CN112529263A - Adaptive network evolution analysis method and system based on improved even-pair approximation - Google Patents

Abstract

The invention discloses a self-adaptive network evolution analysis method and system for improving even-pair approximation. The adaptive network evolution analysis method comprises the following steps: acquiring network initial structure information and variable die body information in a network; acquiring an evolution rule in a network evolution process, and determining an initial condition and a generation result of state transition of a variable die body; acquiring the minimum adhesion of the variable die body and the evolution rule according to the variable die body and the evolution rule; generating a differential map equation set of the variable to be analyzed according to the evolution rule and the minimum adhesion; realizing closure of a differential diagram equation set based on an improved even-pair approximation technology; and analyzing and calculating the variable to be analyzed according to the closed differential diagram equation set so as to obtain the change condition and the stable state of the variable to be analyzed in the adaptive network evolution process. In the adaptive network evolution process, structural changes are fully considered while node state changes are concerned, and the method has high feasibility and universality.

Description

Adaptive network evolution analysis method and system based on improved even-pair approximation

Technical Field

The application relates to the technical field of network dynamics, in particular to an adaptive network evolution analysis method for improving an even-pair approximation and an adaptive network evolution analysis system for improving the even-pair approximation.

Background

In order to reveal the phenomenon of complex network emergence, the development of complex network dynamics research is a necessary basic work which is mainly embodied in two aspects of structure dynamics and state dynamics, and the two aspects also influence and feed back each other in many cases. On one hand, when the change speed of the network structure is much greater than that of the node state, people often focus on exploring the distribution characteristics and structural characteristics of the network nodes from the aspect of statistical physics. In the field of complex networks, a great deal of research is carried out on the dynamics of network structures (such as a classical ER random network model and a BA scale-free network model) through the addition, removal and reconnection of nodes or edges, and the statistical characteristics (degree distribution, aggregation coefficient, correlation, heterogeneity and the like) of the network structures under different mechanisms are shown. On the other hand, when the change speed of the node state is much greater than that of the network structure, people focus on exploring the diffusion range, critical transition and stable state of the network node state. For networks with relatively fixed structures, some of the dynamic processes that occur above can cause large-scale state diffusion (e.g., classical virus propagation models, opinion formation models, cascade failure models, etc.).

However, in many fields such as society, biology, ecology, etc., many phenomena indicate that network structures and node states exhibit coupled dynamic characteristics, i.e., dynamic processes on dynamic networks. For example, in the social network, since Facebook, Twitter, microblog, wechat and the like are emerging from media, communication among people can be performed through online behaviors such as state publishing, forwarding, replying and the like, various state information is spread and spread on the network through a social network association link, and a huge influence can be formed in a short time (for example, "ice bucket challenge" popular in Facebook in 2014, songs such as vicuna camel in desert and uncommon words popular in tremble in 2018), and in the process, the network structure has an important influence on state spreading. Meanwhile, in the information dissemination process, individual nodes may establish connection with other potential nodes through friend recommendations or friends forwarding interested contents, or are not associated with each other because adjacent nodes hold mutually conflicting viewpoints, and the node state change plays an important role in network structure adjustment. Therefore, through the propagation of state information and the reconstruction of a relation structure, the structure and the state of the social network present a coupling dynamic characteristic, and the interleaving of the structure dynamics and the state dynamics is realized. It should be noted that most current researches divide the two dynamic properties, i.e. structure dynamic property and state dynamic property, for processing, or analyze state propagation by using a fixed network structure, or ignore individual states and pay attention to structure change, and lack deep discussion on coupling effect and mutual feedback existing between the two.

When the network structure and the node state both present the characteristic of dynamic change, Gross, Ito, etc. refer to the network with the property of mutual feedback as an adaptive network (adaptive networks), which is widely applicable to the fields of information diffusion on social networks, popularization of emerging technologies, recommendation and marketing of products, and spread and control of diseases. In order to describe the coupled evolution process of the structure and the state of the adaptive network, Holme et al describes the coupled dynamics of structure adjustment and state diffusion through an elector model, and similar work also includes research results of vogue, Vazquez, durett et al, which try to solve the mean value, distribution and critical point of some type of nodes in a stable state through approximate analytical calculation. Taking the classical model of viewpoint dynamics on adaptive networks as an example, a great deal of research has described the node state evolution process on a great number of static networks, and has introduced details about the dynamic propagation of viewpoints. However, these studies are mainly oriented to dynamic processes on the network, and for the adaptive election model, the node state and the network structure are simultaneously changed, which leads to the coexistence problem of viewpoint consistency and viewpoint diversity. The adaptive network dynamic model tightly combines the network dynamics with the dynamics on the network, yielding many wonderful results. On one hand, the network individuals can simulate the states held by the adjacent individuals under the influence of the surrounding social environment, and the network structure deeply influences the evolution of the node states in the process; on the other hand, the network individuals can change the local network structure of the network individuals in a broken edge reconnection mode due to different states between the adjacent individuals, and the node states profoundly influence the self-adaptive adjustment of the network structure in the process.

For the adaptive network evolution process prediction problem, the classical methods have two types: the method comprises the following steps that firstly, computer numerical simulation is used for revealing space-time complexity, mutual connection and difference of different propagation updating mechanisms from a fine-grained level, and because structural features and state distribution under a stable state need to be obtained through a large number of repeated tests, the method is very large in calculation cost; and secondly, theoretical approximate analysis, namely, approximately depicting the evolution relationship of different types of nodes along with time by methods such as a differential equation, a generating function or spectral analysis and the like, and particularly, a differential equation set analysis method based on a Mean Field Approximation (MFA), a Pair Approximation (PA) and an approximate principal equation (AME) can quickly acquire the steady state of system variables.

The prior art mainly has the following technical problems:

1) under the given evolution rule, the research of a large number of differential equation systems usually only focuses on the change of the number of specific types of nodes, the average approximation is carried out on the related structure configuration, the structural change is fully considered while the state change of the nodes is carried out, a set of differential diagram equation construction method with strong universality is established, and the rapid prediction of the dynamic process of the self-adaptive network is realized, so that the problem of great research value is solved.

2) In order to realize the closure of the equation set, some large variable phantoms (motif) need to be approximately decomposed into smaller phantoms, and the current mainstream approximation methods are generally applicable to uniform networks without obvious clustering features or correlations. Therefore, how to improve the accuracy of the approximate solution of these methods in the adaptive network structure and state coupling dynamic process is becoming a very challenging research topic.

Accordingly, a solution is desired to solve or at least mitigate the above-mentioned deficiencies of the prior art.

Disclosure of Invention

The invention aims to provide a self-adaptive network state evolution analysis method for constructing a differential diagram equation set with strong universality, describing a network evolution process and predicting a network stable state.

