A method and apparatus for propagation control
By constructing an initial propagation network and removing edges based on REDL importance values, the problems of high complexity and low applicability of infectious disease propagation control methods are solved, and efficient control of propagation in large-scale networks is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NORTHWESTERN POLYTECHNICAL UNIV
- Filing Date
- 2023-06-30
- Publication Date
- 2026-07-28
AI Technical Summary
Existing methods for controlling the spread of infectious diseases are highly complex and do not take into account the characteristics of transmission, resulting in the need to remove a large number of nodes or edges in large-scale networks to control the spread, thus having low applicability.
Construct an initial propagation network, determine the initial importance sequence and edge importance threshold, judge the importance of edges by REDL importance value, gradually remove edges and construct the first propagation network until the proportion of infected nodes is less than the set value in a stable state, and calculate the proportion of edges that need to be removed.
While simplifying computation, it effectively controls propagation, reduces the number of edges and nodes that need to be removed, and improves the applicability and efficiency of the method.
Smart Images
Figure CN116864144B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of complex network technology, and more specifically to a propagation control method and apparatus. Background Technology
[0002] Research in network science shows that more effective strategies can be developed by studying key individuals or interpersonal connections within a population. In a network, each person can be represented by a node, and connections between people are represented by edges. Therefore, relevant containment measures can be developed from a global perspective. However, these methods often have two drawbacks. First, most ignore the characteristics of epidemics and are designed purely based on network topology, which may render the method ineffective in complex propagation scenarios, requiring the removal of a large number of nodes or edges to control the spread. Second, most methods use greedy strategies to improve performance, but considering that real-world contact networks are typically very large, this makes them difficult to apply in practical scenarios.
[0003] How to incorporate the characteristics of propagation into the method of measuring the importance of edges or nodes, so as to achieve complete control over propagation while removing fewer edges or nodes; when the network scale is large, the amount of computation will increase accordingly, and it may even fail to calculate the result, so a method is needed to simplify the calculation process. However, simplifying the calculation process may reduce the effectiveness of the method, so how to ensure the effectiveness of the method while simplifying the calculation process is a difficult problem to solve.
[0004] In summary, existing methods for controlling the spread of infectious diseases suffer from problems such as excessive complexity and low applicability due to the excessive removal of nodes from the network because they do not consider the characteristics of transmission. Summary of the Invention
[0005] This invention provides a method and apparatus for controlling the spread of infectious diseases, which addresses the problems of existing methods for controlling the spread of infectious diseases, such as excessive complexity and low applicability due to the failure to consider the characteristics of transmission and the resulting excessive removal of nodes from the network.
[0006] This invention provides a propagation control method and apparatus, comprising:
[0007] Construct an initial propagation network, determine the initial importance sequence, initial edge importance threshold, and first importance sequence corresponding to the initial propagation network; remove each edge included in the initial propagation network to obtain the first propagation network;
[0008] Iterate through each edge in the first importance sequence and designate it as the first edge. When the REDL importance value of the first edge is less than the initial edge importance threshold, add the first edge to the head of the first propagation network and the initial importance sequence.
[0009] When the first importance sequence is empty, the initial value of the most important edge of the initial propagation network is determined according to the order of the edges included in the initial importance sequence, and the A most important edges included in the initial propagation network are removed, where A is equal to the initial value of the most important edge.
[0010] When the proportion of infected nodes in a stable state is less than a set value, the proportion of edges that need to be removed to completely control the propagation is determined based on the number of edges removed and the number of edges included in the initial propagation network.
[0011] Preferably, the REDL importance value of the first edge is determined by the following formula:
[0012]
[0013] in, Representing edge e ij The value of REDL importance, k′ i This indicates that e ij The degree of node i after joining the first propagation network, This indicates that e ij After joining the first propagation network, the number of nodes in the maximum connected component of the first propagation network, where Δ is a parameter; k′ j This indicates that e ij The degree of node j after joining the first propagation network.
[0014] Preferably, after traversing each edge included in the first importance sequence and designating it as the first edge, the process further includes:
[0015] When the REDL importance value of the first edge is greater than the initial edge importance threshold, the first edge is added to the end of the second importance sequence, and the second importance sequence is an empty sequence.
[0016] After completing the first round of traversal of the first importance sequence, the first importance sequence is made empty. The edges included in the second importance sequence are added to the end of the first importance sequence, and the first importance sequence is traversed a second time.
[0017] Preferably, before the first importance sequence is empty, the method further includes:
[0018] When the first importance sequence is not empty, the initial edge importance threshold is increased to obtain the first edge importance threshold;
[0019] Iterate through each edge in the first importance sequence, add a first edge to the first propagation network, and determine whether to add the first edge to the head of the first propagation network and the initial importance sequence or to the tail of the first importance sequence based on the relationship between the REDL importance value of the first edge and the importance threshold of the first edge.
