CN110084714B - Social network influence maximization method, device and equipment based on directed tree - Google Patents
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Abstract
The application relates to a social network influence maximization method, a social network influence maximization device and social network influence maximization equipment based on a directed tree, wherein the method comprises the following steps: constructing a directed tree according to the directed graph of each node; calculating the total weight of the expected final active nodes when the influence generated by each preset initial active node combination is propagated and ended according to each preset initial active node combination and the state information of each node in the directed tree; and selecting each node in the preset initial active node combination corresponding to the maximum total weight as an initial active node of the directed tree. According to the method, each node in the preset initial active node combination corresponding to the maximum total weight is selected as the initial active node of the directed tree, influence propagation is probably maximized, and therefore the technical scheme can maximize the influence of information in the social network to a greater extent.
Description
Technical Field
The application relates to the technical field of influence maximization, in particular to a social network influence maximization method, device and equipment based on a directed tree.
Background
With the development of network technology, social interaction with networks as carriers has also been greatly developed, and particularly, information dissemination has also been greatly developed.
For some information, a wide propagation range may be required, and the influence of the node is generally calculated according to an influence propagation model, so that the node with a large influence is selected as an initial node. However, in the impact process, there is a probability of whether an inactive node is impacted, and therefore, it is difficult to decide the maximum expected spread given the general case of nodes in any set.
Disclosure of Invention
In order to overcome the problems in the related art at least to a certain extent, the application provides a social network influence maximization method, device and equipment based on a directed tree.
According to a first aspect of the present application, there is provided a social network influence maximization method based on a directed tree, including:
constructing a directed tree according to the directed graph of each node;
calculating the total weight of the expected final active nodes when the influence generated by each preset initial active node combination is propagated and ended according to each preset initial active node combination and the state information of each node in the directed tree;
and selecting each node in a preset initial active node combination corresponding to the maximum total weight as an initial active node of the directed tree.
Optionally, the state information includes a node type and the number of edge-entering neighbors; the node types comprise leaf nodes, internal nodes which are seed nodes and internal nodes which are not seed nodes.
Optionally, the internal nodes in the directed tree have at most two degrees of income.
Optionally, the calculating, according to each preset initial active node combination and the state information of each node in the directed tree, a total weight of an expected final active node when an influence propagation generated by each preset initial active node combination is ended includes:
when the node v in the directed tree is a leaf node and a node in a preset initial active node combination is more than or equal to 1, calculating the total weight according to a first formula;
the first formula is
Wherein f (k, v, i) is the total weight, and k is a node in the preset initial active node combination;
when the node v in the directed tree is an internal node of the seed node and the node in the preset initial active node combination is more than or equal to 1 and v has two edge-entering neighbors u1And u2Then, the total weight is calculated according to a second formula;
the second formula is
When the node v in the directed tree is an internal node of the seed node and the node in the preset initial active node combination is more than or equal to 1 and v is provided with an edge-entering neighbor u1Then, the total weight is calculated according to a third formula;
the third formula is
When the node v in the directed tree is an internal node of a non-seed node and a node in a preset initial active node combination is more than or equal to 1 and v is provided with two edge-entering neighbors u1And u2Then, the total weight is calculated according to a fourth formula;
the fourth formula is
When the node v in the directed tree is an internal node of a non-seed node and a node in a preset initial active node combination is more than or equal to 1 and v is provided with an edge-entering neighbor u1Then, the total weight is calculated according to a fifth formula;
the fifth formula is
f(k,v,i)＝1+f(k,u1,i+1)。
Optionally, the directed tree is transformed from the directed graph of each node according to a binary tree property.
According to a second aspect of the present application, there is provided a social network influence maximization apparatus based on a directed tree, comprising:
the construction module is used for constructing a directed tree according to the directed graphs of the nodes;
the calculation module is used for calculating the total weight of the expected final active node when the influence generated by each preset initial active node combination is propagated and ended according to each preset initial active node combination and the state information of each node in the directed tree;
and the selecting module is used for selecting each node in a preset initial active node combination corresponding to the maximum total weight as an initial active node of the directed tree.