In one aspect of the present invention, an adaptive network evolution analysis method based on improved even-pair approximation is provided, and the adaptive network evolution analysis method includes:

acquiring a network initial structure and variable die body information in a network;

acquiring an evolution rule in a network evolution process, and determining an initial condition and a generation result of state transition of a variable die body;

acquiring the minimum adhesion of the variable die body and the evolution rule according to the variable die body and the evolution rule;

generating a differential map equation set of the variable to be analyzed according to the evolution rule and the minimum adhesion;

implementing a closure of the differential map equation set based on an improved even-pair approximation technique;

and analyzing and calculating the variable to be analyzed according to the closed differential diagram equation set so as to obtain the change condition and the stable state of the variable to be analyzed in the adaptive network evolution process.

Each node in the adaptive network has a certain state, and the information of the variable motif comprises the state information of each node and the connection relation information between the nodes;

taking a binary adaptive network as an example, the variable motifs typically include:

node a having a forward state;

a node B having a reverse state;

any two nodes with forward states form a connection AA;

any two nodes with reverse states form a connection BB;

any two nodes with different states and connected with each other form a connection AB;

the variables to be analyzed include one or more of the following:

taking the number of the nodes A as variables to be analyzed, and calling the variables as a die body variable [ A ];

taking the number of the node Bs as variables to be analyzed, and calling the variables as a die body variable [ B ];

the number of connected AA is taken as a variable to be analyzed and is called a die body variable [ AA ];

taking the number of connected BB as a variable to be analyzed, and calling the variable as a die body variable [ BB ];

the number of connected AB is used as a variable to be analyzed and is called a die body variable [ AB ];

the number of A node pairs is used as a variable to be analyzed and is called a die body variable [ A ]]²；

The number of B node pairs is used as a variable to be analyzed and is called a die body variable [ B]²；

The number of AB connected pairs is used as the variable to be analyzed, called the die variable [ AB]²；

The variation condition of the variable to be analyzed in the adaptive network evolution process comprises one or more of the following conditions:

die variable [ A ]]Changes in the evolution of the adaptive network, i.e.

Die variable [ B ]]Changes in the evolution of the adaptive network, i.e.

Die variable [ AA ]]Changes in the evolution of the adaptive network, i.e.

Die variable [ BB ]]Changes in the evolution of the adaptive network, i.e.

Die variable [ AB ]]Changes in the evolution of the adaptive network, i.e.

Die variable [ A ]]²Changes in the evolution of the adaptive network, i.e.

Die variable [ B ]]²Changes in the evolution of the adaptive network, i.e.

Die variable [ AB ]]²Changes in the evolution of the adaptive network, i.e.

Further, acquiring an evolution rule in a network evolution process, and determining an initial condition and a result of state transition of a variable die body, wherein the specific evolution rule comprises the following steps:

each node in the binary self-adaptive network holds a forward state A or a reverse state B, for a connection AB with inconsistent strip states, any end point in the connection is reconnected in a self-adaptive structure at each moment by a probability alpha, and the state of the other side is simulated by the probability 1-alpha based on the relative magnitude of the network fitness of the two nodes;

the network fitness of any node in the adaptive network depends on the state of the node itself and the states of the neighboring nodes. Let Pi_AFor the network fitness, pi, of the A node in the AB connection_BFor network adaptability of the node B, the probability that the node A mimics the node B follows Fermi distribution, i.e.

Whereas the probability that the node B mimics the node A is subject to Fermi distribution, i.e.

Where β is the selection coefficient.

Further, acquiring the minimum adhesion of the variable die body according to the variable die body and the evolution rule;

for any given two variables, the motif g₁And g₂And the minimum adhesion between the two is recorded as mg (g)₁,g₂) And matching the two variable motifs in a common cosomain, namely all possible mapping combination modes of the two variable motifs.

Further, the evolution rule comprises an evolution rule left diagram and an evolution rule right diagram, wherein the evolution rule left diagram represents an initial condition of state transition of the variable motif, and the evolution rule right diagram represents a result form generated by the state transition of the variable motif;

according to the evolution rule and the minimum adhesion, the process of generating a differential map equation set of the variable to be analyzed comprises the following four steps:

acquiring a variable die body and an evolution rule left side diagram, and taking the minimum adhesion of the variable die body and the evolution rule left side diagram as variable decrement;

acquiring a variable die body and an evolution rule right side diagram, and taking the minimum adhesion of the variable die body and the evolution rule right side diagram as the future form of variable increment;

carrying out reverse operation of state transition on the future form of the variable increment to obtain the variable increment;

and acquiring a differential map equation set of the variable die body to be analyzed according to the variable decrement and the variable increment.

Further, the network adaptability of the node with the forward state and the network adaptability of the node with the reverse state are obtained, and the probabilities p (A → B) and p (B → A) of state interconversion of the node with the forward state and the node with the reverse state are obtained according to the network adaptability of the node with the forward state and the network adaptability of the node with the reverse state. Acquiring a differential map equation set of a variable die body to be analyzed according to the variable decrement and the variable increment, wherein the differential map equation set related to the first-order variable comprises the following steps:

when the die body variable [ A ] is taken as a variable to be analyzed, acquiring a differential equation of [ A ];

when the die body variable [ B ] is taken as a variable to be analyzed, acquiring a differential equation of [ B ];

when the die body variable [ AA ] is taken as a variable to be analyzed, acquiring a differential equation of the [ AA ];

when the die body variable [ BB ] is taken as a variable to be analyzed, acquiring a differential equation of the [ BB ];

when the die body variable [ AB ] is taken as a variable to be analyzed, acquiring a differential equation of [ AB ];

and differential equations of the die body variables [ A ], [ B ], [ AA ], [ AB ] and [ BB ] form a differential map equation set of the first-order variables.

Acquiring a differential map equation set of a variable die body to be analyzed according to the variable decrement and the variable increment, wherein the differential map equation set related to the high-order variable comprises the following steps:

with said die body variable [ A ]]²When the variable to be analyzed is obtained, [ A ]]²A differential equation of (2);

by the die body variable [ B ]]²When it is a variable to be analyzed, [ B ] is obtained]²Differential map equations of (1);

by the die body variable [ AB]²When the variable to be analyzed is obtained, [ AB ]]²Differential map equations of (1);

with said die body variable [ A ]]、[B]、[AA]、[AB]、[BB]、[A]²、[B]²、[AB]²The differential equations of (a) make up the system of differential map equations.

