CN112202611A - Similarity weight network stability evaluation index calculation method based on robustness analysis - Google Patents

Similarity weight network stability evaluation index calculation method based on robustness analysis Download PDF

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CN112202611A
CN112202611A CN202011056318.3A CN202011056318A CN112202611A CN 112202611 A CN112202611 A CN 112202611A CN 202011056318 A CN202011056318 A CN 202011056318A CN 112202611 A CN112202611 A CN 112202611A
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network
stability
node
weight
attack
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柴立和
张智慧
孙静静
刘思彤
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Tianjin University
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Tianjin University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/14—Network analysis or design
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/12—Discovery or management of network topologies
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/14—Network analysis or design
    • H04L41/142—Network analysis or design using statistical or mathematical methods

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Abstract

The 21 st century is a century of complexity and networking. Since the seventies of the 20 th century, research on complexity has attracted widespread attention both at home and abroad. Scientists from different disciplines in various countries, including physicists, biologists, computer scientists and economists, have no way to discuss and study the complexity of their respective fields. The method of complex network stability analysis requires new definitions to be found from a new perspective, thereby solving more problems, especially similar oriented networks related to the environmental economics related problems. The invention relates to network stability evaluation of a complex network model similarity weight network, fills the blank in the aspect of weighting the network when the network stability is evaluated by the traditional complex network model, and describes the definition and the calculation method of attack strength and stability under the selective attack condition of the similarity weight network by comprehensive robustness analysis and weight-degree correlation.

Description

Similarity weight network stability evaluation index calculation method based on robustness analysis
Technical Field
The invention relates to network stability evaluation of a complex network model similarity weight network, fills the blank in the aspect of weighting the network when the network stability is evaluated by the traditional complex network model, and describes the definition and the calculation method of attack strength and stability under the selective attack condition of the similarity weight network by comprehensive robustness analysis and weight-degree correlation.
Background
The 21 st century is a century of complexity and networking. Since the seventies of the 20 th century, the research on complexity has attracted extensive attention both at home and abroad, and the nonlinear science is interlaced with the complexity research on the chaotic dynamics thereof. Scientists from different disciplines in various countries, including physicists, biologists, computer scientists and economists, have no way to discuss and study the complexity of their respective fields.
The study of complex networks is also actively undertaken by scholars in the field of the environment, in particular those involved in the specialties of environmental economics. The method of complex network stability analysis requires new definitions to be found from a new perspective, thereby solving more problems, especially directed affinity networks related to environmental economics.
The traditional robustness calculation formula is
Figure BSA0000220684790000011
Wherein S (Q) is the scale of the maximum connected subgraph of the network after Q nodes fail, and the value range of R is
Figure BSA0000220684790000012
The larger R is, the stronger the network can resist the malicious attack, and conversely, the smaller R is, the weaker the network can resist the malicious attack. Q may be used to describe the attack scale, Q — qN, where Q is the node failure rate. And S (q) is the proportion of the number of nodes contained in the maximum connected subgraph of the network to the number of initial network nodes after the q-proportion nodes fail. Initially, s (q) is 1, and as the attack progresses, the proportion of failed nodes increases, the number of nodes disconnected from the maximum connected subgraph increases, and s (q) becomes smaller. The slower the reduction of s (q) is, the stronger the network's ability to resist malicious attacks, whereas the faster the reduction of s (q) is, the weaker the network's ability to resist malicious attacks.
Based on the principle of robustness analysis, the network fragmentation degree F after removing one or more nodes from the network is proposed in the united network analysis on the organization of an industrial metallic system published by the university of Tianjin Chaiqi and the subject group Zhang-Qijun, and the calculation method is that
Figure BSA0000220684790000021
Wherein lijIs the symbiotic relationship between nodes, if the symbiotic relationship exists between two nodes, it is lij1, otherwise, < i > lij0. F-0 indicates that the industrial symbiotic network is not destroyed, and F-1 indicates that the industrial symbiotic network is destroyedThe raw network has been completely destroyed. F can be considered a reasonable description of the stability of the industrial symbiotic network.
Disclosure of Invention
In order to make up for the defects of complex network models in the aspects of network stability, vulnerability and the like when the complex network models are applied to the environmental field, based on the network stability calculation method, the invention provides a network stability calculation method from the perspective of a similar weight network from the direction which is not proposed by previous scholars, constructs a new network stability index and is used for judging the stability of the similar weight complex network in the environmental ecological field. The method of the invention. The content of the calculation method is as follows:
n x n adjacency matrix for given complex similarity weight network
Figure BSA0000220684790000022
Step 1: calculating single-row through flow
Figure BSA0000220684790000023
It is expressed as the sum of the row vectors of the original adjacency matrix, which is the sum of the traffic from a certain node to all other nodes.
Step 2: calculating dominance
Figure BSA0000220684790000024
The scale condition of the system is described to be mutually constrained, and the advantage shows the flow order and regularity of the materials in the network.
And step 3: computing redundancy
Figure BSA0000220684790000031
The scale condition entropy is expressed, and the larger the redundancy rate is, the more complicated the system is, and the larger the communication quantity is.
And 4, step 4: the system capacity C is calculated as a + θ, representing the scale uncertainty at the overall system level, with the larger the capacity, the larger the network size.
And 5: computing tradition robustness
Figure BSA0000220684790000032
R represents robustness. The equation shows that the ability of a system to evolve or self-organize includes two aspects: it must be able to exert sufficient directional force (advantage) to maintain its integrity over time; at the same time, it must maintain a flexible mobile (redundant) store that can be used to cope with disturbing stresses.
Step 6: calculating dimensionless node connection quantity
Figure BSA0000220684790000033
Wherein
Figure BSA0000220684790000034
Representing the network mean weight value, MijIs the weight between node i and node j after dimensionless.
And 7: computing selection attack strength
Figure BSA0000220684790000035
Wherein T isiIs the traffic of node i; diThe connectivity of the node i represents the number of nodes which have weight relation with other nodes; i isiN is the number of network nodes in order to select the damage strength to the network, which will be caused when the node i of the network is to be removed.
And 8: computing selection attack stability
Figure BSA0000220684790000036
SiSelecting a stability under attack conditions for a network, SiThe larger the size, the higher the network stability when selecting the attacking node i.
And step 9: computing network stability
Figure BSA0000220684790000037
Indicating the stability of the network.
The invention has the following advantages:
1. by applying the complex network thought, the topological characteristics of the relation network between the environment and the industry can be deeply analyzed, and suggestions are provided for the environment direction optimization of the industry structure.
2. The weighting factors, especially the similar weight influence, are integrated into the traditional network stability algorithm, so that the defect of the conventional weightless network is overcome.
3. The traditional robustness is considered into a calculation formula, and the stability difference is amplified, so that the network stability is more credible.
Detailed Description
N x n adjacency matrix for given complex similarity weight network
Figure BSA0000220684790000041
Step 1: calculating single-row through flow
Figure BSA0000220684790000042
It is expressed as the sum of the row vectors of the original adjacency matrix, which is the sum of the traffic from a certain node to all other nodes.
Step 2: calculating dominance
Figure BSA0000220684790000043
The scale condition of the system is described to be mutually constrained, and the advantage shows the flow order and regularity of the materials in the network.
And step 3: computing redundancy
Figure BSA0000220684790000044
The scale condition entropy is expressed, and the larger the redundancy rate is, the more complicated the system is, and the larger the communication quantity is.
And 4, step 4: the system capacity C is calculated as a + θ, representing the scale uncertainty at the overall system level, with the larger the capacity, the larger the network size.
And 5: computing tradition robustness
Figure BSA0000220684790000045
R represents robustness. The equation shows that the ability of a system to evolve or self-organize includes two aspects: it must be able to exert sufficient directional force (advantage) to maintain its integrity over time; at the same time, it must maintain a flexible mobile (redundant) store for coping with disturbing stressesForce.
Step 6: calculating dimensionless node connection quantity
Figure BSA0000220684790000051
Wherein
Figure BSA0000220684790000052
Representing the network mean weight value, MijIs the weight between node i and node j after dimensionless.
And 7: computing selection attack strength
Figure BSA0000220684790000053
Wherein T isiIs the traffic of node i; diThe connectivity of the node i represents the number of nodes which have weight relation with other nodes; i isiN is the number of network nodes in order to select the damage strength to the network, which will be caused when the node i of the network is to be removed.
And 8: computing selection attack stability
Figure BSA0000220684790000054
SiSelecting a stability under attack conditions for a network, SiThe larger the size, the higher the network stability when selecting the attacking node i.
And step 9: computing network stability
Figure BSA0000220684790000055
Indicating the stability of the semblance network.
The above-described embodiments are merely illustrative and not restrictive, and those skilled in the art can now make various changes and modifications without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (6)

