CN113052713B - Negative information cascade blocking method based on sensitive node immunity - Google Patents
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Abstract
A negative information cascade blocking method based on sensitive node immunity comprises the steps of constructing a negative information propagation model, initializing a network diagram, acquiring community structure information, determining a cascade sensitive node set, determining an optimal cascade sensitive node subset, determining the number d of immune nodes and blocking negative information cascade. On the premise of ensuring that limited resources and network structure survivability are not affected, selecting the least optimal cascade sensitive node in the immune cascade process, so that the negative information transmission speed can be reduced and the negative information transmission range can be limited; in a complex network with obvious community structure, the method has good effect on blocking negative information cascade, has certain feasibility and effectiveness, and can effectively block the propagation speed and the propagation range of the negative information. The invention has the advantages of simple deployment, easy popularization, capability of effectively blocking the propagation of negative information and the like, and can be applied to the technical fields of public opinion, rumors, virus marketing and the like.
Description
Technical Field
The invention belongs to the technical field of complex network application, and particularly relates to a negative information cascade blocking method based on sensitive node immunity.
Background
With the continuous development of the internet industry, the diversity of new media enables the information propagation channel to develop from singleness to diversification, which provides great convenience for the production and daily life of people, but brings negative effects. Today, the flooding of negative information on the internet has a great impact and resistance to the creation of a healthy upward network environment and may even cause unnecessary social panic. Negative information guidance and control is therefore particularly important, and in recent years, more and more students have come to pay attention to the complex network field, from which it is desired to find effective negative information propagation control methods.
In complex networks, node immunity is used as an effective method for information transmission control, and is widely applied to the fields of infectious diseases, rumors and negative information transmission control. In existing studies, classical immunization strategies mainly involve random immunization, target immunization, and deliberate immunization. Researchers have subsequently proposed many improved strategies based on these classical immunization strategies, which are mostly based on a high centrality index to select the nodes to be immunized, which can lead to serious network topology damage and difficult to implement. Based on this, ALex et al propose a method of mitigating cascading failures (PMCF), introducing a method of selecting key nodes that ensures better network survival. However, the application range of the PMCF method is not wide enough, and there is a certain limitation to networks with rich community structures.
Disclosure of Invention
The technical problem to be solved by the invention is to overcome the defects of the prior art, and provide a negative information cascade blocking method based on limited sensitive node immunity, which is simple to deploy and easy to popularize, and is suitable for guiding and controlling information transmission in a social network with obvious community structure.
The technical scheme adopted for solving the technical problems is composed of the following steps:
(1) Constructing negative information propagation model
N nodes in a network are used as cells, N is a finite positive integer, and four elements of a cell space C, a finite state set Q, a cell field V and a cell state conversion rule function delta are constructed into a dynamic susceptibility-easy dyeing-susceptibility negative information propagation model by adopting a cellular automaton method.
(2) Network map initialization
Given a network diagram and initializing, a% of nodes are selected as initial infection sources, and a epsilon (0, 10).
(3) Obtaining community structure information
Obtaining community structure information of the network graph by using a network community dividing method, wherein the community structure information comprises community dividing results of the network graph and node numbers of each community structure.
(4) Determining a cascade set of sensitive nodes
(4a) Selecting a node i in a community structure with the largest node number at first, and determining the node i as a sensitive node according to a formula (1):
in the middle of
For network graph average degree, k i Is the degree of the selected node i and is not 0, q is the information propagation threshold value, 0<q<1。
(4b) And (3) determining at least 2 adjacent sensitive nodes in the sensitive nodes by using a formula (1), namely, cascade sensitive nodes.
(4c) Adding cascade sensitive nodes into cascade sensitive node set.
(4d) And (3) selecting the next node, and repeating the step (4 a) until all nodes are selected, so as to obtain a cascade sensitive node set.
(5) Determining an optimal subset of cascade sensitive nodes
(5a) And ordering the nodes in the cascade sensitive node set from large to small according to the sum of the neighbor degree values of the nodes.
(5b) Sequentially selecting a node meeting the formula (2) from the cascade sensitive node set:
wherein Vc (i) is the number of community structures directly connected with the node i, vc (i) is more than 1,
is the average value of the cascade sensitive node concentration.