The differential equation for the die variable [ A ] is:

the differential equation for the die body variable [ B ] is:

the differential equation for the die variable [ AA ] is:

the differential equation for the die body variable [ BB ] is:

the differential equation for the die variable [ AB ] is:

die variable [ A ]]²The differential equation of (a) is:

die variable [ B ]]²The differential equation of (a) is:

die variable [ AB ]]²The differential equation of (a) is:

in the above equation, α is the probability of reconnecting the adaptive structure at any node at two ends of the AB connection, and 1- α is the probability of simulating the opposite state at any node at two ends of the AB connection;

the ABA is a connection ABA formed by connecting a node A with a node B and connecting the node B with another node A in a ternary chain structure;

[ BAB ] represents a connection BAB formed by connecting a node B with a node A and connecting the node A with another node B in a ternary chain structure, wherein the number of the connection BABs is used as a variable to be analyzed;

[ ABB ] represents the number of connected ABBs as variables to be analyzed, wherein ABB represents a connected ABB formed by connecting a node A with the node B and connecting the node B with another node A in a ternary chain structure;

[ BAA ] represents a connection BAA formed by connecting a node B with a node A and connecting the node A with another node A in a ternary chain structure, wherein the number of the connection BAAs is used as a variable to be analyzed;

[ A + A ] represents the number of pairs of A nodes with no overlap;

[ B + B ] represents the number of B node pairs with no overlap;

[ AB + AB ] represents the number of AB linkage pairs with no overlap;

simulating the transition probability of the B state for node A in the AB connection;

the transition probabilities of the a-state are modeled for the node bs in the AB connection.

Further, the closure of the differential diagram equation system is realized based on an improved even-pair approximation technology, and the method mainly comprises the following steps of approximately representing motif variables [ ABA ] and [ BAB ] of triples ABA and BAB through the number of nodes and the number of connections, specifically:

subjecting said [ ABA]Through [ ABA]＝[AB][AB]/[B_I]The approximate solution is carried out and the solution is,

mixing the [ BAB ] with]By [ BAB ]]＝[AB][AB]/[A_I]Carrying out approximate solution;

wherein,

in the above formula, [ A ]_I]For the number of nodes A, [ B ] in the handover area_I]Is the number of nodes B in the handover area. In addition, k_AIs the average degree, k, of nodes having a forward state_BAverage degree of nodes having reverse state, p_AB＝[AB]/([AA]+[AB]) Probability that a node connected to a node having a forward state is a node having a reverse state, p_AA＝[AA]/([AA]+[AB]) Probability that a node connected to a node having a forward state is a node having a forward state,

the probability of degree k for a node with a forward state.

The application also provides an adaptive network evolution analysis system based on improved even-pair approximation, which comprises:

the network structure acquisition module is used for acquiring network initial structure information and variable die body information in a network structure;

the evolution rule acquisition module is used for acquiring an evolution rule in a network evolution process and determining an initial condition and a generation result of state transition of a variable die body;

the minimum adhesion acquisition module is used for acquiring minimum adhesion of the variable die body according to the variable die body and the evolution rule;

the differential map equation set generating module is used for generating a differential map equation set of the variable to be analyzed according to the evolution rule and the minimum adhesion;

a closure module to implement a closure of the set of differential graph equations based on an improved even-pair approximation technique;

and the evolution analysis module is used for analyzing the variable to be analyzed according to the closed differential map equation set so as to acquire the change condition and the stable state of the variable to be analyzed in the adaptive network evolution process.

Advantageous effects

According to the self-adaptive network evolution analysis, in the network structure evolution process, structural changes are fully considered while node state changes are concerned, the designed differential map equation set can effectively solve the problems of complex network die body structures and large die body quantity and scale, better approximation effect is achieved by improving the even-pair approximation, the self-adaptive network for state-structure co-evolution has stronger feasibility and universality, can be widely applied to practical scenes of social network analysis, system biology, chemical reaction simulation and the like, and is beneficial to disclosing the evolution process and stable state of the networks.

Drawings

FIG. 1 is a flow diagram of an adaptive network evolution analysis method that improves even-to-pair approximation.

Fig. 2 is a schematic diagram of a system device for implementing the adaptive network evolution analysis method shown in fig. 1.

Fig. 3 is a diagram of adaptive network evolution rules and minimal adhesion to node a.

Fig. 4 is a diagram of adaptive network evolution rules and minimal adhesion to node bs.

Fig. 5 is a diagram of adaptive network evolution rules and minimal adhesion to connection AA.

Fig. 6 is a diagram of adaptive network evolution rules and minimal adhesion to connection BB.

Fig. 7 is a diagram of adaptive network evolution rules and minimal adhesion to connection AB.

FIG. 8 is a schematic diagram of long chain motifs in an adaptive network.

Fig. 9 is a schematic diagram of handover regions in the adaptive network evolution process.

Fig. 10 is a graph of performance comparison between simulation results (Sim), even Pair Approximation (PA) and improved even pair approximation (IA) for the number of nodes in the steady state of the adaptive network.

Fig. 11 is a graph of performance comparison between simulation results (Sim), even Pair Approximation (PA) and improved even pair approximation (IA) for the number of connections in the steady state of the adaptive network.

Detailed Description

In order to make the implementation objects, technical solutions and advantages of the present application clearer, the technical solutions in the embodiments of the present application will be described in more detail below with reference to the drawings in the embodiments of the present application. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout the drawings. The described embodiments are a subset of the embodiments in the present application and not all embodiments in the present application. The embodiments described below with reference to the drawings are exemplary and intended to be used for explaining the present application and should not be construed as limiting the present application. 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 application. Embodiments of the present application will be described in detail below with reference to the accompanying drawings.

The adaptive network evolution analysis method for improving the even-pair approximation as shown in fig. 1 comprises the following steps:

step 1: acquiring a network initial structure and variable die body information in a network;

step 2: acquiring an evolution rule in a network evolution process, and determining an initial condition and a generation result of state transition of a variable die body;

and step 3: acquiring the minimum adhesion of the variable die body and the evolution rule according to the variable die body and the evolution rule;

and 4, step 4: generating a differential graph equation set of the variable to be analyzed according to the evolution rule and the minimum adhesion;

and 5: realizing closure of a differential diagram equation set based on an improved even-pair approximation technology;

step 6: and analyzing and calculating the variable to be analyzed according to the closed differential diagram equation set so as to obtain the change condition and the stable state of the variable to be analyzed in the adaptive network evolution process.

The application discloses a self-adaptive network evolution analysis method, which designs an effective approximate analysis technology aiming at a self-adaptive network with coupled and evolved structure and state. In the adaptive network evolution process, by constructing a closed differential graph equation set, the change of the node state is concerned, and the change of the network structure is fully considered, so that the method has strong feasibility and universality.