[0020] Preferably, determining the first importance sequence corresponding to the initial propagation network includes:
[0021] The sum of the degrees of each edge in the initial propagation network is determined, and the edges are sorted in ascending order of the sum of degrees to obtain the first importance sequence corresponding to the initial propagation network.
[0022] The sum of the degrees of each edge in the initial propagation network is determined by the following formula:
[0023]
[0024] in, e represents the sum of degrees. ij Let k represent the edge connecting nodes i and j. i This represents the degree of node i.
[0025] Preferably, it further includes:
[0026] When the proportion of infected nodes in a stable state is greater than or equal to a set value, the initial value of the most important edge of the initial propagation network is increased to obtain the first value of the most important edge of the initial propagation network.
[0027] Based on the first value of the most important edge in the initial propagation network, remove B most important edges from the initial propagation network, where B is equal to the first value of the most important edge.
[0028] This invention provides a propagation control device, comprising:
[0029] A construction unit is used to construct an initial propagation network, determine the initial importance sequence, initial edge importance threshold, and first importance sequence corresponding to the initial propagation network; and remove each edge included in the initial propagation network to obtain a first propagation network.
[0030] The traversal unit is used to traverse each edge included in the first importance sequence and designate it as the first edge. When the REDL importance value of the first edge is less than the initial edge importance threshold, the first edge is added to the head of the first propagation network and the initial importance sequence.
[0031] The removal unit is used to determine the initial value of the most important edge of the initial propagation network according to the order of the edges included in the initial importance sequence when the first importance sequence is empty, and remove A most important edges included in the initial propagation network, where A is equal to the initial value of the most important edge.
[0032] The determining unit is used to determine the proportion of edges that need to be removed to fully control the propagation when the proportion of infected nodes in the determined steady state is less than a set value, based on the number of edges removed and the number of edges included in the initial propagation network.
[0033] Preferably, the REDL importance value of the first edge is determined by the following formula:
[0034]
[0035] in, Representing edge e ij The value of REDL importance, k′ i This indicates that e ij The degree of node i after joining the first propagation network, This indicates that e ij After joining the first propagation network, the number of nodes in the maximum connected component of the first propagation network, where Δ is a parameter; k′ j This indicates that e ij The degree of node j after joining the first propagation network.
[0036] This invention provides a computer device, which includes a memory and a processor. The memory stores a computer program, and when the computer program is executed by the processor, the processor performs the propagation control method described in any of the above-mentioned embodiments.
[0037] This invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform any of the propagation control methods described above.
[0038] This invention provides a propagation control method and apparatus. The method includes: constructing an initial propagation network; determining an initial importance sequence, an initial edge importance threshold, and a first importance sequence corresponding to the initial propagation network; removing each edge included in the initial propagation network to obtain a first propagation network; traversing each edge included in the first importance sequence and designating it as a first edge; when the REDL importance value of the first edge is less than the initial edge importance threshold, adding the first edge to the beginning of the first propagation network and the initial importance sequence; when the first importance sequence is empty, determining the initial value of the most important edge of the initial propagation network according to the order of the edges included in the initial importance sequence, and removing A most important edges included in the initial propagation network, where A is equal to the initial value of the most important edge; when the proportion of infected nodes in a stable state is determined to be less than a set value, determining the proportion of edges that need to be removed to completely control propagation based on the number of edges removed and the number of edges included in the initial propagation network. This method extracts target network information, understands the attributes of target network nodes and edges, constructs an initial propagation network, sorts the edges in the initial propagation network from smallest to largest based on the sum of their degrees, and removes all edges from the initial propagation network to obtain a first propagation network. It then iterates through each edge in the first importance sequence, determines the REDL importance value of each edge, and adds edges with REDL importance values less than the initial edge importance threshold to the head of the initial importance sequence, resulting in an initial importance sequence sorted from largest to smallest REDL importance value. Edges in the initial propagation network are then removed one by one according to the initial importance sequence, and the virus propagation range is calculated after each edge removal. This process continues until the virus propagation range is less than 0.01, at which point the proportion of edges that need to be removed to completely control the spread can be obtained. This method solves the problems of existing infectious disease propagation control methods, such as high complexity and low applicability due to excessive node removal from the network without considering propagation characteristics. Attached Figure Description
[0039] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0040] Figure 1 This is a schematic flowchart of a propagation control method provided in an embodiment of the present invention;
[0041] Figure 2 This is a schematic diagram of the disease transmission control method provided in Embodiment 1 of the present invention;
[0042] Figure 3Table 1 shows an experimental comparison diagram of the propagation control method provided in Embodiment 2 of the present invention and existing propagation control methods on 28 real networks.
