CN111881535A - Time-varying network model construction method and system and rumor propagation time-varying network model construction method - Google Patents
Time-varying network model construction method and system and rumor propagation time-varying network model construction method Download PDFInfo
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Abstract
The application relates to a time-varying network model construction method, a time-varying network model construction system and a rumor propagation time-varying network model construction method, which belong to the technical field of time-varying network model research, wherein a two-dimensional grid network with the node number of N and L is set, node spacing and accumulated edge connection times sum are obtained on the basis of the space coordinates of nodes and the edge connection condition of each moment node, the edge connection preference probability of each moment active node is obtained by combining the node spacing and the accumulated edge connection times sum, and the time-varying network model is obtained by performing edge connection on the basis of the edge connection preference probability of each moment active node; by utilizing the time-varying network model construction method, a node information acquisition module, a preference probability acquisition module, an instantaneous network model forming module and a time-varying network model generating module are obtained, so that a time-varying network model construction system is obtained; and a construction method for obtaining a rumor propagation time-varying network model. Compared with the related art, the method has the effect of reducing the limitation of the time-varying network model to a certain extent.
Description
Technical Field
The present application relates to the technical field of time-varying network model research, and in particular, to a time-varying network model construction method and system, and a rumor propagation time-varying network model construction method.
Background
In real life, the topology of many complex systems is not constant, and the node and edge conditions in the network change with time. With the rapid development of technologies such as the internet of things, big data, artificial intelligence and the like, the data which can be acquired by people is more and more abundant, and the attributes and behavior development tracks of individuals in various complex systems can be recorded in detail and specifically.
At present, most of researches on time-varying network models are based on activity-driven models, but because the connection of adjacent time-step network structures is not considered, a larger gap exists between the generated time-varying network models and a real network. In the related art, after the memory of the nodes is increased on the basis of the activity-driven model, the nodes in the network are simply divided into two types: old neighbors that were once connected and new nodes that have not been interacted with, a node may tend to connect to the old neighbors when selecting a target node.
With respect to the related art among the above, the inventors consider that the following drawbacks exist: after the memory of the node is increased, although the time-varying network model is improved to a certain extent, the time-varying network model still has great limitations.
Disclosure of Invention
In order to reduce the limitation of the time-varying network model to a certain extent, the application provides a time-varying network model construction method and system and a rumor propagation time-varying network model construction method.
In a first aspect, the time-varying network model construction method provided by the present application adopts the following technical scheme:
a time-varying network model construction method comprises the steps of setting a two-dimensional grid network with nodes of L x L of N, obtaining node spacing and accumulated edge connection times sum based on recorded space coordinates of the nodes and edge connection conditions of the nodes at each moment in the network evolution process, obtaining edge connection preference probability of active nodes selecting neighbors at each moment by combining the node spacing and the accumulated edge connection times sum, and carrying out edge connection based on the edge connection preference probability of the active nodes at each moment to obtain a time-varying network model.
By adopting the technical scheme, the edge connection preference probability of the active nodes is determined by the node distance, the accumulated edge connection times and the joint, so that the nodes tend to be connected with the nodes which are high in affinity and close to the nodes, the time-varying network model is closer to a real social network, and the limitation of the time-varying network model is reduced to a certain extent.
Preferably, the specific construction method of the time-varying network model comprises,
acquiring node information, setting the number of nodes of the network to be N as required, uniformly distributing the N nodes in the L-L two-dimensional grid network, and endowing each node in the network structure with corresponding activity a according to activity distributionkAnalyzing the space coordinate position of the node and the edge connecting condition of the node at each moment, and acquiring the node distance and the accumulated edge connecting times sum of the node, wherein N is a positive integer, and k is 1,2, … and N;
obtaining preference probability, obtaining the edge connecting weight of the node based on the accumulated edge connecting times sum of the node, and obtaining preference probability P by combining the node distance, the edge connecting weight and the proportion parameter alphaijThe proportion parameter is used for representing the proportion occupied by the node edge connecting weight and the node distance when the network structure is formed, i is 1,2, …, N, j is 1,2, …, N, and i is not equal to j;
instantaneous network model acquisition, wherein at each moment t, the node combines the activity and preference probability P of the nodeijForming a transient network model Gt(ii) a And the number of the first and second groups,
time-varying network model generation from transient network GtThe model generates a time-varying network model for a certain time period.