(5c) And (5 b) repeating the step until all the nodes are judged, and forming the selected nodes into an optimal cascade sensitive node subset.
(6) Determination of the number of immunonodes d%
Counting the change condition of the ratio of the number of the nodes of the maximum connected subgraph of the residual network to the total nodes of the network along with the increase of the number of immune nodes by adopting a breadth-first search method, and determining the number d% of the immune nodes when the ratio meets 80% -90%.
(7) Blocking negative information cascading
And deleting the node with the d percent of the front part in the optimal cascade sensitive node subset, and blocking the negative information cascade.
In the step of constructing the negative information propagation model in the present invention (1), the cellular space C is: a one-dimensional cell space is initially created that contains N cells. The finite state set Q of the present invention is: the states of the cells corresponding to the nodes are divided into a susceptibility state S and an infection state I, which are respectively represented by 0 and 1, and a finite state set Q is as follows:
Q＝{0,1}
determining the state variable s as follows i (t)：
S in i (t) represents the state variable of node i at time t, s i (t) ∈Q. The cell field V is the relationship between cell neighbors, namely the direct neighbors of the nodes. The cell state transition rule function delta is as follows: at any time t, the cell state transition rule function δ between the S-state and I-state nodes is as follows:
the upper horizontal line represents the inverting operation, h represents the S stateAnd a state transition rule judging function, p, between the I-state nodes i Representing the ratio of the number of nodes in an infected state to the total number of neighbors in the direct neighbor of the node i, q represents an information propagation threshold value, 0<q<1, beta represents recovery rate, 0<β<1, λ represents the judgment value of the recovery rate, and λ is a random value between (0, 1).
In the step (2) of setting up the network map and initializing the network map, the value of a is optimal to be 5.
In the step of determining the cascade sensitive node set in the step (4), q is an information transmission threshold value, and the value of q is optimally 0.2.
Compared with the prior art, the method has the advantages that on the premise of ensuring that limited resources and network structure survival performance are not affected, the least optimal cascade sensitive node in the immune cascade process is selected, so that the negative information transmission speed can be reduced, and the negative information transmission range can be limited; in a complex network with obvious community structure, the method has good effect of blocking negative information cascade, and has certain feasibility and effectiveness. By adopting the method and the random node immunity, the node degree immunity, the node medium immunity and the PMCF method to carry out a comparison simulation experiment, the experimental result shows that the method is superior to the random node immunity, the node degree immunity, the node medium immunity and the PMCF method, and the method can effectively block the transmission speed and the transmission range of negative information. The invention has the advantages of simple deployment, easy popularization, capability of effectively blocking the transmission of negative information and the like, and can be widely applied to the technical fields of public opinion, rumors, virus marketing and the like to block and control the transmission of the negative information.
Drawings
Fig. 1 is a flow chart of embodiment 1 of the present invention.
FIG. 2 is a graph of the survivability P0 of the Zachary network structure versus the number of immunonodes.
Fig. 3 is a graph showing the change of the proportion I (t) of the node infected by the negative information of the Zachary network.
FIG. 4 is a graph of survivability P0 of a potential Books network structure versus the number of immunonodes.
Fig. 5 is a graph showing the change of the proportion I (t) of the negative information infected nodes of the physical book network.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, but the present invention is not limited to the following embodiments.
Example 1
Taking a Zachary network of a hand and foot channel club in a Konect database as an example, the negative information cascade blocking method based on sensitive node immunity of the embodiment comprises the following steps (see fig. 1):
(1) Constructing negative information propagation model
N nodes in a network are used as cells, N is a finite positive integer, and four elements of a cell space C, a finite state set Q, a cell field V and a cell state conversion rule function delta are constructed into a dynamic susceptibility-easy dyeing-susceptibility negative information propagation model by adopting a cellular automaton method.
The cellular space C is as follows: a one-dimensional cell space is initially created that contains N cells.
The finite state set Q is as follows: the states of the cells corresponding to the nodes are divided into a susceptibility state S and an infection state I, which are respectively represented by 0 and 1, and a finite state set Q is as follows:
Q＝{0,1}
determining the state variable s as follows i (t)：
S in i (t) represents the state variable of node i at time t, s i (t)∈Q。
The cell field V is the relationship between cell neighbors, namely the direct neighbors of the nodes.