[0043] Figure 4 Table 1 shows an experimental comparison diagram of the propagation control method provided in Embodiment 3 of the present invention and existing propagation control methods on 28 real networks.
[0044] Figure 5 This is a schematic diagram of a propagation control device provided in an embodiment of the present invention. Detailed Implementation
[0045] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0046] Figure 1 This is a schematic flowchart of a propagation control method provided in an embodiment of the present invention; as shown below. Figure 1 As shown, the propagation control method provided in this embodiment of the invention mainly includes the following steps:
[0047] Step 101: Construct an initial propagation network, determine the initial importance sequence, initial edge importance threshold, and first importance sequence corresponding to the initial propagation network; remove each edge included in the initial propagation network from the initial propagation network to obtain the first propagation network;
[0048] Step 102: Traverse each edge included in the first importance sequence and designate it as the first edge. When the REDL importance value of the first edge is less than the initial edge importance threshold, add the first edge to the head of the first propagation network and the initial importance sequence.
[0049] Step 103: When the first importance sequence is empty, determine the initial value of the most important edge of the initial propagation network according to the order of the edges included in the initial importance sequence, and remove A most important edges included in the initial propagation network, where A is equal to the initial value of the most important edge.
[0050] Step 104: When the proportion of infected nodes in the stable state is less than a set value, determine the proportion of edges that need to be removed to completely control the propagation based on the number of edges removed and the number of edges included in the initial propagation network.
[0051] The transmission control method provided in this invention primarily targets the transmission control of diseases. The following description uses disease transmission control as an example to detail the transmission control method provided in this invention.
[0052] In step 101, before constructing the initial propagation network, it is necessary to determine the relevant data of the people involved in the virus transmission, such as personal information, number of individuals, connections between individuals, and probability of virus transmission. Further, using individuals in the virus transmission population data as nodes and connections between individuals as edges, a virus transmission network corresponding to the virus transmission population data is constructed, which is the initial propagation network mentioned in step 101 of this embodiment of the invention. Further, based on the constructed initial propagation network, the initial importance sequence corresponding to the initial propagation network is determined, and an edge importance threshold is also set, which can also be called the initial edge importance threshold.
[0053] In the example, the virus propagation network can be represented as G(N,M), where N represents the set of nodes and M represents the set of edges. The initial importance sequence can be represented as: S e ={}, where the initial edge importance threshold is denoted as l.
[0054] Furthermore, once the initial propagation network, the initial importance sequence corresponding to the initial propagation network, and the initial edge importance threshold are determined, the degree of each edge can be determined based on the edges included in the initial propagation network. Specifically, the sum of the degrees of each edge included in the initial propagation network is determined using the following formula (1):
[0055]
[0056] in, e represents the sum of degrees. ij Let k represent the edge connecting nodes i and j. i This represents the degree of node i.
[0057] Once the sum of the degrees of each edge in the initial propagation network is determined, the edges can be sorted according to the magnitude of the sum of degrees (from smallest to largest) to obtain the first importance sequence corresponding to the initial propagation network.
[0058] Furthermore, each edge included in the initial propagation network is removed from the initial propagation network to obtain the first propagation network. It should be noted that the difference between the first propagation network and the initial propagation network is that the first propagation network does not include edges, while the initial propagation network does include edges.
[0059] In step 102, each edge in the first importance sequence is traversed, and the edge that is visited in each turn is referred to as the first edge. Specifically, the first edge in the first importance sequence is traversed, the REDL importance value of the first edge is determined, and based on the relationship between the determined importance value of the first edge and the initial edge importance threshold determined in step 101, it is determined whether to add the first edge to the head or the tail of the first propagation network and the initial importance sequence.
[0060] Specifically, in this embodiment of the invention, the value of the REDL importance of the first side is determined by the following formula (2):
[0061]
[0062] in, Representing edge e ij The value of REDL importance, k′ i This indicates that e ij The degree of node i after joining the first propagation network, This indicates that e ij After joining the first propagation network, the number of nodes in the maximum connected component of the first propagation network, where Δ is a parameter; k′ j This indicates that e ij The degree of node j after joining the first propagation network.
[0063] It should be noted that in this embodiment of the invention, Δ is set to 0.5, where a connected component refers to a connected subnet in the network, and nodes in different connected components are not connected to each other, and the largest connected component refers to the connected component with the most nodes.
