure of the subway network, and does not fully consider the actual passenger flow distribution condition of each station in the actual passenger flow transmission of the line and the traffic transmission characteristic in the subway network, and has stronger universality.
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Fig. 1 shows a schematic flow diagram of an embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer, the present invention will be described in further detail with reference to the accompanying drawings, and it is apparent that the described embodiments are only a part of the embodiments of the present invention, not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Fig. 1 shows a schematic flow diagram of an embodiment of the invention. A subway network fragile line identification method based on a Rich curvature comprises the following steps:
step 1, establishing a subway network based on subway line data and station passenger flow volume data, and giving passenger flow volume to a station as weight;
step 2, calculating a Reed-Cookie value of a line in the subway network;
and 3, sequencing the lines according to the sequence from negative to positive of the Rich cookie values, sequentially removing the lines in the subway network, and calculating the relative size change of the maximum connected subgraphs so as to identify the fragile lines.
Specifically, the station passenger flow volume data is converted into passenger flow volume characteristics on the station according to inbound and outbound information of subway card swiping data; the step 1 comprises the following steps:
step 101: constructing a subway network by taking actual stations as nodes and lines connecting two adjacent stations as edges;
step 102: counting the occurrence frequency of each station in the subway card swiping data, namely counting the total passenger flow of each station;
step 103: and dividing the total passenger flow of the station by the node degree of the station to serve as the weight of the station.
The riedge curvature, also called orlivirgi curvature value, in the method of the invention is a complex network analysis index which can be used for measuring the energy transmission property in the network.
Step (ii) ofThe formula for calculating the richness value of the line described in 2 is:
indicating the line between adjacent site S and site T
Value of the cookie, mSRepresenting the distribution of the passenger traffic to be transmitted into the S site between the S site neighbors, mTIt indicates that the line is going to be passed
Distribution of passenger flow to other sites adjacent to the T site, W1(mS,mT) The optimal transmission distance between two passenger flow distributions of passenger flow distribution to be transmitted and passenger flow distribution to be transmitted is required to be calculated, d (S, T) represents the length of the shortest path between a station S and a station T in the subway network, d (S, T) between adjacent stations is 1, and the step 2 comprises the following steps:
step 201: normalizing the actual passenger flow distribution of each site adjacent to site S to order WSRepresents the sum of the weights of the other stations adjacent to station S, WSiRepresenting the weight value of site Si adjacent to site S, the normalization formula is WSi/WS；
Step 202: normalizing the actual passenger flow distribution of each site adjacent to site T to order WTRepresents the sum of the weights of other stations adjacent to station T, WTiThe weight value of a site Ti adjacent to the site T is represented, and the normalization formula is WTi/WT；
Step 203: line in a computing network
Value of the cookie
Step 204: repeating the step 201 to the step 203 to obtain each edge in the subway network, namelyThe value of the richness of each line e, RicO(e)。
The relative size of the maximum connected subgraph in the step 3 refers to the ratio LCC of the number of nodes owned by the maximum connected subgraph in the network to the number of nodes in the original network, and the step 3 comprises the following steps:
step 301: sorting the lines according to the sequence from negative to positive of the Rich cookie values;
step 302: removing lines in the subway network in sequence, and calculating the relative size change LCC of the maximum connected subgraph;
step 303: and setting a threshold value delta, comparing the relative size LCC of the maximum connected subgraph with the threshold value delta, and extracting the removed line set if the relative size LCC is lower than the threshold value. The extracted line set is a fragile line of the subway network.
In the embodiment of the invention, by using a Shenzhen city subway line network and Shenzhen general card swiping data on the 09, month and 01 day of 2018, according to the flow shown in fig. 1, firstly, a passenger flow weighted subway network is constructed, wherein the subway network is composed of 166 nodes and 190 edges. And secondly, calculating the Olivie curvature of each edge in the subway network under the real passenger flow distribution. And finally, sequencing the edges according to the increasing sequence of the Rich cookie values, sequentially removing the edges in the subway network, calculating the relative size of the maximum connected subgraph, setting a threshold tau according to the network scale, judging the size relation between the relative size of the maximum connected subgraph and the threshold tau, and extracting the removed line.