By adopting the technical scheme, the intimacy between the nodes is represented by the continuous edge weight, on the basis of activity driving, the preference probability of the continuous edges between different nodes is obtained by combining the continuous edge weight between the nodes and the distance relation, so that the instantaneous network model is obtained by combining the preference probability, the relevance of the network topological structure of the time-varying network at different moments is further obtained, and the limitation of the time-varying network model is reduced to a certain extent.
Preferably, the specific method for obtaining the preference probability includes,
acquiring node connection probability, wherein the nodes become active nodes and inactive nodes according to the activity degree; for a certain active node, putting the nodes which establish the connecting edge with the active node before the time t into a set R, and obtaining the node connection probability p according to the set R1And p2，
Where n represents the total number of elements in the set R, c is a bias constant, p1Representing the probability, p, that an active node selects a node in the connection set R2Representing the probability of the active node selecting a new node which is connected with the edge which is never connected;
acquiring node pair connection probability, and regarding a time t, taking a node connected with the active node as a target node, wherein the active node and a certain target node form a node pair; when the target node is in the set R, the node pair connection probability p is obtained by combining the connection edge weight, the distance and the proportion parameter alpha of two nodes in the node pair21，
When the target node does not belong to the set R, acquiring node pair connection probability p based on node pair distance22，
Wherein, wijRepresenting the edge-to-edge weight of a node pair, dijRepresenting node pair spacing;
calculating preference probability (102-3), and combining the node connection probability and the node pair connection probability to obtain preference probability Pij，
By adopting the technical scheme, the currently active nodes have higher probability of being connected with the old nodes which are connected before the current time, and in the old nodes, the preference probability is related to the connection edge weight and the distance, the greater the connection edge weight is, namely the intimacy is higher, and the probability of establishing the connection edge between the nodes which are closer is higher; and for a new node, the connection weight is zero, the preference probability is only related to the node distance, the network node attribute is more finely given through calculation of the preference probability, and the limitation of a time-varying network model is reduced to a certain extent.
Preferably, the specific method for acquiring the instantaneous network model comprises,
at each moment t, the node becomes an active node or an inactive node according to the activity of the node;
the active nodes are connected with m connected edges according to own connected edge preference probability to form an instant network model GtAnd the number m of the connecting edges is set according to practical application.
By adopting the technical scheme, the active nodes at each moment are connected according to the preference probability to generate the instant network model, so that the instant network model is closer to a real social network, and the limitation of the time-varying network model is further favorably improved.
Preferably, the liveness distribution conforms to a power law distribution, and the power exponent and the maximum value of the liveness distribution are set according to the topological structure of the actual network.
Through adopting above-mentioned technical scheme, set for the activity value of node with the help of power law distribution for the activity of node more is close to real network interaction person's activity, and then helps reducing the limitation of time-varying network model.
Preferably, the node pitch is a manhattan distance.
By adopting the technical scheme, the distance between the nodes is constructed by using the Manhattan distance, so that the distance between the nodes is closer to the distance of a real network interactor, and the limitation of a time-varying network model is further reduced.
In a second aspect, the time-varying network model construction system provided by the present application adopts the following technical scheme:
a time-varying network model building system, the building system comprising,
the node information acquisition module sets the number of nodes of the network as N as required, uniformly distributes the N nodes in the L-L two-dimensional grid network, and endows each node in the network structure with corresponding activity a according to activity distributionkAnalyzing the space coordinate position of the node and the edge connecting condition of the node at each moment, and acquiring the node distance and the accumulated edge connecting times sum of the node, wherein N is a positive integer, and k is 1,2, … and N;
the preference probability acquisition module is used for acquiring the edge connection weight of the node based on the accumulated edge connection times sum of the node and acquiring the preference probability P by combining the node distance, the edge connection weight and the proportion parameter alphaijThe proportion parameter is used for representing the proportion occupied by the node edge connecting weight and the node distance when the network structure is formed, i is 1,2, …, N, j is 1,2, …, N, and i is not equal to j;
a module for forming instantaneous network model, wherein at each time t, the node combines the activity and preference probability P of the nodeijForming a transient network model Gt(ii) a And the number of the first and second groups,
a time-varying network model generation module according to the instantaneous network GtThe model generates a time-varying network model for a certain time period.
By adopting the technical scheme, the time-varying network model construction method is utilized, on the basis of activity drive, the node connecting edge weight and the node distance, namely the memory property and the spatial property of the nodes, are increased, and the node information acquisition module, the preference probability acquisition module, the instantaneous network model forming module and the time-varying network model generating module are obtained to display the correlation of network topological structures at different times, so that the limitation of the time-varying network model is reduced.