[0064] Furthermore, in formula (2), k′ i ×k′ j The propagation threshold of SIS It is deduced that, <k>and <k 2 > represent the average degree of all nodes in the network and the average of the squares of the degrees of all nodes, respectively. If the propagation threshold is greater than the quotient of the infection probability and the recovery probability, the virus will continue to propagate (ρ>0 in a stationary state); otherwise, ρ=0 in a stationary state, where ρ is the proportion of infected nodes. Since the infection probability and the recovery probability are constants, the propagation control method provided in this embodiment aims to make the threshold greater than the quotient of the infection probability and the recovery probability while removing as few edges as possible. Based on this, k′ is derived. i ×k′ j The smaller the value, the less important the edge is.
[0065] Furthermore, in formula (2) The idea is to limit the spread of a virus by controlling the size of the largest connected component. Generally, an outbreak starts with a small number of people, so the maximum spread of the disease is limited to the closed area where it exists. For example, if the people in a village have no contact with the outside world, the disease will only spread within that village. Applying this to networks, the above phenomenon shows that the size of the connected component where the source node exists limits the scope of the disease outbreak. Therefore, if the size of the connected component where the seed node is located is small, the spread will also be small. Because in reality, sources of transmission are usually randomly generated, they are more likely to appear in the largest connected component. Therefore, the propagation control method provided in this embodiment of the invention can suppress propagation by inhibiting the size of the largest connected component. Based on this, we obtain... The smaller the value, the less important the edge is.
[0066] Furthermore, after determining the REDL importance value of the first edge, if the REDL importance value of the first edge is less than the initial edge importance threshold, then the first edge is added to the head of the first propagation network and the initial importance sequence; if the REDL importance value of the first edge is greater than the initial edge importance threshold, then the first edge is added to the tail of the second importance sequence, until every edge included in the first importance sequence has been traversed.
[0067] In this embodiment of the invention, the second importance sequence is an empty sequence, used to store edges that were not added to the first propagation network and the initial importance sequence in the current traversal. In practical applications, after traversing each edge included in the first importance sequence, if the second importance sequence is not empty, the first importance sequence needs to be made empty first, and then the edges included in the second importance sequence are added back to the first importance sequence, i.e., the second importance sequence is empty, and then the next traversal is entered until the first importance sequence is empty.
[0068] In this embodiment of the invention, the second importance sequence is used to store edges that were not added to the network and the initial edge importance sequence in the current traversal. Because the initial edge importance threshold increases in each traversal of the first importance sequence, if the REDL importance value in the current traversal is greater than the initial edge importance threshold, then in the next traversal of the first importance sequence, the REDL importance value may be less than the increased initial edge importance threshold. Finally, as the initial edge importance threshold increases, all edges are added to the first propagation network and the initial importance sequence until both the first and second importance sequences are empty.
[0069] In this embodiment of the invention, the initial value of the initial edge importance threshold can be set to 1.01. Modifying the initial edge importance threshold means increasing the initial edge importance threshold. In one example, the first edge importance threshold is obtained through the following formula:
[0070] I1 = I0 × 1.1 (3)
[0071] Where I0 represents the initial edge importance threshold and I1 represents the first edge importance threshold.
[0072] It should be noted that in step 102 above, the process of traversing the edges included in the first importance sequence is the process of adding the edges included in the first importance sequence to the first propagation network and the initial importance sequence. Therefore, after traversing the edges included in the first importance sequence, the number of edges included in the first propagation network and the initial importance sequence will change.
[0073] In step 103, when the first importance sequence is empty, the initial value of the most important edge of the initial propagation network can be determined according to the order of the edges included in the initial importance sequence. Then, the A most important edges included in the initial propagation network are removed from the initial propagation network, where A is equal to the initial value of the most important edge.
[0074] In practical applications, the initial value of the most important edge is usually 1.
[0075] Furthermore, fixed infection and recovery probabilities are set, and 10% of the nodes in the initial propagation network are randomly selected and initialized as infection sources. The spread of the disease is simulated in the SIS model to obtain the proportion of infected nodes in a stable state.
[0076] For example, if the recovery probability is set to 0.5, the infection probabilities are set to 0.02, 0.05, 0.1, 0.2, ..., 1.0 respectively. Specifically, the infection probability refers to the probability that an infected node will spread the virus to an uninfected node directly connected to it in a time step, and the recovery probability is the probability that an infected node will become an uninfected node in a time step; the initial proportion of infected nodes is 0.1.
[0077] In step 104, after determining the proportion of infected nodes in a stable state in the above steps, it can be determined whether to re-execute step 103 or end the loop based on the relationship between the proportion of infected nodes in a stable state and the set value, so as to obtain the proportion of edges that need to be removed to completely control the propagation.