The specific implementation steps are as follows:
step A: constructing a Shenzhen city subway network, wherein the network consists of 166 nodes and 190 edges;
and B: counting the occurrence frequency of each site in the 09 and 01 th Shenzhen universal card swiping data in 2018;
and C: the ratio of the frequency to the node degree is taken as a weight and assigned to each station in the subway network, and the passenger flow weighted subway network is constructed;
step D: normalizing the actual passenger flow distribution of each site adjacent to site S to order WSRepresents the sum of the weights of the other stations adjacent to station S, WSiTo representThe weight value of site Si adjacent to site S is WSi/WS；
Step E: normalizing the actual passenger flow distribution of each site adjacent to site T to order WTRepresents the sum of the weights of other stations adjacent to station T, WTiThe weight value of a site Ti adjacent to the site T is represented, and the normalization formula is WTi/WT；
Step F: line in a computing network
The orlyvirrich cookie value has the calculation formula of
Wherein m isSRepresenting the distribution of the passenger traffic to be transmitted into the S site between the S site neighbors, mTIt indicates that the line is going to be passed
The passenger flow to other sites adjacent to the T site is distributed. W1(mS，mT) The optimal transmission distance between the two passenger flow distributions of the passenger flow to be transmitted and the passenger flow to be transmitted is calculated. d (S, T) represents the shortest path length from the station S to the station T in the subway network, and d (S, T) between adjacent stations is 1;
step G: and D, repeating the steps D to F to obtain the Rich cookie value Ric of each edge e in the subway networkO(e)；
Step H: sorting the lines according to the sequence of the cookie values from small to large;
step I: removing lines in the subway network in sequence, and observing the change of the relative size LCC of the maximum connected subgraph;
step J: and setting a threshold delta to be 0.25 based on the scale of the subway network, and comparing the relative size LCC of the maximum connected subgraph with the threshold delta to extract 29 fragile lines.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
Claims (3)
1. A subway network fragile line identification method based on a Rich curvature is characterized by comprising the following steps:
step 1, establishing a subway network based on subway line data and station passenger flow volume data, and giving passenger flow volume to a station as weight;
step 2, calculating a Reed-Cookie value of a line in the subway network;
step 3, sorting the lines according to the sequence from negative to positive of the Rich cookie values, sequentially removing the lines in the subway network, and calculating the relative size change of the maximum connected subgraphs so as to identify the fragile lines;
the calculation formula of the circuit cookie value in the step 2 is as follows:
indicating the line between adjacent site S and site T
Value of the cookie, mSRepresenting the distribution of the passenger traffic to be transmitted into the S site between the S site neighbors, mTIt indicates that the line is going to be passed
Distribution of passenger flow to other sites adjacent to the T site, W1(mS,mT) Indicating the need to calculate to be propagated inThe optimal transmission distance between two passenger flow distributions of passenger flow distribution and passenger flow to be transferred out, d (S, T) represents the shortest path length from a station S to a station T in the subway network, d (S, T) between adjacent stations is 1, and the step 2 comprises the following steps:
step 201: normalizing the actual passenger flow distribution, W, of the stops adjacent to stop SSRepresents the sum of the weights of the other stations adjacent to station S, WSiRepresenting the weight value of site Si adjacent to site S, the normalization formula is WSi/WSThe normalized passenger flow distribution is mS；
Step 202: normalizing the actual passenger flow distribution, W, of the stops adjacent to stop TTRepresents the sum of the weights of other stations adjacent to station T, WTiIndicating a site T adjacent to the site TiThe weight value of (1) is then normalized by the formula WTi/WTThe normalized passenger flow distribution is mT；
Step 203: line in a computing network
Value of the cookie
Step 204: repeating the steps 201 to 203 to obtain the Rich cookie value Ric of each edge, namely each line e in the subway networkO(e)。
2. A method for identifying a fragile line in a subway network as claimed in claim 1, wherein said relative size of the maximum connected subgraph in step 3 is a ratio LCC of the number of nodes owned by the maximum connected subgraph in the network to the number of nodes in the original network, and step 3 specifically includes the following steps:
step 301: sorting the lines according to the sequence from negative to positive of the Rich cookie values;
step 302: removing lines in the subway network in sequence, and calculating the relative size change LCC of the maximum connected subgraph;
step 303: and setting a threshold value delta, comparing the relative size LCC of the maximum connected subgraph with the threshold value delta, and extracting the removed line set if the relative size LCC is lower than the threshold value.
3. A method as claimed in claim 1 or 2, wherein said station traffic data is converted into traffic characteristics at the station based on inbound and outbound information of subway card swiping data; the step 1 comprises the following steps:
step 101: constructing a subway network by taking actual stations as nodes and lines connecting two adjacent stations as edges;
step 102: counting the occurrence frequency of each station in the subway card swiping data, namely counting the total passenger flow of each station;
step 103: and dividing the total passenger flow of the station by the node degree of the station to serve as the weight of the station.
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