In a third aspect, the method for constructing a rumor propagation time-varying network model provided by the application adopts the following technical scheme:
a rumor propagation time-varying network model construction method includes,
setting a two-dimensional grid network with nodes of L and L, wherein the number of the nodes is N, acquiring node spacing and cumulative edge connecting times sum based on recorded space coordinates of the nodes and the edge connecting condition of each moment node in the network evolution process, acquiring edge connecting preference probability of active nodes selecting neighbors at each moment based on the cumulative edge connecting times sum and the edge connecting weight, acquiring edge connecting preference probability of each moment active node selecting neighbors by combining the node spacing, the edge connecting weight and a proportion parameter alpha, and performing edge connecting based on the edge connecting preference probability of each moment active node to acquire a time-varying network model, wherein the proportion parameter is used for expressing the proportion of the node edge connecting weight and the node spacing when a network structure is formed, and the value of the proportion parameter is set as regulation input; and the number of the first and second groups,
based on the time-varying network model, the nodes are set as unknown persons, propagators and immune persons according to requirements, the infection rate of the rumor is set as lambda, the recovery rate of the nodes is set as mu, and the time-varying network model of the rumor propagation is obtained.
By adopting the technical scheme, the rumor propagation time-varying network model is obtained based on the obtained time-varying network model construction method, and the obtained rumor propagation time-varying network model is based on the node connection weight and the node distance, namely the node spatiality and the memory, so that the rumor propagation time-varying network model is closer to a real rumor propagation social network, and the limitation of the rumor propagation time-varying network model is further reduced to a certain extent.
In summary, the present application includes at least one of the following beneficial technical effects:
1. according to the time-varying network model construction method, the connection preference probability of active nodes is determined by the node distance and the accumulated connection times and the joint, so that the nodes tend to be connected with the nodes which are high in affinity and close to the nodes, the time-varying network model is closer to a real social network, and the limitation of the time-varying network model is further reduced to a certain extent;
2. the current active nodes have higher probability to connect with the old nodes which are connected before the current time, and in the old nodes, the preference probability is related to the node distance and the connection edge weight among the nodes, the larger the connection edge weight is, namely the higher the intimacy degree among the nodes is, the higher the probability of establishing the connection edge among the nodes which are closer is; for a new node, the edge connecting weight is zero, the edge connecting probability is only related to the node distance, the attribute of the network node is more finely given through calculation of preference probability, and the limitation of a time-varying network model is reduced to a certain extent;
3. according to the time-varying network model building system, by utilizing the time-varying network model building method, on the basis of activity driving, node connecting edge weights and node intervals, namely the memory property and the spatial property of nodes, are increased, and the node information obtaining module, the preference probability obtaining module, the instantaneous network model forming module and the time-varying network model generating module are obtained, so that the relation of network topology structures at different moments is shown, and the limitation of the time-varying network model is reduced.
Drawings
FIG. 1 is a schematic flow chart diagram illustrating a time-varying network model construction method according to an embodiment of the present disclosure;
fig. 2 is a schematic diagram of a two-dimensional structure of a rumor propagation time-varying network model according to an embodiment of the present application;
fig. 3 is a graph illustrating simulation effects of introducing node spacing and edge weights on a rumor propagation time-varying network model according to an embodiment of the present disclosure;
fig. 4 is a graph illustrating the simulation effect of the proportional parameter α on the rumor propagation time-varying network model according to the present application;
fig. 5 is a diagram illustrating the actual verification effect of the time-varying rumor propagation network model based on the mail traffic data in the real mail network.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
Any feature disclosed in this specification (including any accompanying drawings) may be replaced by alternative features serving equivalent or similar purposes, unless expressly stated otherwise. That is, unless expressly stated otherwise, each feature is only an example of a generic series of equivalent or similar features.
The present application is described in further detail below with reference to figures 1-5.
The embodiment of the application discloses a time-varying network model construction method. Referring to fig. 1, the construction method includes setting a two-dimensional lattice network with nodes at L × L of N, obtaining node spacing and cumulative edge connection frequency sum based on recorded spatial coordinates of the nodes and edge connection conditions of the nodes at each moment in the network evolution process, obtaining edge connection preference probability of each active node selecting neighbors at each moment by combining the node spacing and the cumulative edge connection frequency sum, and performing edge connection based on the edge connection preference probability of each active node at each moment to obtain a time-varying network model.