[0078] Specifically, when the proportion of infected nodes in the stable state is greater than or equal to a set value, the initial value of the most important edge of the initial propagation network needs to be increased to obtain the first value of the most important edge of the initial propagation network. Then, based on the obtained first value of the most important edge of the initial propagation network, step 103 is re-executed until the proportion of infected nodes in the stable state is less than the set value.
[0079] It should be noted that the initial value of the most important edge of the initial propagation network is increased here using the following formula (4):
[0080] m r1 =m r0 +1 (4)
[0081] Where, m r0 Let m represent the initial value of the most important edge in the initial propagation network. r1 This represents the first value of the most important edge in the initial propagation network, or it can represent the number of edges that need to be removed if the proportion of infected nodes that have not reached a stable state is less than a set value.
[0082] After determining the first value of the most important edge in the initial propagation network, step 103 is executed, that is, according to the first value of the most important edge in the initial propagation network, B most important edges included in the initial propagation network are removed, where B is equal to the first value of the most important edge.
[0083] In this embodiment of the invention, if the initial value of the most important edge is 1, then according to formula (4), the first value of the most important edge is 2.
[0084] Furthermore, when the proportion of infected nodes in a stable state is less than a set value, the proportion of edges that need to be removed to completely control the propagation can be determined based on the number of edges removed and the number of edges included in the initial propagation network.
[0085] Specifically, the proportion of edges that need to be removed to fully control propagation is determined by the following formula (5):
[0086] ζ=m r1 / m (5)
[0087] Where, m r1 ζ represents the number of edges that need to be removed if the proportion of infected nodes that have reached a stable state is less than a set value. m represents the number of edges included in the initial propagation network, and ζ represents the proportion of edges that need to be removed to fully control propagation.
[0088] In this embodiment of the invention, ζ is used to measure the number of edges that need to be removed for control propagation. The smaller the value, the smaller the cost of control propagation, that is, the better the effect of the method.
[0089] It should be noted that the setting value mentioned in the above steps can generally be 0.01.
[0090] In summary, this invention provides a propagation control method and apparatus. The method extracts target network information, understands the attributes of target network nodes and edges, constructs an initial propagation network, sorts the edges in the initial propagation network from smallest to largest according to the sum of their degrees, and removes all edges from the initial propagation network to obtain a first propagation network. It iterates through each edge in the first importance sequence, determines the REDL importance value of each edge, and adds edges with REDL importance values less than the initial edge importance threshold to the head of the initial importance sequence, resulting in an initial importance sequence sorted from largest to smallest REDL importance value. Edges in the initial propagation network are removed one by one according to the initial importance sequence, and the virus propagation range is calculated after each edge removal until the virus propagation range is less than 0.01. This yields the proportion of edges that need to be removed to completely control propagation. This method solves the problems of existing infectious disease propagation control methods, such as high complexity and low applicability due to excessive node removal from the network without considering propagation characteristics.
[0091] To more clearly illustrate the propagation control method provided in the embodiments of the present invention, the following is combined with... Figure 2 The provided flowchart of the disease transmission control method is used to illustrate the transmission control method provided in the embodiments of the present invention. Specifically, as shown in the diagram... Figure 2 As shown:
[0092] Step 201: Input relevant data on the population involved in virus transmission, including individual information, number of individuals, relationships between individuals, and the probability of virus transmission. Using individuals in the virus transmission population data as nodes and relationships between individuals as edges, construct a virus transmission network G(N,M) corresponding to the virus transmission population data, where N represents the set of nodes and M represents the set of edges. Initialize the importance sequence of edges, i.e., the initial importance sequence S. e ={}, set an edge importance threshold, i.e., the initial edge importance threshold l;
[0093] Step 202: Sort all edges in the virus propagation network G in ascending order of the sum of the degrees of the two nodes they connect to obtain the first importance sequence S of the edges. k1 ;
[0094] Step 203: Remove all edges from the virus propagation network G to obtain the first propagation network G0;
[0095] Step 204, let the edge sequence S unocc =S k1 The second most important sequence is an empty sequence, i.e., S. k2 ={};
[0096] Step 205, traverse S from front to back unocc All edges included in the sequence, with zero being the first edge. If the REDL importance value of the first edge is less than the initial edge importance threshold l, then the first edge is added to the first propagation network G0 and the initial importance sequence S. e The first part, otherwise, add the first side to the second importance sequence S. k2 The tail;
[0097] It should be noted that when the REDL importance value of the first edge is greater than the initial edge importance threshold l, the second importance sequence S is directly added to the first edge. k2 The tail, until S is completely traversed. unocc All edges included in the sequence, i.e., after traversing the first importance sequence S. k1 In practical applications, after traversing the first importance sequence S... k1 After each included edge, if the second importance sequence S k2 If it is not empty, then the first importance sequence S needs to be made... k1 If it is empty, then the second importance sequence S is... k2 The included edges are re-added to the first importance sequence S. k1 In the middle, that is, when the second importance sequence S k2 If the sequence is not empty, proceed to the next round of traversal until the first importance sequence S is reached. k1 Empty.