Optionally, the state information includes a node type and the number of edge-entering neighbors; the node types comprise leaf nodes, internal nodes which are seed nodes and internal nodes which are not seed nodes.
Optionally, the internal nodes in the directed tree have at most two degrees of income.
Optionally, the calculation module includes:
the first calculation unit is used for calculating the total weight according to a first formula when a node v in the directed tree is a leaf node and a node in a preset initial active node combination is greater than or equal to 1;
the first formula is
Wherein f (k, v, i) is the total weight, and k is a node in the preset initial active node combination;
a second computing unit, configured to, when a node v in the directed tree is an internal node of a seed node and a node in a preset initial active node combination is greater than or equal to 1 and v has two edge-entering neighbors u1And u2Then, the total weight is calculated according to a second formula;
the second formula is
A third calculating unit, configured to, when a node v in the directed tree is an internal node of a seed node and a node in a preset initial active node combination is greater than or equal to 1 and v has an edge-entering neighbor u1Then, the total weight is calculated according to a third formula;
the third formula is
A fourth calculating unit, configured to, when a node v in the directed tree is an internal node of a non-seed node and a node in a preset initial active node combination is greater than or equal to 1 and v has two edge-entering neighbors u1And u2Then, the total weight is calculated according to a fourth formula;
the fourth formula is
A fifth calculating unit, configured to, when a node v in the directed tree is an internal node of a non-seed node and a node in a preset initial active node combination is greater than or equal to 1 and v has an edge-entering neighbor u1Then, the total weight is calculated according to a fifth formula;
the fifth formula is
f(k,v,i)＝1+f(k,u1,i+1)。
According to a third aspect of the present application, there is provided a social network influence maximizing device based on a directed tree, comprising:
a processor, and a memory coupled to the processor;
the memory is configured to store a computer program at least for performing a directed tree based social network impact maximization method as follows:
constructing a directed tree according to the directed graph of each node;
calculating the total weight of the expected final active nodes when the influence generated by each preset initial active node combination is propagated and ended according to each preset initial active node combination and the state information of each node in the directed tree;
and selecting each node in a preset initial active node combination corresponding to the maximum total weight as an initial active node of the directed tree.
Optionally, the state information includes a node type and the number of edge-entering neighbors; the node types comprise leaf nodes, internal nodes which are seed nodes and internal nodes which are not seed nodes.
Optionally, the internal nodes in the directed tree have at most two degrees of income.
Optionally, the calculating, according to each preset initial active node combination and the state information of each node in the directed tree, a total weight of an expected final active node when an influence propagation generated by each preset initial active node combination is ended includes:
when the node v in the directed tree is a leaf node and a node in a preset initial active node combination is more than or equal to 1, calculating the total weight according to a first formula;
the first formula is
Wherein f (k, v, i) is the total weight, and k is a node in the preset initial active node combination;
when the node v in the directed tree is an internal node of the seed node and the node in the preset initial active node combination is more than or equal to 1 and v has two edge-entering neighbors u1And u2Then, the total weight is calculated according to a second formula;
the second formula is
When the node v in the directed tree is an internal node of the seed node and the node in the preset initial active node combination is more than or equal to 1 and v is provided with an edge-entering neighbor u1Then, the total weight is calculated according to a third formula;
the third formula is
When the node v in the directed tree is an internal node of a non-seed node and a node in a preset initial active node combination is more than or equal to 1 and v is provided with two edge-entering neighbors u1And u2Then, the total weight is calculated according to a fourth formula;
the fourth formula is
When the node v in the directed tree is an internal node of a non-seed node and a node in a preset initial active node combination is more than or equal to 1 and v is provided with an edge-entering neighbor u1Then, the total weight is calculated according to a fifth formula;
the fifth formula is
f(k,v,i)＝1+f(k,u1,i+1)。
Optionally, the directed tree is transformed from the directed graph of each node according to a binary tree property.
The processor is used for calling and executing the computer program in the memory.