In the implementation mode of the time-varying network model construction method, the connection preference probability of the active nodes is determined by the node distance and the accumulated connection times and the joint, so that the nodes tend to be connected with the nodes which are high in affinity and close to the nodes. The node spacing is embodied by node spatiality, and the edge connection weight is embodied by node memorability, so that the time-varying network model obtained by the method is based on node spatiality and memorability. The preference of the nodes in selecting the connecting edges is fully reflected, and the relation among topological structures contained in the real network is depicted. Therefore, the time-varying network model is closer to a real social network, and the limitation of the time-varying network model is further reduced to a certain extent.
The specific construction method of the time-varying network model comprises the following implementation modes:
the preference probability obtaining 102 obtains the edge connecting weight of the node based on the accumulated edge connecting times sum of the node, and obtains the preference probability P by combining the node distance, the edge connecting weight and the proportion parameter alphaijThe proportion parameter is used for representing the proportion occupied by the node edge connecting weight and the node distance when the network structure is formed, i is 1,2, …, N, j is 1,2, …, N, and i is not equal to j;
instantaneous network model acquisition 103, each time t, a node combines the activity and preference probability P of the nodeijForming a transient network model Gt(ii) a And the number of the first and second groups,
time-varying network model generation 104 from transient network GtThe model generates a time-varying network model for a certain time period.
As a specific embodiment of the present application, the node distance is a manhattan distance, the liveness distribution conforms to a power law distribution, and the power exponent and the most significant value of the liveness distribution are set according to a topology structure of an actual network. Therefore, the nodes are closer to the interactors in the real network, and the gap between the nodes and the real network is reduced.
In the implementation mode of the time-varying network model construction, the intimacy between the nodes is represented by the connecting edge weight, and on the basis of activity driving, the preference probability of the connecting edge between different nodes is obtained by combining the connecting edge weight and the distance relation between the nodes, so that the instantaneous network model is obtained based on the preference probability, the relevance of the network topological structure of the time-varying network at different times is further obtained, and the limitation of the time-varying network model is reduced to a certain extent. The obtained time-varying network model is simple and clear, and the influence proportion of each driving factor can be conveniently adjusted to describe the time-varying network under different types and different scenes by modifying the proportional parameters.
The specific method for obtaining the preference probability 102 includes the following embodiments:
acquiring node connection probability 102-1, wherein the nodes become active nodes and inactive nodes according to the activity, and each node has the probability a in each discrete time step delta tkΔ t becomes active; for a certain active node, putting the nodes which establish the connecting edge with the active node before the time t into a set R, and obtaining the node connection probability p according to the set R1And p2，
Where n represents the total number of elements in the set R, c is a bias constant, and in this embodiment, c is 1, p1Representing the probability, p, that an active node selects a node in the connection set R2Representing the probability of the active node selecting a new node which is connected with the edge which is never connected;
acquiring node pair connection probability 102-2, wherein at the moment t, the node connected with the active node is used as a target node, and the active node and a certain target node form a node pair; when the target node is in the set R, the node pair connection probability p is obtained by combining the connection edge weight, the distance and the proportion parameter alpha of two nodes in the node pair21，
When the target node does not belong to the set R, acquiring node pair connection probability p based on node pair distance22，
Wherein, wijRepresenting the edge-to-edge weight of a node pair, dijRepresenting node pair spacing;
calculating preference probability 102-3, and combining node connection probability and node pair connection probability to obtain preference probability Pij，
In the above embodiment of obtaining the preference probability, the intimacy between nodes is measured by the cumulative edge-connecting weight between node pairs. The greater the weight of the corresponding side, the greater the probability that the side will occur repeatedly. At the same time, nodes may also tend to connect to nodes that are close to them. Therefore, the node-to-node connection probability of the target node belonging to the set R is determined by the connection edge weight and the distance between the node pairs, and the node-to-node connection probability of the target node not belonging to the set R is determined by the node distance. Wherein, how many activity values the node reaches is changed into an active state is set by a user.
As a specific embodiment of the present application, nodes in a network are simply classified into two types: old nodes that have been connected and new nodes that have not been connected. And if the node selects the old node appearing before in the first step, the edge connection weight and the distance jointly determine the edge connection preference probability. The larger the weight and the closer the distance, the greater the probability that the node becomes the target node. The influence proportion of the two driving factors can be adjusted by a proportionality coefficient alpha; if the first step selects new edges which do not appear, the selection of the target node is only determined by the distance between the nodes.