In this embodiment, the adaptive network has a limited node state and a controllable node scale, each node has a certain state, and the interaction relationship between the nodes forms a connecting edge. The node state and the network structure influence each other, and adaptive state change and structure adjustment occur, such as viewpoint propagation in a social network, crisis diffusion in an economic network, congestion phenomenon in a traffic network, and high-quality and low-quality in an ecological network.

In this embodiment, the node state in the adaptive network refers to a certain attribute possessed by the node or certain information held by the node. For example, the node status in the social network may be the attitude (forwarding, commenting, praise, etc.) of certain events among people through social media such as Facebook, Twitter, microblog, wechat, etc. It is well known that the popular "ice bucket challenge" in Facebook 2014, and the popular desert camel, rarely-used word and other songs in buffalo in 2018 are widely spread on social networks. In addition, each node in the network may establish a connection with other potential nodes by recommending or forwarding content of interest by neighboring nodes, or may be disassociated from each other because neighboring nodes hold conflicting perspectives, thereby resulting in structural adjustments resulting from state evolution.

In the present embodiment, the adaptive network is a typical binary network, that is, the node states include a forward state and a reverse state, the solid circles in fig. 3 to 9 represent nodes in the forward state, and the hollow circles represent nodes in the reverse state. For a binary adaptive network, the node state and the network structure of the binary adaptive network present a coupling dynamic evolution process. For example, in a discussion of a preference topic, some people agree with sweet uncongealed tofu and others agree with salty uncongealed tofu for uncongealed tofu as a food. Thus, in such a view network, each node has a state, either a sweet jellied bean curd cognate or a salty jellied bean curd cognate. In the self-adaptive network evolution process, the forward state and the reverse state can be mutually converted, namely, the node for recognizing the sweet uncongealed beancurd can recognize the salty uncongealed beancurd due to the external influence; similarly, the nodes of the cognizant salty uncongealed beancurd can be converted into the cognizant sweet uncongealed beancurd. At the same time, the network structure may also change, for example, a broken link may be reconnected to neighboring nodes holding different states. Aiming at the coupled dynamic process caused by the state evolution and the structure adjustment of the binary self-adaptive network, the method carries out the following steps of the implementation of the method and the device for carrying out the evolution analysis.

Step 1: in this embodiment, the variable die information includes the state of each node and the connection relationship information between the nodes;

in the binary adaptive network, the variable die body comprises various nodes in the network and a subgraph formed by connection:

the variable die body mainly comprises:

node a having a forward state;

a node B having a reverse state;

any two nodes with forward states form a connection AA;

any two nodes with reverse states form a connection BB;

any two nodes with different states and connected to each other form a connection AB.

In this embodiment, the variables to be analyzed include one or more of the following:

taking the number of the nodes A as variables to be analyzed, and calling the variables as a die body variable [ A ];

taking the number of the node Bs as variables to be analyzed, and calling the variables as a die body variable [ B ];

the number of connected AA is taken as a variable to be analyzed and is called a die body variable [ AA ];

taking the number of connected BB as a variable to be analyzed, and calling the variable as a die body variable [ BB ];

the number of connected AB is used as a variable to be analyzed and is called a die body variable [ AB ];

the number of A node pairs is used as a variable to be analyzed and is called a die body variable [ A ]]²；

The number of B node pairs is used as a variable to be analyzed and is called a die body variable [ B]²；

The number of AB connected pairs is used as the variable to be analyzed, called the die variable [ AB]²；

The variation condition of the variable to be analyzed in the adaptive network evolution process comprises one or more of the following conditions:

die variable [ A ]]Changes in the evolution of the adaptive network, i.e.

Die variable [ B ]]Changes in the evolution of the adaptive network, i.e.

Die variable [ AA ]]Changes in the evolution of the adaptive network, i.e.

Die variable [ BB ]]Changes in the evolution of the adaptive network, i.e.

Die variable [ AB ]]Changes in the evolution of the adaptive network, i.e.

Die variable [ A ]]²Changes in the evolution of the adaptive network, i.e.

Die variable [ B ]]²Changes in the evolution of the adaptive network, i.e.

Die variable [ AB ]]²Changes in the evolution of the adaptive network, i.e.

Step 2: in this embodiment, an evolution rule in a network evolution process is obtained, an initial condition of state transition of a variable motif and a result are determined, and the specific evolution rule includes:

each node in the binary self-adaptive network holds a forward state A or a reverse state B, for a connection AB with inconsistent strip states, any end point in the connection is subjected to self-adaptive structure reconnection at each moment by a probability alpha, and the state of the other side is simulated by the probability 1-alpha based on the relative magnitude of the network fitness of the two nodes;

the network adaptability of any node in the self-adaptive network depends on the state of the node and the states of adjacent nodes; let Pi_AFor the network fitness, pi, of the A node in the AB connection_BFor network adaptability of the node B, the probability that the node A mimics the node B follows Fermi distribution, i.e.

Whereas the probability that the node B mimics the node A is subject to Fermi distribution, i.e.

Where β is the selection coefficient.

And step 3: in this embodiment, obtaining the minimum adhesion of the variable phantom according to the variable phantom and the evolution rule includes:

for any given two variables, the motif g₁And g₂The minimum adhesion (minor glues) of the two was recorded as mg (g)₁,g₂) The two variable motifs are matched in a common cosomain set, namely all possible mapping combination modes of the two variants.

Referring to fig. 3 to 7, in the present embodiment, the evolution rule includes an evolution rule left diagram and an evolution rule right diagram, where the evolution rule left diagram represents an initial condition that a variable motif has a state transition, and the evolution rule right diagram represents a generation result that the variable motif has a state transition; for example, Rule in fig. 3 is an evolution Rule, where L in Rule is an evolution left diagram and R is an evolution right diagram.

Referring to fig. 3 to 7, the minimum bonding of the graphs refers to matching two graph structures (an evolutionary rule graph and a variable motif) with nodes having certain states to form all possible combination forms (i.e., the minimum bonding part on the right side in fig. 3 to 7), and the bonded node states and the connection relations must be consistent in the matching process.

And 4, step 4: in the present embodiment, a differential map equation set of the variable to be analyzed is generated according to the evolution rule and the minimum adhesion with the variable phantom. Specifically, according to the evolution rule and the minimum adhesion, generating a differential map equation set of the variable to be analyzed by the following four steps:

acquiring a variable die body and an evolution rule left side image L, and taking the minimum adhesion of the variable die body and the evolution rule left side image as variable decrement;

acquiring a variable die body and an evolution rule right side graph R, and taking the minimum adhesion of the variable die body and the evolution rule right side graph as a future form of variable increment;

carrying out reverse operation of state transition on the future form of the variable increment to obtain the variable increment;

and acquiring a differential map equation set of the variable die body to be analyzed according to the variable decrement and the variable increment.