1. The method for calculating the stability evaluation index of the similarity weight network based on robustness analysis is applied to the similarity weight complex network, fills the blank of the robustness calculation of the traditional complex network system in the aspect of a weighting network, but the formula involved in the calculation process is not suitable for the calculation of the network stability of the different weight network and the system survivability under the condition of selective attack.
2. Computing with robustness
Figure FSA0000220684780000011
As a revised parameter in the calculation process, the difference in the stability calculation process is magnified.
3. Defining dimensionless node connection volumes
Figure FSA0000220684780000012
Wherein
Figure FSA0000220684780000013
Representing the network mean weight value, MijIs the weight between node i and node j after dimensionless.
4. Defining selection attack strength
Figure FSA0000220684780000014
Wherein T isiIs the traffic of node i; diThe connectivity of the node i represents the number of nodes which have weight relation with other nodes; i isiN is the number of network nodes in order to select the damage strength to the network, which will be caused when the node i of the network is to be removed.
5. Defining selection attack stability
Figure FSA0000220684780000015
SiSelecting a stability under attack conditions for a network, SiThe larger the size, the higher the network stability when selecting the attacking node i.
6. Defining computing network stability
Figure FSA0000220684780000016
Indicating the stability of the network.
CN202011056318.3A 2020-09-30 2020-09-30 Similarity weight network stability evaluation index calculation method based on robustness analysis Pending CN112202611A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113452548A (en) * 2021-05-08 2021-09-28 浙江工业大学 Index evaluation method and system for network node classification and link prediction
CN113490267A (en) * 2021-05-18 2021-10-08 浙江传媒学院 Generalized pre-control method for robust stability

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113452548A (en) * 2021-05-08 2021-09-28 浙江工业大学 Index evaluation method and system for network node classification and link prediction
CN113452548B (en) * 2021-05-08 2022-07-19 浙江工业大学 Index evaluation method and system for network node classification and link prediction
CN113490267A (en) * 2021-05-18 2021-10-08 浙江传媒学院 Generalized pre-control method for robust stability
CN113490267B (en) * 2021-05-18 2023-11-07 浙江传媒学院 Generalized pre-control method for robust stability

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