[0098] Step 206, determine the first importance sequence S k1 Is it an empty sequence? If it is not an empty sequence, proceed to steps 207 and 204; if it is an empty sequence, proceed to step 208.
[0099] Step 207: Increase the initial edge importance threshold l to obtain the first edge importance threshold;
[0100] Step 208, determine the initial importance sequence S e The edges are included in descending order of importance, according to the initial importance sequence S. e The order of the edges determines the most important m in the initial propagation network G. r0 Edge,
[0101] Step 209, select the most important m in the initial propagation network G. r0 Edge removal, where m r0 The initial value is 1;
[0102] Step 210: Set fixed infection and recovery probabilities, initialize a subset of nodes as infection sources, then simulate the spread of the disease in the SIS model, and obtain the proportion ρ of infected nodes in the steady state.
[0103] Step 211: Determine the relationship between the proportion of infected nodes in the stable state and the set value. If ρ≥0.01, proceed to step 212; if ρ<0.01, proceed to step 213.
[0104] Step 212, execute m r1 =m r0 +1 means increasing the initial value of the most important edge of the initial propagation network to obtain the first value of the most important edge of the initial propagation network;
[0105] Step 213: Based on the initial value of the most important edge of the initial propagation network and the ratio of the number of edges included in the initial propagation network, i.e., according to ζ = m r0 / m determines the proportion of edges that need to be removed to fully control propagation.
[0106] Figure 3 This is a schematic diagram showing the experimental comparison between the propagation control method provided in Embodiment 2 of the present invention and existing propagation control methods on 28 real networks as shown in Table 1. The network information of the 28 real networks is shown in Table 1. Figure 3 In this context, REDL represents the propagation control method provided in this embodiment of the invention, and LF and SHKS are the proportions (ζ) of edges that need to be removed to achieve complete control of propagation by the methods provided by the prior art in comparison.
[0107] Figure 3 In the diagram, n represents the number of network nodes, β represents the infection probability, and the recovery probability is fixed at 0.5. Each point in the subgraph represents a specific case (i.e., a specific network, infection probability, and recovery probability). The x-coordinate of each point represents the proportion of edges that the REDL method provided in this embodiment of the invention needs to remove to completely control the virus in this case, while the y-coordinate represents the proportion of edges that the compared method needs to remove to completely control the virus in this case. The first and second subgraphs respectively represent the comparison results between REDL and LF and SHKS. The results show that almost all points are above the line y = x, indicating that in most cases, the propagation control method provided in this embodiment of the invention requires fewer edge removals, i.e., it is superior to the two compared methods.
[0108] Table 1
[0109]
[0110]
[0111] Figure 4 Table 1 shows an experimental comparison of the propagation control method provided in Embodiment 3 of the present invention with existing propagation control methods on 28 real networks. The network information of the 28 real networks is shown in Table 1. REDL represents the propagation control method provided in the embodiment of the present invention, and LF and SHKS are the proportions (ζ) of edges that need to be removed to achieve complete propagation control by the methods provided by the prior art being compared.
[0112] Figure 4 In this context, n represents the number of network nodes. <k>α and β are parameters used when generating the network, β represents the infection probability, and the recovery probability is fixed at 0.5. A point in each subgraph represents a specific case (i.e., a specific network, infection probability, and recovery probability). The x-coordinate of each point represents the proportion of edges that the REDL method needs to remove to completely control disease transmission in this case, and the y-coordinate represents the proportion of edges that the comparative method needs to remove to completely control the virus in this case. The first and second subgraphs represent the results of comparing REDL with LF and SHKS, respectively. The results show that almost all points are above the line y = x, indicating that in most cases, the transmission control method provided by this embodiment is superior to the two compared methods.
[0113] Based on the same inventive concept, this invention provides a propagation control device. Since the principle by which this device solves the technical problem is similar to that of a propagation control method, the implementation of this device can refer to the implementation of the method, and the repeated parts will not be described again.
[0114] Figure 5 This is a schematic diagram of a propagation control device provided in an embodiment of the present invention, as shown below. Figure 5 As shown, the device includes: a construction unit 302, a traversal unit 302, a removal unit 303, and a determination unit 304.
[0115] Construction unit 301 is used to construct an initial propagation network, determine the initial importance sequence, initial edge importance threshold, and first importance sequence corresponding to the initial propagation network; and remove each edge included in the initial propagation network from the initial propagation network to obtain a first propagation network.