The activity of the nodes determines the number of effective nodes in the network at each moment, and the connection edge weight and the node distance of the nodes can jointly influence the formation of connection edges between the network nodes. The nodes and the connecting edges form a transient network topology structure, so that the functions of the network are determined, and the dynamic behaviors of the network are influenced.
Specifically, since the active nodes at different time are different, and the target nodes selected and interacted by the active nodes are also different, the network structure may evolve over time. The aim of constructing the model is to reflect the actual network characteristic attributes and the like through the evolution mechanism of the model, so that the simulation experiment on the model generation network has higher credibility and actual reference value. In the model provided in the embodiment of the present application, firstly, an active node has a higher probability to connect to an old node that has been connected before the current time, and secondly, in the old neighbors, a preference probability is determined according to the cumulative weight of connected edges between different nodes and the length of the connected edges. The larger the weight is, that is, the higher the intimacy degree is, the greater the probability that the closer nodes establish the connecting edge is. For the new node, the weight of the connected edge is zero, and the probability of the connected edge is only related to the distance. Compared with the existing model, the method gives the attributes of the nodes in the network more carefully, reflects the evolution of the network structure and simultaneously delineates the association of the network structures at different moments.
The specific method for acquiring the transient network model 103 includes the following embodiments:
at each moment t, the node becomes an active node or an inactive node according to the activity of the node;
the active nodes are connected with m connected edges according to own connected edge preference probability to form an instant network model GtAnd the number m of the connecting edges is set according to practical application.
In the embodiment of the instantaneous network model obtaining 103, each active node at any moment is connected according to the preference probability to generate an instantaneous network model, so that the instantaneous network model is closer to a real social network, and the limitation of the instantaneous network model is further reduced to a certain extent; the number m of the connecting edges has different values according to different practical application scenes. For example, when a one-to-one chat is performed by software such as WeChat, the number m of connected edges is 1; when a one-to-many chat, i.e., a group chat is performed using software such as WeChat, the number of links exceeds 1.
The time-varying network model construction method disclosed by the application references some related network models, such as an activity driving model, and changes the network from static state to time-varying by introducing the activity of the nodes; the Kleinberg spatial model simply gives a node coordinate attribute, so that the influence of a spatial position on the formation of a network topological structure is reflected; the memory evolution model (RP) based on activity driving introduces the memory of the nodes, and divides the nodes in the network into two types of new nodes and old nodes. The method integrates the advisability of the model, and further considers the relationship between the intimacy and the distance between the nodes on the basis of liveness driving, so as to depict the relevance of the network topology structure of the time-varying network at different moments.
The embodiment of the application also discloses a time-varying network model construction system, which comprises,
the node information acquisition module sets the number of nodes of the network as N as required, uniformly distributes the N nodes in the L-L two-dimensional grid network, and endows each node in the network structure with corresponding activity a according to activity distributionkAnalyzing the space coordinate position of the node and the edge connecting condition of the node at each moment, and acquiring the node distance and the accumulated edge connecting times sum of the node, wherein N is a positive integer, and k is 1,2, … and N;
the preference probability acquisition module is used for acquiring the edge connection weight of the node based on the accumulated edge connection times sum of the node and acquiring the preference probability P by combining the node distance, the edge connection weight and the proportion parameter alphaijWhere α represents a proportion of a node connection weight when forming a network structure, i ≠ 1,2, …, N, j ≠ 1,2, …, N, and i ≠ j;
a module for forming instantaneous network model, wherein at each time t, the node combines the activity and preference probability P of the nodeijForming a transient network model Gt(ii) a And the number of the first and second groups,
a time-varying network model generation module according to the instantaneous network GtThe model generates a time-varying network model for a certain time period.
In the implementation mode of the time-varying network model building system, the time-varying network model building method is used, on the basis of activity drive, node connecting edge weight and node spacing, namely the memory property and the spatial property of the nodes, are increased, and the node information obtaining module, the preference probability obtaining module, the instantaneous network model forming module and the time-varying network model generating module are obtained to display the relevance of network topology structures at different time, so that the limitation of the time-varying network model is reduced.