The technical scheme provided by the application can comprise the following beneficial effects: firstly, a directed tree is built according to a directed graph of each node, then, the total weight of the expected final active nodes when the influence propagation generated by each preset initial active node combination is finished is calculated according to each preset initial active node combination and the state information of each node in the directed tree, and finally, each node in the preset initial active node combination corresponding to the maximum total weight is selected as the initial active node of the directed tree. The method and the device for the information transmission of the directed tree have the advantages that the total weight of all the active nodes expected when the influence transmission is finished is calculated, each preset initial active node combination corresponds to the total weight of all the active nodes expected, the larger the total weight is, the more the active nodes are when the influence transmission is finished are shown, the larger the transmission range is, therefore, the influence transmission is probably maximized most probably by selecting each node in the preset initial active node combination corresponding to the largest total weight as the initial active node of the directed tree, and therefore the information influence in the social network can be maximized to the greatest extent.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the application.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present application and together with the description, serve to explain the principles of the application.
FIG. 1 is a schematic view of impact propagation.
Fig. 2 is a flowchart illustrating a social network influence maximization method based on a directed tree according to an embodiment of the present application.
Fig. 3 is a schematic structural diagram of a social network influence maximization apparatus based on a directed tree according to a second embodiment of the present application.
Fig. 4 is a schematic structural diagram of a social network influence maximization device based on a directed tree according to a third embodiment of the present application.
Detailed Description
Reference will now be made in detail to the exemplary embodiments, examples of which are illustrated in the accompanying drawings. When the following description refers to the accompanying drawings, like numbers in different drawings represent the same or similar elements unless otherwise indicated. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present application. Rather, they are merely examples of apparatus and methods consistent with certain aspects of the present application, as detailed in the appended claims.
The influence propagation model defines the way and mechanism of influence propagation in the social network, and is the basis for researching the maximization of the influence of the social network. Influence maximization is a basic problem in the research of the social network information dissemination field, and can be described as follows: given a social network G, an influence propagation model m and a positive integer k, finding k nodes with the largest final influence range in the social network, and taking the k nodes as an initial active node set to enable the number of the finally influenced nodes to be the largest through influence propagation in the social network.
Each node of the social network diagram in the influence maximization research has two states, namely 0 and 1, wherein 0 is in an inactive state, and 1 is in an active state. When a node transitions from an inactive state to an active state, the node may attempt to affect its neighbor nodes in the inactive state. If the activation is successful, its neighbor node changes from the inactive state to the active state. As shown in fig. 1, initial node a is active and has the ability to attempt to affect its neighboring inactive state nodes b, c, and e. This time is divided into two cases: in one case, if the node a does not successfully activate the node c, the node c is still in the inactive state; alternatively, node a successfully activates node b, so node b changes from an inactive state to an active state, in which case node b has the ability to affect its neighboring nodes, e.g., node b may activate node d. This process of an influencing node changing from an inactive state to an active state is referred to as propagation of the influence.
Currently, the most widely studied impact propagation models in academia are the independent cascade model (IC model) and the linear threshold model (LT model).
Among them, the linear threshold model is proposed based on the threshold model of the collective behavior proposed by the influence of the surrounding people participating in a certain collective activity studied in 1978 by Mark Granovetter (Mark grannovett).
The linear threshold model allocates a threshold value theta (v) epsilon [0,1 to each node v]The threshold value represents how easily this node is affected. The nodes w adjacent to the node v have non-negative weights bv,wHas an influence on v and b of all neighbors w of vv,wThe sum is less than or equal to 1. For a node v in an inactive state, the node v will be activated only if the sum of the influences of its active neighbor nodes is greater than or equal to its threshold, i.e. the decision of an individual in the network depends on the decisions of all its neighbor nodes. And active neighbor nodes of node v may participate in activating v multiple times.
The propagation algorithm specifically comprises:
(1) an initial set of active nodes a.
(2) At time t, all the neighbor nodes of the node v in the active state attempt to activate v, and if the sum of the influence of all the neighbor active nodes exceeds the activation threshold of v, the node v transitions to the active state at time t + 1.
(3) The above process is repeated continuously until the sum of the influence of any active node existing in the network cannot activate the neighbor node in the inactive node state, and the propagation process is ended.