Specifically, in the present embodiment, the generalized differential map equation of the variable phantom to be analyzed is

Wherein, [ g ]]Representing a variable die body to be analyzed; k is a radical of_rIs the rate of evolution.

In general, the network evolution rules may be defined in the following general form:

γ:＝(L→R,k_γ)

it means that the left diagram L in fig. 3 to 7 is driven at k under regular driving_rThe rate generates the right graph R and this change maintains a one-to-one mapping of nodes.

To obtain the probability of a transition between a forward state and a node having a reverse state, two situations are usually considered:

1) regardless of the node configuration, that is, the states of the adjacent nodes are different, and the two affect the state of the other with equal probability:

p(A→B)＝p(B→A)

2) influenced by node configuration, namely the states of adjacent nodes are different, and the probability of the two influencing the state of the opposite party depends on the respective network fitness:

wherein, pi_AConfiguring the corresponding fitness, pi, for the structure of the node A_BAnd configuring the corresponding fitness for the structure of the node B. The calculation of the fitness of a node depends on the state of the node itself, as well as the state of the neighboring nodes, i.e. the node is a node that is a member of the network

This situation indicates the competitiveness of the network node with respect to its presence in the networkIs closely related.

Specifically, a differential diagram equation set of a variable die body to be analyzed is obtained according to the variable decrement and the variable increment, wherein the differential diagram equation set related to the first-order variable comprises:

acquiring state interconversion probabilities p (A → B) and p (B → A) according to the network fitness of the forward state node and the network fitness of the reverse state node, and acquiring a differential map equation set of a variable motif to be analyzed according to variable decrement and variable increment, wherein the specific content comprises the following steps:

when the die body variable [ A ] is taken as a variable to be analyzed, acquiring a differential equation of [ A ];

when the die body variable [ B ] is taken as a variable to be analyzed, acquiring a differential equation of [ B ];

when the die body variable [ AA ] is taken as a variable to be analyzed, acquiring a differential equation of the [ AA ];

when a die body variable [ BB ] is taken as a variable to be analyzed, acquiring a differential equation of the [ BB ];

when the die body variable [ AB ] is taken as a variable to be analyzed, acquiring a differential equation of [ AB ];

using die body variable [ A ]]²When the variable to be analyzed is obtained, [ A ]]²A differential equation of (2);

using die body variable [ B ]]²When it is a variable to be analyzed, [ B ] is obtained]²Differential map equations of (1);

using die variable [ AB ]]²When the variable to be analyzed is obtained, [ AB ]]²Differential map equations of (1);

and forming a differential diagram equation set by the differential equations of the die body variables.

The differential equation of the die body variable [ A ] in the binary adaptive network is as follows:

the differential equation for the die body variable [ B ] is:

the differential equation for the die variable [ AA ] is:

the differential equation for the die body variable [ BB ] is:

the differential equation for the die variable [ AB ] is:

die variable [ A ]]²The differential equation of (a) is:

die variable [ B ]]²The differential equation of (a) is:

die variable [ AB ]]²The differential equation of (a) is:

in the above equation, α is the probability of reconnecting the adaptive structure at any node at two ends of the AB connection, and 1- α is the probability of simulating the opposite state at any node at two ends of the AB connection;

the ABA is a connection ABA formed by connecting a node A with a node B and connecting the node B with another node A in a ternary chain structure;

[ BAB ] represents a connection BAB formed by connecting a node B with a node A and connecting the node A with another node B in a ternary chain structure, wherein the number of the connection BABs is used as a variable to be analyzed;

[ ABB ] represents the number of connected ABBs as variables to be analyzed, wherein ABB represents a connected ABB formed by connecting a node A with the node B and connecting the node B with another node A in a ternary chain structure;

[ BAA ] represents a connection BAA formed by connecting a node B with a node A and connecting the node A with another node A in a ternary chain structure, wherein the number of the connection BAAs is used as a variable to be analyzed;

[ A + A ] represents the number of pairs of A nodes with no overlap;

[ B + B ] represents the number of B node pairs with no overlap;

[ AB + AB ] represents the number of AB linkage pairs with no overlap;

simulating the transition probability of the B state for node A in the AB connection;

the transition probabilities of the a-state are modeled for the node bs in the AB connection.

In this embodiment, for any one second order variable [ X ]]ⁿIt can be written as:

if there is no overlapping area between the two motifs, [ X ]]²＝[X+X]The specific number can be calculated as:

specifically, assuming X is a particular type of node, it is therefore possible to:

wherein a is_n,iThe number of Stirling is shown as follows:

a_n+1,i＝ia_n,i+a_n,i-1

the final universal expression form was obtained as follows:

and 5: in the embodiment, the closure of the differential map equation system is realized based on an improved even-pair approximation technology, and on the basis of the even-pair approximation, some motifs including the subgraphs of the junction regions are refined.

For example, through the construction of the differential equations above, we have found that the variable phantom and the regular bipartite graph (L, R) are bonded to produce larger-scale phantoms, such as that shown in fig. 8, where the variable phantom is connected to AB, and AB within the dashed circle is changed to AA by state propagation, then new phantoms produced by minimal bonding, such as ABA, ABB, etc., will appear to the right of the analysis phantom of the variable phantom AB. Specifically, due to AB → AA, the situation observed at a larger view angle of the figure would be: ABA → AAA, ABB → AAB, etc., the state changes of these long chain motifs result in some side effects affecting the number of variable motifs AB, e.g., ABA → AAA results in the disappearance of an extra set of AB linkages, while ABB → AAB results in the creation of a new set of AB linkages.

In view of the fact that new motifs constantly appear on the right side of the differential map equation set model, in order to realize the solvability of the equation set, equations need to be further constructed by using the motifs as variables to realize the solvability of the equation set, that is, differential equations need to be continuously constructed on the variable motifs ABA, ABB and the like. This inevitably leads to an ever increasing size of the system of equations. In order to reduce the number of differential map equations, effective approximation techniques are used to represent larger-scale motifs by smaller-scale motifs, thereby achieving the closure of the equation set and controlling the scale of the equation set within a certain range.

In this embodiment, the method adopted by the present application is: the even-pair approximation is improved to implement the closure of the equation set, as follows:

the Pair Approximation (PA) is an approximation of a larger motif by the following form, based on the thought and conditional independence assumptions of na iotave bayes:

however, the approximation method assumes that the connections in the network are uniformly distributed, which is obviously inconsistent with the structural characteristics of the adaptive network, and particularly, some structural associations may cause the number of denominator subgraphs Y to be easily overestimated, thereby affecting the accuracy of the whole approximation process. In order to reduce the approximation error, the method introduces the correlation of the network structure into the process of even-pair approximation, improves the accuracy of approximation solution, and discriminates intersection between subgraphs, so that the condition assumption is more reasonable.