The cell state transition rule function delta is as follows: at any time t, the cell state transition rule function δ between the S-state and I-state nodes is as follows:
the upper horizontal line represents the inverting operation, h represents the state transition rule judging function between the S state node and the I state node, and p i Representing the ratio of the number of nodes in an infected state to the total number of neighbors in the direct neighbor of the node i, q represents an information propagation threshold value, 0<q<1, q in this example has a value of 0.2, and β represents the recovery rate, 0<β<1, the value of β in this embodiment is 0.2, λ represents the judgment value of the recovery rate, and λ is randomly valued between (0, 1).
(2) Network map initialization
Taking a node number 34 of a Zachary network of the club of the free hand in the Konect database; initializing the network, selecting a% of nodes as initial infection sources, and a epsilon (0, 10), wherein the value of a in the embodiment is 5.
(3) Obtaining community structure information
Dividing community structures of the Zachary networks of the jessay club by using a network community division method to obtain community structure information of the network graph, wherein the community structure information comprises community division results of the network graph and node numbers of each community structure; the Zachary network is divided into 2 community structures, and the number of nodes of the community structures is 16 and 18 respectively.
(4) Determining a cascade set of sensitive nodes
(4a) Selecting a node i in a community structure with the largest node number at first, and determining the node i as a sensitive node according to a formula (1):
in the middle of
For network graph average degree, k i Is the degree of the selected node i and is not 0,q is information propagation threshold value, 0<q<1, q in this example takes a value of 0.2.
(4b) And (3) determining at least 2 adjacent sensitive nodes in the sensitive nodes by using a formula (1), namely, cascade sensitive nodes.
(4c) Adding cascade sensitive nodes into cascade sensitive node set.
(4d) And (3) selecting the next node, and repeating the step (4 a) until all nodes are selected, so as to obtain a cascade sensitive node set.
(5) Determining an optimal subset of cascade sensitive nodes
(5a) And ordering the nodes in the cascade sensitive node set from large to small according to the sum of the neighbor degree values of the nodes.
(5b) Sequentially selecting a node meeting the formula (2) from the cascade sensitive node set:
wherein Vc (i) is the number of community structures directly connected with the node i, vc (i) is more than 1,
is the average value of the cascade sensitive node concentration.
(5c) And (5 b) repeating the step until all the nodes are judged, and forming the selected nodes into an optimal cascade sensitive node subset.
(6) Determination of the number of immunonodes d%
Counting the change condition of the ratio of the number of the nodes of the maximum connected subgraph of the residual network to the total nodes of the network along with the increase of the number of immune nodes by adopting a breadth-first search method, and determining the number d% of the immune nodes when the ratio meets 80% -90%.
(7) Blocking negative information cascading
And deleting the node with the d percent of the front part in the optimal cascade sensitive node subset, and blocking the negative information cascade.
Example 2
Taking a Zachary network of a hand and foot channel club in a Konect database as an example, the negative information cascade blocking method based on sensitive node immunity of the embodiment comprises the following steps:
(1) Constructing negative information propagation model
This step is the same as in example 1.
(2) Network map initialization
The node number 34 of the Zachary network of the club of the empty hand and the channel is taken from the Konect database, the network is initialized, a% of nodes are selected as initial infection sources, a epsilon (0, 10), and the value of a in the embodiment is 1.
(3) Obtaining community structure information
This step is the same as in example 1.
(4) Determining a cascade set of sensitive nodes
(4a) Selecting a node i in a community structure with the largest node number at first, and determining the node i as a sensitive node according to a formula (1):
in the middle of
For network graph average degree, k i Is the degree of the selected node i and is not 0, q is the information propagation threshold value, 0<q<1, q in this example takes a value of 0.1.
The other steps of this step are the same as those of example 1.
The other steps were the same as in example 1. And (5) completing a negative information cascade blocking method based on sensitive node immunity.
Example 3
Taking a Zachary network of a hand and foot channel club in a Konect database as an example, the negative information cascade blocking method based on sensitive node immunity of the embodiment comprises the following steps:
(1) Constructing negative information propagation model
This step is the same as in example 1.