In addition, the independent cascade model is a probabilistic model proposed by Jacob golden berg (jacobs Goldenberg) et al in studying marketing. The algorithm of the model is as follows: the probability of success of a node u attempting to activate its neighbor node v is puvEvent of (1), puvRepresents the probability that node u affects v by an edge (u, v), and the probability that a node in an inactive state is activated by a neighbor node that just entered the active state is independent of the activities that had previously attempted to activate the node's neighbors. In addition, any node u in the model network only has one chance to try to activate the neighbor node v, and no matter whether the node u succeeds or not, at the later moment, although the u itself still keeps the active state, the node u does not have influence any more, and the node is an active node without influence.
The method specifically comprises the following steps:
(1) an initial set of active nodes a.
(2) At time t, the most recently activated node u has an effect on its neighboring node v with a probability of success puvIf there are multiple neighboring nodes that have been the most recently activated nodes, then these nodes will attempt to activate node v in any order.
(3) If the node v is successfully activated, at the moment t +1, the node v is converted into an active state, and the influence on the adjacent inactive node is generated; otherwise, the state of the node t +1 does not change at the moment.
(4) The above process is repeated continuously until there are no influential active nodes in the network, and the propagation process ends.
The problem of maximizing influence proves to be the NP-Hard problem. Bharathi et al extended the IC model and merged the competing factors, given an approximation algorithm based on a special bi-directional tree, the objective of the study was to maximize its influence, and indicated that "the influence maximization problem was NPC, which we guessed is also true for tree structures".
Based on the above conclusions, when solving the problem of influence maximization, the academia currently only starts from the influence of each preset initial active node, and selects the initial active node according to the influence, and the probability that the non-active node is influenced in the propagation process cannot be taken into consideration, so that the initial active node is selected only according to the influence of the preset initial active node to perform subsequent influence propagation, and the largest influence propagation range cannot be generated to a great extent.
The inventor proves that a solution of polynomial time exists in the influence maximization problem based on a tree structure, namely based on a directed tree, and provides the social network influence maximization method, device and equipment based on the directed tree according to an algorithm provided by the proving process. The technical solution of the present application will be described in detail by way of examples.
Example one
Referring to fig. 2, fig. 2 is a flowchart illustrating a social network influence maximizing method based on a directed tree according to an embodiment of the present application.
As shown in fig. 2, the method for maximizing social network influence based on a directed tree provided by this embodiment includes:
and step 21, constructing a directed tree according to the directed graphs of the nodes.
And step 22, calculating the total weight of the expected final active nodes when the influence propagation generated by each preset initial active node combination is finished according to each preset initial active node combination and the state information of each node in the directed tree.
And 23, selecting each node in the preset initial active node combination corresponding to the maximum total weight as an initial active node of the directed tree.
The method comprises the steps of firstly constructing a directed tree according to a directed graph of each node, then calculating the total weight of expected final active nodes when influence propagation generated by each preset initial active node combination is finished according to each preset initial active node combination and the state information of each node in the directed tree, and finally selecting each node in the preset initial active node combination corresponding to the maximum total weight as the initial active node of the directed tree. The method and the device have the advantages that the total weight of all the expected active nodes when the influence propagation is finished is calculated, each preset initial active node combination corresponds to the total weight of all the expected active nodes, the larger the total weight is, the more the active nodes are when the influence propagation is finished are shown, the larger the propagation range is, therefore, the influence propagation is most probably maximized by selecting each node in the preset initial active node combination corresponding to the largest total weight as the initial active node of the directed tree, and therefore, the information influence in the social network can be maximized to the greater extent.
In step 21, the directed graph is a directed graph with propagation directions according to a given social network transition, wherein the directed tree is transformed from the directed graph of each node according to the property of a binary tree, and the internal nodes in the directed tree have at most two introductions.
The method for ensuring that the internal node has at most two introductions may be to add a virtual node to the directed tree, and define the weight of the virtual node as 0 and the weight of the non-virtual node as 1.
In step 22, the state information includes the node type and the number of the edge-entering neighbors; the node types comprise leaf nodes, internal nodes which are seed nodes and internal nodes which are not seed nodes.