[0116] Traversal unit 302 is used to traverse each edge included in the first importance sequence and designate it as the first edge. When the REDL importance value of the first edge is less than the initial edge importance threshold, the first edge is added to the head of the first propagation network and the initial importance sequence.
[0117] The removal unit 303 is used to determine the initial value of the most important edge of the initial propagation network according to the order of the edges included in the initial importance sequence when the first importance sequence is empty, and remove A most important edges included in the initial propagation network, where A is equal to the initial value of the most important edge.
[0118] The determining unit 304 is used to determine the proportion of edges that need to be removed to fully control the propagation when the proportion of infected nodes in the determined stable state is less than a set value, based on the number of edges removed and the number of edges included in the initial propagation network.
[0119] Preferably, the construction unit 301 is further configured to: determine the sum of the degrees of each edge included in the initial propagation network, and sort them in ascending order of the sum of degrees to obtain the first importance sequence corresponding to the initial propagation network;
[0120] The sum of the degrees of each edge in the initial propagation network is determined by the following formula:
[0121]
[0122] in, e represents the sum of degrees. ij Let k represent the edge connecting nodes i and j. i This represents the degree of node i.
[0123] Preferably, the traversal unit 302 is further configured to:
[0124] When the REDL importance value of the first edge is greater than the initial edge importance threshold, the first edge is added to the end of the second importance sequence, and the second importance sequence is an empty sequence.
[0125] After completing the first round of traversal of the first importance sequence, the first importance sequence is made empty. The edges included in the second importance sequence are added to the end of the first importance sequence, and the first importance sequence is traversed a second time.
[0126] Preferably, the REDL importance value of the first edge is determined by the following formula:
[0127]
[0128] in, Representing edge e ij The value of REDL importance, k′ i This indicates that e ij The degree of node i after joining the first propagation network, This indicates that e ij After joining the first propagation network, the number of nodes in the maximum connected component of the first propagation network, where Δ is a parameter; k′ j This indicates that e ij The degree of node j after joining the first propagation network.
[0129] Preferably, the removal unit 303 is further configured to:
[0130] When the first importance sequence is not empty, the initial edge importance threshold is increased to obtain the first edge importance threshold;
[0131] Iterate through each edge in the first importance sequence, add a first edge to the first propagation network, and determine whether to add the first edge to the head of the first propagation network and the initial importance sequence or to the tail of the first importance sequence based on the relationship between the REDL importance value of the first edge and the importance threshold of the first edge.
[0132] Preferably, the determining unit 304 is further configured to:
[0133] When the proportion of infected nodes in a stable state is greater than or equal to a set value, the initial value of the most important edge of the initial propagation network is increased to obtain the first value of the most important edge of the initial propagation network.
[0134] Based on the first value of the most important edge in the initial propagation network, remove B most important edges from the initial propagation network, where B is equal to the first value of the most important edge.
[0135] It should be understood that the units included in the above-described propagation control device are merely a logical division based on the functions implemented by the device. In practical applications, the units can be superimposed or split. Furthermore, the functions implemented by the propagation control device provided in this embodiment correspond one-to-one with the propagation control method provided in the above-described embodiment. The more detailed processing flow implemented by this device has been described in detail in the first embodiment of the method described above, and will not be described in detail here.
[0136] Another embodiment of the present invention provides a computer device, the computer device including: a processor and a memory; the memory is used to store computer program code, the computer program code including computer instructions; when the processor executes the computer instructions, the electronic device executes each step of a propagation control method in the method flow shown in the above method embodiment.
[0137] Another embodiment of the present invention provides a computer-readable storage medium storing computer instructions that, when executed on a computer device, cause the computer device to perform various steps of a propagation control method in the method flow shown in the above method embodiment.
[0138] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.