(2) Network map initialization
The node number 34 of the Zachary network of the club of the empty hand and the Zachary network is taken from the Konect database, the network is initialized, a% of nodes are selected as initial infection sources, a epsilon (0, 10), and the value of a in the embodiment is 10.
(3) Obtaining community structure information
This step is the same as in example 1.
(4) Determining a cascade set of sensitive nodes
(4a) Selecting a node i in a community structure with the largest node number at first, and determining the node i as a sensitive node according to a formula (1):
in the middle of
For network graph average degree, k i Is the degree of the selected node i and is not 0, q is the information propagation threshold value, 0<q<1, q in this example has a value of 0.9.
The other steps of this step are the same as those of example 1.
The other steps were the same as in example 1. And (5) completing a negative information cascade blocking method based on sensitive node immunity.
Example 4
Taking the U.S. Political book network as an example in the Konect database, the negative information cascade blocking method based on sensitive node immunity of the embodiment comprises the following steps:
(1) Constructing negative information propagation model
N nodes in a network are used as cells, N is a finite positive integer, and four elements of a cell space C, a finite state set Q, a cell field V and a cell state conversion rule function delta are constructed into a dynamic susceptibility-easy dyeing-susceptibility negative information propagation model by adopting a cellular automaton method.
The cellular space C is as follows: a one-dimensional cell space is initially created that contains N cells.
The finite state set Q is as follows: the states of the cells corresponding to the nodes are divided into a susceptibility state S and an infection state I, which are respectively represented by 0 and 1, and a finite state set Q is as follows:
Q＝{0,1}
determining the state variable s as follows i (t)：
S in i (t) represents the state variable of node i at time t, s i (t)∈Q。
The cell field V is the relationship between cell neighbors, namely the direct neighbors of the nodes.
The cell state transition rule function delta is as follows: at any time t, the cell state transition rule function δ between the S-state and I-state nodes is as follows:
the upper horizontal line represents the inverting operation, h represents the state transition rule judging function between the S state node and the I state node, and p i Representing the ratio of the number of nodes in an infected state to the total number of neighbors in the direct neighbor of the node i, q represents an information propagation threshold value, 0<q<1, q in this example has a value of 0.2, and β represents the recovery rate, 0<β<1, the value of β in this embodiment is 0.2, λ represents the judgment value of the recovery rate, and λ is randomly valued between (0, 1).
(2) Network map initialization
The U.S. Political book Politcal Books network was taken in the Konect database, politcal Books network node number 105. Initializing the network, selecting a% of nodes as initial infection sources, and a epsilon (0, 10), wherein the value of a in the embodiment is 5.
(3) Obtaining community structure information
Dividing the community structure of the American politics book physical book network by using a network community dividing method to obtain community structure information of the network graph, wherein the community structure information comprises community dividing results of the network graph and node numbers of each community structure; the potential book network is divided into 4 community structures, and the number of nodes of the community structures is 5, 41, 12 and 47 respectively.
(4) Determining a cascade set of sensitive nodes
(4a) Selecting a node i in a community structure with the largest node number at first, and determining the node i as a sensitive node according to a formula (1):
in the middle of
For network graph average degree, k i Is the degree of the selected node i and is not 0, q is the information propagation threshold value, 0<q<1, q in this example takes a value of 0.2.
(4b) And (3) determining at least 2 adjacent sensitive nodes in the sensitive nodes by using a formula (1), namely, cascade sensitive nodes.
(4c) Adding cascade sensitive nodes into cascade sensitive node set.
(4d) And (3) selecting the next node, and repeating the step (4 a) until all nodes are selected, so as to obtain a cascade sensitive node set.
The other steps were the same as in example 1. And (5) completing a negative information cascade blocking method based on sensitive node immunity.
Example 5
Taking the U.S. Political book network as an example in the Konect database, the negative information cascade blocking method based on sensitive node immunity of the embodiment comprises the following steps:
(1) Constructing negative information propagation model
This procedure is the same as in example 4.
(2) Network map initialization
The U.S. Political book, the Political book network node number 34, is taken from the Stanford and Konect databases, the network is initialized, a% of nodes are selected as initial infection sources, a epsilon (0, 10), and the value of a in the embodiment is 1.
(3) Obtaining community structure information
This procedure is the same as in example 4.