In addition, since the LT model and the IC + model are equivalent, the calculation of the total weight for the LT model may specifically be:
when the node v in the directed tree is a leaf node and the node in the preset initial active node combination is more than or equal to 1, calculating the total weight according to a first formula;
the first formula is
Wherein f (k, v, i) is the total weight, and k is a node in the preset initial active node combination;
when the node v in the directed tree is an internal node of the seed node and the node in the preset initial active node combination is more than or equal to 1 and v has two edge-entering neighbors u1And u2Then, the total weight is calculated according to a second formula;
the second formula is
When the node v in the directed tree is an internal node of the seed node and the node in the preset initial active node combination is more than or equal to 1 and v is provided with an edge-entering neighbor u1Then, the total weight is calculated according to a third formula;
the third formula is
When a node v in the directed tree is an internal node of a non-seed node and a node in a preset initial active node combination is more than or equal to 1 and v is provided with two edge-entering neighbors u1And u2Then, the total weight is calculated according to a fourth formula;
the fourth formula is
When the node v in the directed tree is an internal node of a non-seed node and a node in a preset initial active node combination is more than or equal to 1 and v is provided with an edge-entering neighbor u1Then, the total weight is calculated according to a fifth formula;
the fifth formula is
f(k,v,i)＝1+f(k,u1,i+1)。
The running time is O (nk).
Wherein, the IC + model is the deformation of the IC model, specifically: in each step, one inactive node is allowed to accept the influence of only one incoming adjacent active node. Assuming that v has h incoming neighbors u1 … uh, then the following h +1 events are unique.
The neighboring active node ui has an influence on its neighboring node v with a probability of success of
Wherein, i is 1,2, h, the probability of no activation is
It should be noted that, for the deterministic impact model, i.e. the IC model with 100% impact reception, the calculation process is also described here:
similarly, when v is a leaf node, the total weight may be calculated by the sixth formula
When v is an internal node and has two edge-entering neighbors u1And u2When k is greater than or equal to 1, the total weight can be calculated according to a seventh formula
When v is an internal node and has an edge-entering neighbor u1When k is equal to or greater than 1, the total weight may be calculated according to an eighth formula of f (k, v) ═ w (v) + f (k, u)1)。
The above formula gives a dynamic programming algorithm with run time O (n 'k), where n' is the number of nodes in T.
It should be noted that the technical scheme of the application can be applied to various social networks, and in the aspect of national defense, the emergency messages can be quickly spread from the seed nodes to a large number of people at the lowest cost. In marketing, it is very useful to know how to maximize our advertising spending in the best way. In practical fields such as political elections, candidates seek to effectively spread his awareness or political view among the voters. Information about an emergency such as an earthquake emergency needs to be quickly spread to every resident of the community within a limited time. In social science, we can track the progress of ideas or innovations between different groups, such as civilization or business. In epidemiological investigations, we can map how the disease is spread from individual to individual.
Example two
Referring to fig. 3, fig. 3 is a schematic structural diagram of a social network influence maximization apparatus based on a directed tree according to a second embodiment of the present application.
As shown in fig. 3, the social network influence maximizing device based on the directed tree according to the present embodiment includes:
a building module 31, configured to build a directed tree according to the directed graph of each node;
a calculating module 32, configured to calculate, according to each preset initial active node combination and state information of each node in the directed tree, a total weight of an expected final active node when propagation of an influence generated by each preset initial active node combination is finished;
and a selecting module 33, configured to select each node in the preset initial active node combination corresponding to the largest total weight as an initial active node of the directed tree.
Further, the state information comprises the node type and the number of the edge-entering neighbors; the node types comprise leaf nodes, internal nodes which are seed nodes and internal nodes which are not seed nodes.
In addition, there are at most two degrees of entry for the internal nodes in the directed tree.