In the adaptive network evolution model, due to the combined action of state transition and broken link reconnection, the number of AB connections is continuously reduced, and the positions of the AB connections in the network have strong correlation. In the even-pair approximation, [ ABA]＝[AB][AB]/[B]，[BAB]＝[AB][AB]/[A]Here number of nodes [ A ]]Or [ B]Both are somewhat overestimated and in fact both contain two parts of content (as shown in fig. 9): one part is a node located in the handover area, i.e. adjacent to a node in a different state, and the other part is a node located in the non-handover area, i.e. adjacent to a node in the same state only. To improve the pair-wise approximation, one needs to use the number of nodes in the handover area [ A ]_I]Or [ B_I]As denominator, para [ ABA]Or [ BAB ]]By approximation, i.e.[ABA]＝[AB][AB]/[B_I]，[BAB]＝[AB][AB]/[A_I]This method of improving the even-to-even approximation may also be referred to as an Interface Approximation (IA).

As to [ A ]_I]Or [ B_I]The invention approximates it as follows:

wherein k is_AIs the average degree, k, of nodes having a forward state_BIs the average of the nodes with the inverted state. p is a radical of_AB＝[AB]/([AA]+[AB]) Probability that a node connected to a node having a forward state is a node having a reverse state, p_AA＝[AA]/([AA]+[AB]) Probability that a node connected to a node having a forward state is a node having a forward state,

the probability of degree k for a node with a forward state.

It is understood that, in this embodiment, other triplet chain structures, for example, [ BAA ], [ ABB ], may adopt an even-pair approximation or other manners to perform closure processing, which is the prior art and will not be described herein again.

Referring to the embodiment of fig. 10, for the evolution situation of the number of various nodes along with the reconnection coefficient α, compared with the conventional pair approximation, the improved pair approximation of the present application has a performance that is greatly improved compared to the prior art. Wherein curve 1 is the simulation result, curve 2 is the improved even-to-pair approximation result, and curve 3 is the even-to-pair approximation result.

Referring to fig. 11, in the embodiment, for the evolution situation of the number of various types of connections along with the reconnection coefficient α, compared with the conventional pair approximation, the performance of the improved pair approximation is greatly improved. Wherein curve 1 is the simulation result, curve 2 is the improved even-to-pair approximation result, and curve 3 is the even-to-pair approximation result.

As can be seen from fig. 10 and 11, the adaptive network evolution analysis method based on the improved pair approximation more approximates the result of numerical simulation than the conventional pair approximation, which illustrates that the method can provide a more accurate prediction result for the state evolution and the structure adjustment behavior occurring in the complex network evolution process, and is helpful to reveal the stable state of the structure and the state coupling dynamics process from the analysis and analysis perspective.

The application also provides a self-adaptive network evolution analysis system, the self-adaptive network evolution analysis device comprises a network structure acquisition module, an evolution rule acquisition module, a minimum adhesion acquisition module, a differential graph equation set generation module, a closure module and an analysis module. The network structure acquisition module is used for acquiring network initial structure information and variable die body information in a network structure; the evolution rule acquisition module is used for acquiring an evolution rule in a network evolution process and determining an initial condition and a generation result of state transition of a variable die body; the minimum adhesion acquisition module is used for acquiring the minimum adhesion of the variable die body according to the variable die body and the evolution rule; the differential map equation set generating module is used for generating a differential map equation set of the variable to be analyzed according to the evolution rule and the minimum adhesion; the closure module is used for realizing closure of the differential diagram equation system based on an improved even-pair approximation technology; the analysis module is used for analyzing the variable to be analyzed according to the closed differential diagram equation set so as to acquire the change condition and the stable state of the variable to be analyzed in the adaptive network evolution process.

It should be noted that the foregoing explanation of the method embodiment is also applicable to the system of this embodiment, and is not repeated here.

The present application further provides an electronic device comprising a memory, a processor and a computer program stored in the memory and capable of running on the processor, wherein the processor executes the computer program to implement the above method for adaptive network evolution analysis for improving even-pair approximation.

The present application further provides a computer-readable storage medium storing a computer program, which when executed by a processor, is capable of implementing the above method for adaptive network evolution analysis for improving even-to-pair approximation.

Fig. 2 is an exemplary block diagram of an electronic device capable of implementing an adaptive network evolution analysis method for improving an even-pair approximation provided according to an embodiment of the present application.

As shown in fig. 2, the electronic device includes an input device 501, an input interface 502, a central processor 503, a memory 504, an output interface 505, and an output device 506. The input interface 502, the central processing unit 503, the memory 504 and the output interface 505 are connected to each other through a bus 507, and the input device 501 and the output device 506 are connected to the bus 507 through the input interface 502 and the output interface 505, respectively, and further connected to other components of the electronic device. Specifically, the input device 504 receives input information from the outside and transmits the input information to the central processor 503 through the input interface 502; the central processor 503 processes the input information based on computer-executable instructions stored in the memory 504 to generate output information, temporarily or permanently stores the output information in the memory 504, and then transmits the output information to the output device 506 through the output interface 505; the output device 506 outputs the output information to the outside of the electronic device for use by the user.

That is, the electronic device shown in fig. 2 may also be implemented to include: a memory storing computer executable instructions; and one or more processors that, when executing the computer-executable instructions, may implement the adaptive network evolution analysis method for improving even-pair approximation described in connection with fig. 1.

In one embodiment, the electronic device shown in fig. 2 may be implemented to include: a memory 504 configured to store executable program code; one or more processors 503 configured to execute the executable program code stored in the memory 504 to perform the adaptive network evolution analysis method for improving the even-pair approximation in the above embodiments.

In a typical configuration, a computing device includes one or more processors (CPUs), input/output interfaces, network interfaces, and memory.

The memory may include forms of volatile memory in a computer readable medium, Random Access Memory (RAM) and/or non-volatile memory, such as Read Only Memory (ROM) or flash memory (flash RAM). Memory is an example of a computer-readable medium.

Computer-readable media include both non-transitory and non-transitory, removable and non-removable media that implement information storage by any method or technology. The information may be computer readable instructions, data structures, modules of a program, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), other types of Random Access Memory (RAM), Read Only Memory (ROM), Electrically Erasable Programmable Read Only Memory (EEPROM), flash memory or other memory technology, compact disc read only memory (CD-ROM), Digital Versatile Discs (DVD) or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information that can be accessed by a computing device.

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.