(4) Determining a cascade set of sensitive nodes
This procedure is the same as in example 4.
The other steps were the same as in example 4. And (5) completing a negative information cascade blocking method based on sensitive node immunity.
Example 6
Taking the U.S. Political book network as an example in the Konect database, the negative information cascade blocking method based on sensitive node immunity of the embodiment comprises the following steps:
(1) Constructing negative information propagation model
This procedure is the same as in example 4.
(2) Network map initialization
The nodes 34 of the Politcal Books network of the American politics book are taken from the Konect database, the network is initialized, a% of the nodes are selected as initial infection sources, a E (0, 10), and the value of a in the embodiment is 10.
(3) Obtaining community structure information
This procedure is the same as in example 4.
(4) Determining a cascade set of sensitive nodes
This procedure is the same as in example 4.
The other steps were the same as in example 4. And (5) completing a negative information cascade blocking method based on sensitive node immunity.
In order to verify the beneficial effects of the present invention, the inventors conducted comparative simulation experiments using the negative information cascade blocking method based on sensitive node immunity (SNI for short in experiment) and No policy (No Strategy), random node immunity (Random Nodes), node immunity (Degree Centrality), node intermediate immunity (Betweenness Centrality) and cascade fault mitigation (PMCF) methods of examples 1 and 4 of the present invention, the experimental conditions were as follows:
Simulation experiments are carried out by adopting the negative information cascade blocking method based on sensitive node immunity of the embodiment 1 of the invention, and the experimental results are shown in figures 2 and 3, wherein in figure 2, the abscissa is the number of Zachary network immunity nodes, the ordinate is the survivability P0 of the network structure, and the survivability of the network structure is equal to the ratio of the number of nodes of the maximum connected subgraph of the rest network to the total nodes of the network; in fig. 3, the abscissa is the proportion I (t) of the negative information infected node of the Zachary network, and the ordinate is the time t. As can be seen from fig. 2, in the Zachary network, the survivability po of the network structure gradually decreases as the number of immune nodes increases. When the number proportion of the immune nodes is less than 12%, the method of the embodiment 1 can ensure that the survivability of the network structure reaches 85%, not only can the transmission of negative information be blocked, but also the network damage degree caused by the immune nodes is very weak, and the survivability of the network is not affected. Given the need to meet network architecture survivability, it can be used to control the number of immune nodes. As can be seen from fig. 3, other node immunization strategies control the propagation of negative information in terms of both propagation speed and propagation range, compared to no strategy, with the same number of immunized nodes. The control strength of node degree immunity and node betweenness immunity is even higher than that of the method of the embodiment 1, but as can be seen from fig. 2, the survivability of the network structure is lower than 30%, and the relative integrity of the network structure and the survivability of the network are seriously damaged, so that in the Zachary network, the node degree immunity and the node betweenness immunity strategies are not recommended. The PMCF method ensures high survivability of the network structure, but its control effect is lower than that of the example 1 method. In combination with the above, the example 1 method is superior to the other four immunization methods in the Zachary network.
Simulation experiments are carried out by adopting the negative information cascade blocking method based on sensitive node immunity of the embodiment 4 of the invention, the experimental results are shown in fig. 4 and 5, in fig. 4, the abscissa is the number of immune nodes of a potential book network, the ordinate is the survivability P0 of the network structure, and the survivability of the network structure is equal to the ratio of the number of nodes of the maximum connected subgraph of the rest network to the total nodes of the network; in fig. 5, the abscissa is the proportion I (t) of the negative information infected node of the potential book network, and the ordinate is the time t. As can be seen from fig. 4 and 5, in the case of the same immune node ratio, in the physical book network, the method of embodiment 4 is superior to other four immune strategies, so that the propagation speed and propagation range of the negative information are effectively controlled, and the survivability of the network structure is ensured.
From the above analysis, it can be seen from the results of experiments 1 and 2 in combination: (1) Under the condition that the limited resource management and control and the basic survival performance of the network structure are not affected, the method is superior to a random node immunity, node degree immunity, node medium immunity and PMCF method, and can effectively block the propagation speed and the propagation range of negative information; (2) Both the Zachary network and the Political book network can be seen, and the method has good effect on blocking negative information cascade in complex networks with obvious community structures, and has certain practicability and effectiveness.