Specifically, the calculation module includes:
the first calculation unit is used for calculating the total weight according to a first formula when the node v in the directed tree is a leaf node and the node in the preset initial active node combination is greater than or equal to 1;
the first formula is
Wherein f (k, v, i) is the total weight, and k is a node in the preset initial active node combination;
a second computing unit, configured to, when a node v in the directed tree is an internal node of the seed node and a node in a preset initial active node combination is greater than or equal to 1 and v has two edge-entering neighbors u1And u2Then, the total weight is calculated according to a second formula;
the second formula is
A third calculating unit, configured to, when a node v in the directed tree is an internal node of the seed node and a node in the preset initial active node combination is greater than or equal to 1 and v has an edge-entering neighbor u1Then, the total weight is calculated according to a third formula;
the third formula is
A fourth computing unit, configured to, when a node v in the directed tree is an internal node of a non-seed node and a node in a preset initial active node combination is greater than or equal to 1 and v has two edge-entering neighbors u1And u2Then, the total weight is calculated according to a fourth formula;
the fourth formula is
A fifth calculating unit, configured to, when a node v in the directed tree is an internal node of a non-seed node and a node in a preset initial active node combination is greater than or equal to 1 and v has an edge-entering neighbor u1Then, the total weight is calculated according to a fifth formula;
the fifth formula is
f(k,v,i)＝1+f(k,u1,i+1)。
EXAMPLE III
Referring to fig. 4, fig. 4 is a schematic structural diagram of a social network influence maximization apparatus based on a directed tree according to a third embodiment of the present application.
As shown in fig. 4, the social network influence maximizing device based on the directed tree according to the present embodiment includes:
a processor 41, and a memory 42 connected to the processor;
the memory is configured to store a computer program, the computer program at least being configured to perform the social network influence maximization method based on the directed tree according to the first embodiment;
the processor is used to call and execute the computer program in the memory.
The device can be mobile communication intelligent devices such as a mobile phone and a tablet, and can also be devices such as a computer with a processor and a memory. An algorithm program developed based on the method of the first embodiment may be installed in the device, the maximum influence which can be achieved by the initial active nodes of different combinations is calculated through simulation for different social network platforms, and finally the active node combination which can achieve the maximum influence is found out. According to the calculation result of the algorithm program in the equipment, the possibility that the influence maximization can be achieved is improved, and the spread information can be applied to various industries, such as marketing, political election, emergency notification, national defense and military industry and the like.
With regard to the apparatus in the above-described embodiment, the specific manner in which each module performs the operation has been described in detail in the embodiment related to the method, and will not be elaborated here.
It is understood that the same or similar parts in the above embodiments may be mutually referred to, and the same or similar parts in other embodiments may be referred to for the content which is not described in detail in some embodiments.
It should be noted that, in the description of the present application, the terms "first", "second", etc. are used for descriptive purposes only and are not to be construed as indicating or implying relative importance. Further, in the description of the present application, the meaning of "a plurality" means at least two unless otherwise specified.
Any process or method descriptions in flow charts or otherwise described herein may be understood as representing modules, segments, or portions of code which include one or more executable instructions for implementing specific logical functions or steps of the process, and the scope of the preferred embodiments of the present application includes other implementations in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the present application.
It should be understood that portions of the present application may be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, the various steps or methods may be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, any one or combination of the following techniques, which are known in the art, may be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application specific integrated circuit having an appropriate combinational logic gate circuit, a Programmable Gate Array (PGA), a Field Programmable Gate Array (FPGA), or the like.
It will be understood by those skilled in the art that all or part of the steps carried by the method for implementing the above embodiments may be implemented by hardware related to instructions of a program, which may be stored in a computer readable storage medium, and when the program is executed, the program includes one or a combination of the steps of the method embodiments.
In addition, functional units in the embodiments of the present application may be integrated into one processing module, or each unit may exist alone physically, or two or more units are integrated into one module. The integrated module can be realized in a hardware mode, and can also be realized in a software functional module mode. The integrated module, if implemented in the form of a software functional module and sold or used as a stand-alone product, may also be stored in a computer readable storage medium.
The storage medium mentioned above may be a read-only memory, a magnetic or optical disk, etc.
In the description herein, reference to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the application. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
Although embodiments of the present application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present application, and that variations, modifications, substitutions and alterations may be made to the above embodiments by those of ordinary skill in the art within the scope of the present application.