The embodiment of the application also discloses a rumor propagation time-varying network model construction method, which comprises the following steps,
setting a two-dimensional grid network with nodes of L and L, wherein the number of the nodes is N, acquiring node spacing and cumulative edge connecting times sum based on recorded space coordinates of the nodes and the edge connecting condition of each moment node in the network evolution process, acquiring edge connecting preference probability of active nodes selecting neighbors at each moment based on the cumulative edge connecting times sum and the edge connecting weight, acquiring edge connecting preference probability of each moment active node selecting neighbors by combining the node spacing, the edge connecting weight and a proportion parameter alpha, and performing edge connecting based on the edge connecting preference probability of each moment active node to acquire a time-varying network model, wherein the proportion parameter is used for expressing the proportion of the node edge connecting weight and the node spacing when a network structure is formed, and the value of the proportion parameter is set as regulation input; and the number of the first and second groups,
based on the time-varying network model, the nodes are set as unknown persons, propagators and immune persons according to requirements, the infection rate of the rumor is set as lambda, the recovery rate of the nodes is set as mu, and the time-varying network model of the rumor propagation is obtained.
In the implementation of the method for constructing the rumor propagation time-varying network model, the time-varying network model construction method is applied to the rumor propagation time-varying network model, and the obtained rumor propagation time-varying network model is based on the node connection edge weight and the node spacing, namely the node spatiality and the memory, so that the rumor propagation time-varying network model is closer to a real rumor propagation social network, and the limitation of the rumor propagation time-varying network model is further reduced to a certain extent.
The edge connecting weight of the nodes is related to the cumulative edge connecting times of the nodes, so that the edge connecting weight is embodied by node memorability, and the node spacing is embodied by node spatiality, and therefore the rumor propagation time-varying network model obtained by the method can be called a time-varying spatial memory model.
In a social network, nodes represent users, and edges represent information interaction among users. At each moment, some users in the network become active and interact with other users.
The following explains the role played by the connection edge weights and node distances of the nodes in selecting the target node and the influence on the network topology structure in the time-varying network generation process by combining simulation and actual verification of the rumor propagation time-varying network model of the application.
Referring to fig. 2, fig. 2 is a schematic diagram of a two-dimensional structure of a constructed time-varying rumor propagation network model, in which nodes have three states, namely, unknown, propagator and immune. When the node pair has a continuous edge, the information can be interacted between the two nodes. If the propagator interacts with the unknown, the propagator will transmit the rumor to the unknown at the infection rate λ, and the unknown becomes the propagator if the infection is successful. If two propagators interact with each other or the propagator interacts with the immunizer, one may realize that this is a rumor or find that this information is known to everyone, so the interest in continuing to propagate this information will decrease and the propagator will become the immunizer with a recovery rate μ. As shown in fig. 2, T1 represents the network structure diagram before rumor propagation, and T2 represents the network structure diagram after rumor propagation.
Referring to fig. 3, a rumor propagation time-varying network model was compared with an existing network model for simulation. The time-varying network model for rumor propagation sets the following parameters: number of nodes N is 105The network side length L is 317, and the minimum value of the activity a is 10-3And the distribution of activity degree obeys F (a). alpha.a-2.8The number of connected edges m created by the active node each time is 1, the infection rate λ of the rumor propagation time-varying network model is 1, and the recovery rate μ is 0.6. The resulting ratio variation of unknown people in the rumor propagation time-varying network model of the present application, i.e., the time-varying spatial memory model (TSM), and other models is shown in fig. 3. The ML model represents an activity driving network, the AD model represents a time-varying network model only introducing node intervals, the IRP represents a time-varying network model only introducing node connection edge weights, the horizontal axis represents rumor propagation time, and the vertical axis represents the proportion of an unknown person. As can be seen from the overall trend in fig. 3, the unknown proportion gradually decreases and eventually levels off with time, and the unknown proportion tends to level off representing rumor propagation, i.e., rumor propagation is suppressed. And the propagation speed and the range are further controlled on the network generated by the time-varying spatial memory model TSM. So that the combined action of intimacy and distance between nodes can be seenThe preference of the node connecting edge is enhanced, the randomness is weakened, the strong connection and the weak connection in the network are more obvious, the relevance of the network structure at different time is enhanced, and therefore the influence on the transmission process is increased.