Furthermore, it will be obvious that the term "comprising" does not exclude other elements or steps. A plurality of units, modules or devices recited in the device claims may also be implemented by one unit or overall device by software or hardware.

The flowchart and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present application. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks identified in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.

The Processor in this embodiment may be a Central Processing Unit (CPU), other general purpose Processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field-Programmable Gate Array (FPGA) or other Programmable logic device, a discrete Gate or transistor logic device, a discrete hardware component, and so on. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.

The memory may be used to store computer programs and/or modules, and the processor may implement various functions of the apparatus/terminal device by running or executing the computer programs and/or modules stored in the memory, as well as by invoking data stored in the memory. The memory may mainly include a storage program area and a storage data area, wherein the storage program area may store an operating system, an application program required by at least one function (such as a sound playing function, an image playing function, etc.), and the like; the storage data area may store data (such as audio data, a phonebook, etc.) created according to the use of the cellular phone, and the like. In addition, the memory may include high speed random access memory, and may also include non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash Card (Flash Card), at least one disk storage device, a Flash memory device, or other volatile solid state memory device.

In this embodiment, the device/terminal equipment integrated module/unit, if implemented in the form of a software functional unit and sold or used as a separate product, may be stored in a computer readable storage medium. Based on such understanding, all or part of the flow of the method according to the embodiments of the present invention may be implemented by a computer program, which is stored in a computer readable storage medium and used for instructing related hardware to implement the steps of the above methods when executed by a processor. Wherein the computer program comprises computer program code, which may be in the form of source code, object code, an executable file or some intermediate form, etc. The computer readable medium may include: any entity or device capable of carrying computer program code, recording medium, usb disk, removable hard disk, magnetic disk, optical disk, computer Memory, Read-Only Memory (ROM), Random Access Memory (RAM), electrical carrier wave signals, telecommunications signals, software distribution medium, and the like. It should be noted that the content of the computer readable medium can be increased or decreased as required by legislation and patent practice in the jurisdiction. Although the present application has been described with reference to the preferred embodiments, it is not intended to limit the present application, and any person skilled in the art can make modifications and changes without departing from the spirit and scope of the present application.

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.

Furthermore, it will be obvious that the term "comprising" does not exclude other elements or steps. A plurality of units, modules or devices recited in the device claims may also be implemented by one unit or overall device by software or hardware.

Although the invention has been described in detail hereinabove with respect to a general description and specific embodiments thereof, it will be apparent to those skilled in the art that modifications or improvements may be made thereto based on the invention. Accordingly, such modifications and improvements are intended to be within the scope of the invention as claimed.

Claims (10)

1. An adaptive network evolution analysis method for improving even-pair approximation, the adaptive network evolution analysis method comprising:

acquiring a network initial structure and variable die body information in a network;

acquiring an evolution rule in a network evolution process, and determining an initial condition and a generation result of state transition of a variable die body;

acquiring the minimum adhesion of the variable die body and the evolution rule according to the variable die body and the evolution rule;

generating a differential map equation set of the variable to be analyzed according to the evolution rule and the minimum adhesion;

implementing a closure of the differential map equation set based on an improved even-pair approximation technique;

and analyzing and calculating the variable to be analyzed according to the closed differential diagram equation set so as to obtain the change condition and the stable state of the variable to be analyzed in the adaptive network evolution process.

2. The adaptive network evolution analysis method for improved even-pair approximation as claimed in claim 1, characterized in that: the variable die body information comprises the state of each node and the connection relation information between the nodes;

in the binary adaptive network, the variable die body comprises various nodes in the network and a subgraph formed by connection:

each node in the network holds a forward state A or a reverse state B;

any two nodes with forward states form a connection AA;

any two nodes with reverse states form a connection BB;

any two nodes with different states and connected with each other form a connection AB;

the variables to be analyzed include one or more of the following:

taking the number of the nodes A as variables to be analyzed, and calling the variables as a die body variable [ A ];

taking the number of the node Bs as variables to be analyzed, and calling the variables as a die body variable [ B ];

the number of connected AA is taken as a variable to be analyzed and is called a die body variable [ AA ];

taking the number of connected BB as a variable to be analyzed, and calling the variable as a die body variable [ BB ];

the number of connected AB is used as a variable to be analyzed and is called a die body variable [ AB ];

the number of A node pairs is used as a variable to be analyzed and is called a die body variable [ A ]]²；

The number of B node pairs is used as a variable to be analyzed and is called a die body variable [ B]²；

The number of AB connected pairs is used as the variable to be analyzed, called the die variable [ AB]²；

The variation condition of the variable to be analyzed in the adaptive network evolution process comprises one or more of the following conditions:

die variable [ A ]]Changes in the evolution of the adaptive network, i.e.

Die variable [ B ]]Changes in the evolution of the adaptive network, i.e.

Die variable [ AA ]]Changes in the evolution of the adaptive network, i.e.

Die variable [ BB ]]Changes in the evolution of the adaptive network, i.e.

Die variable [ AB ]]Changes in the evolution of the adaptive network, i.e.

Die variable [ A ]]²Changes in the evolution of the adaptive network, i.e.

Die variable [ B ]]²Changes in the evolution of the adaptive network, i.e.

Die variable [ AB ]]²Changes in the evolution of the adaptive network, i.e.

3. The adaptive network evolution analysis method for improved even-pair approximation as claimed in claim 2, characterized in that: acquiring an evolution rule in a network evolution process, and determining an initial condition and a generation result of state transition of a variable die body, wherein the specific evolution rule comprises the following steps:

each node in the binary self-adaptive network holds a forward state A or a reverse state B, for a connection AB with each inconsistent state, any endpoint in the connection is subjected to self-adaptive structure reconnection at each moment by a probability alpha, and the state of the other side is simulated by the probability 1-alpha based on the relative magnitude of the network fitness of the two nodes;

the network fitness of any node in the self-adaptive network depends on the state of the node and the states of adjacent nodes; let Pi_ANetwork fitness, pi, of node A in AB connection_BFor node B's network fitness, then node A obeys Fermi distribution with the probability of mimicking node B, i.e.

Whereas the probability that node B mimics node A also follows a Fermi distribution, i.e.

Where β is the selection coefficient.

4. The improved even-pair approximation adaptive network evolution analysis method of claim 3, wherein the minimum adhesion of variable motifs is obtained according to the variable motifs and the evolution rules;

for any given two variables, the motif g₁And g₂And the minimum adhesion between the two is recorded as mg (g)₁,g₂) And matching the two variable motifs in a common cosomain, namely all possible mapping combination modes of the two variable motifs.