Claims (4)
1. A social network influence maximization method based on a directed tree is characterized by comprising the following steps:
constructing a directed tree according to the directed graph of each node;
calculating the total weight of the expected final active nodes when the influence generated by each preset initial active node combination is propagated and ended according to each preset initial active node combination and the state information of each node in the directed tree;
selecting each node in a preset initial active node combination corresponding to the maximum total weight as an initial active node of the directed tree, wherein the larger the total weight is, the more active nodes are when the influence propagation is finished are, and the larger the propagation range is;
the state information comprises a node type and the number of edge-entering neighbors; the node types comprise leaf nodes, internal nodes which are seed nodes and internal nodes which are not seed nodes, and the internal nodes in the directed tree have at most two introductions;
the calculating the total weight of the expected final active nodes when the influence propagation generated by each preset initial active node combination is finished according to each preset initial active node combination and the state information of each node in the directed tree includes:
when the node v in the directed tree is a leaf node and a node in a preset initial active node combination is more than or equal to 1, calculating the total weight according to a first formula;
the first formula is
Wherein f (k, v, i) is the total weight, and k is a node in the preset initial active node combination;
when the node v in the directed tree is an internal node of the seed node and the node in the preset initial active node combination is more than or equal to 1 and v has two edge-entering neighbors u1And u2Then, the total weight is calculated according to a second formula;
the second formula is
When the node v in the directed tree is an internal node of the seed node and the node in the preset initial active node combination is more than or equal to 1 and v is provided with an edge-entering neighbor u1Then, the total weight is calculated according to a third formula;
the third formula is
When the node v in the directed tree is an internal node of a non-seed node and a node in a preset initial active node combination is more than or equal to 1 and v is provided with two edge-entering neighbors u1And u2Then, the total weight is calculated according to a fourth formula;
the fourth formula is
When the node v in the directed tree is an internal node of a non-seed node and a node in a preset initial active node combination is more than or equal to 1 and v is provided with an edge-entering neighbor u1Then, the total weight is calculated according to a fifth formula;
the fifth formula is
f(k,v,i)＝1+f(k,u1,i+1)。
2. The method of claim 1, wherein the directed tree is transformed from a directed graph of nodes according to binary tree properties.
3. A social network influence maximization device based on a directed tree is characterized by comprising:
the construction module is used for constructing a directed tree according to the directed graphs of the nodes;
the calculation module is used for calculating the total weight of the expected final active node when the influence generated by each preset initial active node combination is propagated and ended according to each preset initial active node combination and the state information of each node in the directed tree;
the selecting module is used for selecting each node in a preset initial active node combination corresponding to the maximum total weight as an initial active node of the directed tree, and the larger the total weight is, the more active nodes are when the influence propagation is finished are, and the larger the propagation range is;
the state information comprises a node type and the number of edge-entering neighbors; the node types comprise leaf nodes, internal nodes which are seed nodes and internal nodes which are not seed nodes, and the internal nodes in the directed tree have at most two introductions;
the calculation module is specifically configured to:
when the node v in the directed tree is a leaf node and a node in a preset initial active node combination is more than or equal to 1, calculating the total weight according to a first formula;
the first formula is
Wherein f (k, v, i) is the total weight, and k is a node in the preset initial active node combination;
when the node v in the directed tree is an internal node of the seed node and the node in the preset initial active node combination is more than or equal to 1 and v has two edge-entering neighbors u1And u2Then, the total weight is calculated according to a second formula;
the second formula is
When the node v in the directed tree is an internal node of the seed node and the node in the preset initial active node combination is more than or equal to 1 and v is provided with an edge-entering neighbor u1Then, the total weight is calculated according to a third formula;
the third formula is
When the node v in the directed tree is an internal node of a non-seed node and a node in a preset initial active node combination is more than or equal to 1 and v is provided with two edge-entering neighbors u1And u2Then, the total weight is calculated according to a fourth formula;
the fourth formula is
When the node v in the directed tree is an internal node of a non-seed node and a node in a preset initial active node combination is more than or equal to 1 and v is provided with an edge-entering neighbor u1Then, the total weight is calculated according to a fifth formula;
the fifth formula is
f(k,v,i)＝1+f(k,u1,i+1)。
4. A social network influence maximization device based on a directed tree, characterized by comprising:
a processor, and a memory coupled to the processor;
the memory for storing a computer program for performing at least the directed tree based social network impact maximization method of claim 1 or claim 2;
the processor is used for calling and executing the computer program in the memory.
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