Referring to fig. 4, the effect of the scaling parameter α on the network structure and rumor propagation process is shown when it takes different values. Wherein the horizontal axis represents rumor propagation time and the vertical axis represents unknown proportion. The numerical value of the proportional parameter α represents the edge-to-edge weight of the node, i.e., the proportion of the memorability of the node. As can be seen from fig. 4, the larger the value of α, the better the unknown ratio tends to be in a plateau in the shorter rumor propagation time, and the earlier the rumor is suppressed, i.e., the more dominant the memory of the node in the time-varying spatial memory model is to the preferred connection of the node. Specifically, when the node selects a target neighbor from the set R when α is 0, only the distance from the node is considered, and the closer the distance is, the greater the probability of connecting edges is, and the propagation range of the rumor in the simulation network is close to 60%. When α > 0, the intimacy of the node pair affects the choice of the connecting edge, and as α increases, the intimacy affects the specific gravity, and the inhibition of the sum range of the speed of rumor propagation increases gradually. For example, when α is 1, the propagation range is reduced to around 43%, whereas when α is 2, only about 20% of nodes know the rumor. This indicates that the spatial memory model has a dominant memory property compared to the spatial one.
Through the simulation result, the introduction of node spacing and edge connecting weight, namely node spatiality and memorability, can be preliminarily obtained to have an inhibition effect on rumor propagation.
Referring to fig. 5, the structural properties of a real mail network are counted, model parameters are adjusted to simulate the actual network, and the obtained result is shown in fig. 5, wherein an email model represents the real mail network, an RP model represents a memory evolution model, an ML model represents an activity driving network, and an AD model represents a time-varying network model only introducing node distances. Wherein the data set is mail-to-mail data of 803 days of about 1000 workers in a European institute downloaded from a Stanford university data website SNAP. It can be seen that in the several models shown, the rumor propagation results on the network generated by the time-varying spatial memory model are closest to the rumor propagation results of the actual network. The rationality of the time-varying network model network evolution mechanism provided by the application is verified, and the network structure and the dynamic behavior on the network structure are indeed influenced by various attributes of the nodes.
Through the actual verification results, the introduction of node spacing and edge connecting weights, namely node spatiality and memorability, can be verified to have an inhibition effect on rumor propagation. Namely, the rumor propagation time-varying network model based on the time-varying network structure model is closer to the real rumor propagation social network. Furthermore, the time-varying network model construction method and system and the rumor propagation time-varying network model construction method disclosed by the application are lower in limitation and closer to an actual network.
The change of the network structure by the time-varying network model construction method provided by the application is explained by combining the simulation result and the actual verification result of the rumor propagation time-varying network model, and the rationality and the accuracy of the time-varying network model provided by the application are reflected by comparing the time-varying network model construction method with other existing models.
In real life, the topological result of many complex systems is not constant, and the node and edge conditions in the network change with time. With the rapid development of technologies such as the internet of things, big data, artificial intelligence and the like, the data which can be acquired by people is more and more abundant, and the attributes and behavior development tracks of individuals in various complex systems can be recorded in detail and specifically. The massive data and the complex network theory knowledge provide a foundation and a reference for researching network structure change and constructing a time-varying network model. The network topology at each moment and the correlation of the topological structures among the moments are more accurately described by introducing the time variability, the space system and the memory performance of the nodes, so that the characteristics of an actual network are reflected. The method is used for solving the problems of researching dynamic behaviors such as information transmission, disease infection and the like on a generated network and optimizing and controlling the network, and the obtained conclusion has more practical application value.
Claims (8)
1. A time-varying network model construction method is characterized by comprising the steps of setting a two-dimensional grid network with nodes of L x L, wherein the number of the nodes is N, obtaining node spacing and accumulated edge connection times sum based on recorded space coordinates of the nodes and edge connection conditions of the nodes at each moment in the network evolution process, obtaining edge connection preference probability of active nodes selecting neighbors at each moment by combining the node spacing and the accumulated edge connection times sum, and carrying out edge connection based on the edge connection preference probability of the active nodes at each moment to obtain a time-varying network model.
2. The time-varying network model construction method according to claim 1, wherein the time-varying network model is constructed by a specific method including,
acquiring node information (101), setting the number of nodes of the network to be N as required, uniformly distributing the N nodes in the L x L two-dimensional grid network, and endowing each node in the network structure with corresponding activity a according to activity distributionkAnalyzing the space coordinate position of the node and the edge connecting condition of the node at each moment, and acquiring the sum of the node distance and the accumulated edge connecting times of the node, wherein N is a positive integer;
preference probability obtaining (102) obtains the edge connecting weight of the node based on the accumulated edge connecting times sum of the node, and obtains preference probability P by combining the node distance, the edge connecting weight and the proportion parameter alphaijThe proportion parameter is used for representing the proportion occupied by the node edge connecting weight and the node distance when the network structure is formed, i is 1,2, …, N, j is 1,2, …, N, and i is not equal to j;
instantaneous network model acquisition (103), each time t, the node combines the activity and preference probability P of the nodeijForming a transient network model Gt(ii) a And the number of the first and second groups,
time-varying network model generation (104) from transient network GtThe model generates a time-varying network model for a certain time period.