5. The adaptive network evolution analysis method for improved even-pair approximation as claimed in claim 4,

the evolution rule comprises an evolution rule left graph and an evolution rule right graph, wherein the evolution rule left graph represents an initial condition of state transition of the variable die body, and the evolution rule right graph represents a result form generated by the state transition of the variable die body;

according to the evolution rule and the minimum adhesion, the process of generating a differential map equation set of the variable to be analyzed comprises the following four steps:

acquiring a variable die body and an evolution rule left side diagram, and taking the minimum adhesion of the variable die body and the evolution rule left side diagram as variable decrement;

acquiring a variable die body and an evolution rule right side diagram, and taking the minimum adhesion of the variable die body and the evolution rule right side diagram as the future form of the variable increment;

carrying out reverse operation of state transition on the future form of the variable increment to obtain the variable increment;

and acquiring a differential map equation set of the variable die body to be analyzed according to the variable decrement and the variable increment.

6. The adaptive network evolution analysis method for improving even-pair approximation as claimed in claim 5, wherein a differential map equation set of a variable phantom to be analyzed is obtained according to the variable decrement and the variable increment, wherein the differential map equation set related to a first order variable comprises:

acquiring the network adaptability of a node with a forward state and the network adaptability of a node with a reverse state, and acquiring the probabilities p (A → B) and p (B → A) of state interconversion of the node with the forward state and the node with the reverse state according to the network adaptability of the node with the forward state and the node with the reverse state:

when the die body variable [ A ] is taken as a variable to be analyzed, acquiring a differential equation of [ A ];

when the die body variable [ B ] is taken as a variable to be analyzed, acquiring a differential equation of [ B ];

when the die body variable [ AA ] is taken as a variable to be analyzed, acquiring a differential equation of the [ AA ];

when the die body variable [ BB ] is taken as a variable to be analyzed, acquiring a differential equation of the [ BB ];

when the die body variable [ AB ] is taken as a variable to be analyzed, acquiring a differential equation of [ AB ];

and differential equations of the die body variables [ A ], [ B ], [ AA ], [ AB ] and [ BB ] form a differential map equation set of the first-order variable.

7. The method for improving adaptive network evolution analysis of even-pair approximation as claimed in claim 6, wherein a differential map equation set of a variable phantom to be analyzed is obtained according to the variable decrement and the variable increment, wherein the differential map equation set related to high-order variables comprises:

acquiring network fitness of a node with a forward state and network fitness of a node with a reverse state, and acquiring state interconversion probabilities p (A → B) and p (B → A) according to the network fitness of the node with the forward state and the network fitness of the node with the reverse state:

with said die body variable [ A ]]²When the variable to be analyzed is obtained, [ A ]]²A differential equation of (2);

by the die body variable [ B ]]²When it is a variable to be analyzed, [ B ] is obtained]²Differential map equations of (1);

by the die body variable [ AB]²When the variable to be analyzed is obtained, [ AB ]]²Differential map equations of (1);

with said die body variable [ A ]]、[B]、[AA]、[AB]、[BB]、[A]²、[B]²、[AB]²The differential equations of (a) make up the system of differential map equations.

8. The adaptive network evolution analysis method for improved even-pair approximation as claimed in claim 7,

the differential equation for the die variable [ A ] is:

the differential equation for the die body variable [ B ] is:

the differential equation for the die variable [ AA ] is:

the differential equation for the die body variable [ BB ] is:

the differential equation for the die variable [ AB ] is:

die variable [ A ]]²The differential equation of (a) is:

die variable [ B ]]²The differential equation of (a) is:

die variable [ AB ]]²The differential equation of (a) is:

in the above equation, α is the probability of reconnecting the adaptive structure at any node at two ends of the AB connection, and 1- α is the probability of simulating the opposite state at any node at two ends of the AB connection;

the ABA represents a connection ABA formed by connecting a node A with a node B and connecting the node B with another node A in a ternary chain structure;

[ BAB ] represents a connection BAB formed by connecting a node B with a node A and connecting the node A with another node B in a ternary chain structure, wherein the number of the connection BABs is used as a variable to be analyzed;

[ ABB ] represents a connection ABB formed by connecting a node A with the node B and connecting the node B with another node A in a ternary chain structure, wherein the quantity of the connection ABBs is used as a variable to be analyzed;

[ BAA ] represents a connection BAA formed by connecting a node B with a node A and connecting the node A with another node A in a ternary chain structure, wherein the number of the connection BAAs is used as a variable to be analyzed;

[ A + A ] represents the number of pairs of A nodes with no overlap;

[ B + B ] represents the number of B node pairs with no overlap;

[ AB + AB ] represents the number of AB linkage pairs with no overlap;

simulating the transition probability of the B state for node A in the AB connection;

the transition probabilities of the a-state are modeled for the node bs in the AB connection.

9. The adaptive network evolution analysis method for improving the pairwise approximation as claimed in claim 8, wherein the implementing of the closure of the differential graph equation set based on the improved pairwise approximation technique mainly includes approximating the motif variables [ ABA ] and [ BAB ] of the triplets ABA and BAB by the number of nodes and the number of connections, specifically:

subjecting said [ ABA]Through [ ABA]＝[AB][AB]/[B_I]The approximate solution is carried out and the solution is,

mixing the [ BAB ] with]By [ BAB ]]＝[AB][AB]/[A_I]Carrying out approximate solution;

wherein,

in the above formula, [ A ]_I]For the number of nodes A, [ B ] in the handover area_I]Is the number of node bs in the handover area. In addition, k_AIs the average degree, k, of nodes having a forward state_BAverage degree of nodes with inverted state, p_AB＝[AB]/([AA]+[AB]) Probability that a node connected to a node having a forward state is a node having a reverse state, p_AA＝[AA]/([AA]+[AB]) Probability that a node connected to a node having a forward state is a node having a forward state,

the probability of degree k for a node with a forward state.

10. An adaptive network evolution analysis system for improving an even-pair approximation, the adaptive network evolution analysis system comprising:

the network structure acquisition module is used for acquiring network initial structure information and variable die body information in a network;

the evolution rule acquisition module is used for acquiring an evolution rule in a network evolution process and determining an initial condition and a generation result of state transition of a variable die body;

the minimum adhesion acquisition module is used for acquiring minimum adhesion of the variable die body according to the variable die body and the evolution rule;

the differential map equation set generating module is used for generating a differential map equation set of the variable to be analyzed according to the evolution rule and the minimum adhesion;

a closure module to implement a closure of the differential map equation set based on an improved even-pair approximation technique;

and the evolution analysis module is used for analyzing the variable to be analyzed according to the closed differential map equation set so as to acquire the change condition and the stable state of the variable to be analyzed in the adaptive network evolution process.

Images