[0139] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Thus, if these modifications and variations fall within the scope of the claims of this invention and their equivalents...< / k> < / k>
Claims
1. A propagation control method, characterized in that, include: Construct an initial propagation network, and determine the initial importance sequence, initial edge importance threshold, and first importance sequence corresponding to the initial propagation network; Each edge included in the initial propagation network is removed from the initial propagation network to obtain the first propagation network; Iterate through each edge in the first importance sequence and designate it as the first edge. When the REDL importance value of the first edge is less than the initial edge importance threshold, add the first edge to the head of the first propagation network and the initial importance sequence. When the first importance sequence is empty, the initial value of the most important edge of the initial propagation network is determined according to the order of the edges included in the initial importance sequence, and the A most important edges included in the initial propagation network are removed, where A is equal to the initial value of the most important edge. When the proportion of infected nodes in a stable state is less than a set value, the proportion of edges that need to be removed to completely control the propagation is determined based on the number of edges removed and the number of edges included in the initial propagation network. Before constructing the initial propagation network, the following steps are also included: The relevant data of the population involved in virus transmission are determined, including personal information, number of individuals, connections between individuals, and probability of virus transmission; using individuals in the virus transmission population data as nodes and connections between individuals as edges, a virus transmission network corresponding to the virus transmission population data is constructed, and the virus transmission network is determined as the initial transmission network. The REDL importance value of the first side is determined by the following formula: Determining the first importance sequence corresponding to the initial propagation network includes: The sum of the degrees of each edge in the initial propagation network is determined, and the edges are sorted in ascending order of the sum of degrees to obtain the first importance sequence corresponding to the initial propagation network. The sum of the degrees of each edge in the initial propagation network is determined by the following formula: in, Representing an edge The importance value of REDL, Indicates will After joining the first propagation network, the node The degree, Indicates will After joining the first propagation network, the maximum number of connected nodes in the first propagation network. For parameters; Indicates will After joining the first propagation network, the node The degree, Represents the sum of degrees. Indicates the connection node and The edge, Represents a node The degree.
2. The method as described in claim 1, characterized in that, After traversing each edge of the first importance sequence and designating it as the first edge, the process further includes: When the REDL importance value of the first edge is greater than the initial edge importance threshold, the first edge is added to the end of the second importance sequence, and the second importance sequence is an empty sequence. After completing the first round of traversal of the first importance sequence, the first importance sequence is made empty. The edges included in the second importance sequence are added to the end of the first importance sequence, and the first importance sequence is traversed a second time.
3. The method as described in claim 1, characterized in that, Before the first importance sequence is empty, the following is also included: When the first importance sequence is not empty, the initial edge importance threshold is increased to obtain the first edge importance threshold; Iterate through each edge in the first importance sequence, add a first edge to the first propagation network, and determine whether to add the first edge to the head of the first propagation network and the initial importance sequence or to the tail of the first importance sequence based on the relationship between the REDL importance value of the first edge and the importance threshold of the first edge.
4. The method as described in claim 1, characterized in that, Also includes: When the proportion of infected nodes in a stable state is greater than or equal to a set value, the initial value of the most important edge of the initial propagation network is increased to obtain the first value of the most important edge of the initial propagation network. Based on the first value of the most important edge in the initial propagation network, remove B most important edges from the initial propagation network, where B is equal to the first value of the most important edge.
5. A propagation control device, characterized in that, include: A construction unit is used to construct an initial propagation network and determine the initial importance sequence, initial edge importance threshold, and first importance sequence corresponding to the initial propagation network. Each edge included in the initial propagation network is removed from the initial propagation network to obtain the first propagation network; The traversal unit is used to traverse each edge included in the first importance sequence and designate it as the first edge. When the REDL importance value of the first edge is less than the initial edge importance threshold, the first edge is added to the head of the first propagation network and the initial importance sequence. The removal unit is used to determine the initial value of the most important edge of the initial propagation network according to the order of the edges included in the initial importance sequence when the first importance sequence is empty, and remove A most important edges included in the initial propagation network, where A is equal to the initial value of the most important edge. The determining unit is used to determine the proportion of edges that need to be removed to completely control the propagation when the proportion of infected nodes in the determined steady state is less than a set value, based on the number of edges removed and the number of edges included in the initial propagation network. The construction unit is also used to: determine relevant data of the population involved in virus transmission, including personal information, number of individuals, connections between individuals and the probability of virus transmission; construct a virus transmission network corresponding to the virus transmission population data using individuals in the virus transmission population data as nodes and connections between individuals as edges, and determine the virus transmission network as the initial transmission network. The REDL importance value of the first side is determined by the following formula: The construction unit is further configured to: determine the sum of the degrees of each edge included in the initial propagation network, and sort them in ascending order of the sum of degrees to obtain the first importance sequence corresponding to the initial propagation network; The sum of the degrees of each edge in the initial propagation network is determined by the following formula: in, Representing an edge The importance value of REDL, Indicates will After joining the first propagation network, the node The degree, Indicates will After joining the first propagation network, the maximum number of connected nodes in the first propagation network. For parameters; Indicates will After joining the first propagation network, the node The degree, Represents the sum of degrees. Indicates the connection node and The edge, Represents a node The degree.
6. A computer device, characterized in that, The computer device includes a memory and a processor, the memory storing a computer program that, when executed by the processor, causes the processor to perform the propagation control method as described in any one of claims 1-4.
7. A computer-readable storage medium, characterized in that, The system contains a computer program that, when executed by a processor, causes the processor to perform the propagation control method as described in any one of claims 1-4.