3. The method of constructing a time-varying network model according to claim 2, wherein the specific method of preference probability acquisition (102) comprises,
obtaining node connection probability (102-1), the node according to activityThe jumping degrees are changed into active nodes and inactive nodes; for a certain active node, putting the nodes which establish the connecting edge with the active node before the time t into a set R, and obtaining the node connection probability p according to the set R1And p2，
Where n represents the total number of elements in the set R, c is a bias constant, p1Representing the probability, p, that an active node selects a node in the connection set R2Representing the probability of the active node selecting a new node which is connected with the edge which is never connected;
acquiring node pair connection probability (102-2), wherein at the moment t, the node connected with the active node is used as a target node, and the active node and a certain target node form a node pair; when the target node is in the set R, the node pair connection probability p is obtained by combining the connection edge weight, the distance and the proportion parameter alpha of two nodes in the node pair21，
When the target node does not belong to the set R, acquiring node pair connection probability p based on node pair distance22，
Wherein, wijRepresenting the edge-to-edge weight of a node pair, dijRepresenting node pair spacing;
calculating preference probability (102-3), and combining the node connection probability and the node pair connection probability to obtain preference probability Pij，
4. The time-varying network model construction method according to claim 2, characterized in that the specific method of transient network model acquisition (103) comprises,
at each moment t, the node becomes an active node or an inactive node according to the activity of the node;
the active nodes are connected with m connected edges according to own connected edge preference probability to form an instant network model GtAnd the number m of the connecting edges is set according to practical application.
5. The time-varying network model building method according to any one of claims 2 to 4, wherein the liveness distribution conforms to a power law distribution, and a power exponent and a maximum value of the liveness distribution are set according to a topology structure of an actual network.
6. The method of constructing a time-varying network model according to any one of claims 1 to 5, wherein the node spacing is a Manhattan distance.
7. A time-varying network model construction system, characterized in that the construction system comprises,
the node information acquisition module sets the number of nodes of the network as N as required, uniformly distributes the N nodes in the L-L two-dimensional grid network, and endows each node in the network structure with corresponding activity a according to activity distributionkAnalyzing the space coordinate position of the node and the edge connecting condition of the node at each moment, and acquiring the node distance and the accumulated edge connecting times sum of the node, wherein N is a positive integer, and k is 1,2, … and N;
the preference probability acquisition module is used for acquiring the edge connection weight of the node based on the accumulated edge connection times sum of the node and acquiring the preference probability P by combining the node distance, the edge connection weight and the proportion parameter alphaijWherein the proportion parameter is used for expressing the ratio of the node edge weight and the node distance when the network structure is formedHeavy, i ≠ 1,2, …, N, j ≠ 1,2, …, N, and i ≠ j;
a module for forming instantaneous network model, wherein at each time t, the node combines the activity and preference probability P of the nodeijForming a transient network model Gt(ii) a And the number of the first and second groups,
a time-varying network model generation module according to the instantaneous network GtThe model generates a time-varying network model for a certain time period.
8. A rumor propagation time-varying network model construction method is characterized by comprising the following steps,
setting a two-dimensional grid network with nodes of L and L, wherein the number of the nodes is N, acquiring node spacing and cumulative edge connecting times sum based on recorded space coordinates of the nodes and the edge connecting condition of each moment node in the network evolution process, acquiring edge connecting preference probability of active nodes selecting neighbors at each moment based on the cumulative edge connecting times sum and the edge connecting weight, acquiring edge connecting preference probability of each moment active node selecting neighbors by combining the node spacing, the edge connecting weight and a proportion parameter alpha, and performing edge connecting based on the edge connecting preference probability of each moment active node to acquire a time-varying network model, wherein the proportion parameter is used for expressing the proportion of the node edge connecting weight and the node spacing when a network structure is formed, and the value of the proportion parameter is set as regulation input; and the number of the first and second groups,
based on the time-varying network model, the nodes are set as unknown persons, propagators and immune persons according to requirements, the infection rate of the rumor is set as lambda, the recovery rate of the nodes is set as mu, and the time-varying network model of the rumor propagation is obtained.
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