Although embodiments of the present disclosure have been described above with reference to the accompanying drawings, the present disclosure is not limited to the specific embodiments and fields of application described above, which are merely illustrative, instructive, and not restrictive. Those skilled in the art, having the benefit of this disclosure, may make numerous forms, and departures from the present disclosure as come within the scope of the invention as defined in the appended claims.
Claims (4)
1. A negative information cascade blocking method based on sensitive node immunity is characterized by comprising the following steps:
(1) Constructing negative information propagation model
N nodes in a network are used as cells, N is a finite positive integer, and a cell space C, a finite state set Q, a cell field V and a cell state conversion rule function delta are constructed into a dynamic susceptibility-easy dyeing-susceptibility negative information propagation model by adopting a cellular automaton method;
(2) Network map initialization
Giving a network diagram and initializing, and selecting a% of nodes as initial infection sources, wherein a is E (0, 10);
(3) Obtaining community structure information
Obtaining community structure information of a network graph by using a network community dividing method, wherein the community structure information comprises community dividing results of the network graph and node numbers of each community structure;
(4) Determining a cascade set of sensitive nodes
(4a) Selecting a node i in a community structure with the largest node number at first, and determining the node i as a sensitive node according to a formula (1):
in the middle of
For network graph average degree, k i Is the degree of the selected node i and is not 0, q is the information propagation threshold value, 0<q<1；
(4b) Determining at least 2 adjacent sensitive nodes in the sensitive nodes by using the formula (1), namely cascade sensitive nodes;
(4c) Adding cascade sensitive nodes into a cascade sensitive node set;
(4d) Selecting the next node, and repeating the step (4 a) until all nodes are selected, so as to obtain a cascade sensitive node set;
(5) Determining an optimal subset of cascade sensitive nodes
(5a) Ordering nodes in the cascade sensitive node set from big to small according to the sum of the neighbor degree values of the nodes;
(5b) Sequentially selecting a node meeting the formula (2) from the cascade sensitive node set;
wherein Vc (i) is the number of community structures directly connected with the node i, vc (i) is more than 1,
is the average value of cascade sensitive node concentration;
(5c) Repeating the step (5 b) until all the nodes are judged, and forming the selected nodes into an optimal cascade sensitive node subset;
(6) Determination of the number of immunonodes d%
Counting the change condition of the ratio of the number of nodes of the maximum connected subgraph of the residual network to the total nodes of the network along with the increase of the number of immune nodes by adopting a breadth-first search method, and determining the number d of immune nodes when the ratio meets 80% -90%;
(7) Blocking negative information cascading
And deleting the node with the d percent of the front part in the optimal cascade sensitive node subset, and blocking the negative information cascade.
2. The method for blocking negative information cascade based on immunity of sensitive nodes according to claim 1, wherein in the step of (1) constructing a negative information propagation model, the cellular space C is: establishing a one-dimensional cell space containing N cells at the initial moment;
the finite state set Q is as follows: the states of the cells corresponding to the nodes are divided into a susceptibility state S and an infection state I, which are respectively represented by 0 and 1, and a finite state set Q is as follows:
Q＝{0,1}
determining the state variable s as follows i (t)：
S in i (t) represents the state variable of node i at time t, s i (t)∈Q；
The cell field V is the relationship between cell neighbors, namely the direct neighbors of nodes;
the cell state transition rule function delta is as follows: at any time t, the cell state transition rule function δ between the S-state and I-state nodes is as follows:
the upper horizontal line represents the inverting operation, h represents the state transition rule judging function between the S state node and the I state node, and p i Representing the ratio of the number of nodes in an infected state to the total number of neighbors in the direct neighbor of the node i, q represents an information propagation threshold value, 0<q<1, beta represents recovery rate, 0<β<1, λ represents the judgment value of the recovery rate, and λ is a random value between (0, 1).
3. The negative information cascade blocking method based on sensitive node immunity according to claim 1, characterized in that: in the step (2) of setting a network diagram and initializing, the value of a is 5.
4. The negative information cascade blocking method based on sensitive node immunity according to claim 1, characterized in that: in the step of determining the cascade sensitive node set in the step (4), q is an information transmission threshold value, and the value of q is 0.2.
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