Method for predicting the network size and reliability of hypergraph networks after deliberate attacks

Abstract

The present invention discloses a method for predicting the network scale and reliability of a hypergraph network after a deliberate attack, belonging to the technical field of hypergraph network attack evaluation. The method comprises a hypergraph network construction step, a hypergraph conversion step, a node over-degree calculation and assignment step, a self-consistent equation introduction step and a simulation verification step. The hypergraph network is converted into a factor graph, and a deliberate attack method is used to adjust the probability of node removal according to the size of the node over-degree to judge and calculate the scale of the network. The self-consistent equation is introduced in the calculation, and the number of nodes in the factor graph is finally calculated to be the final scale of the network. The method is an effective evaluation method for analyzing the network scale and reliability after a deliberate attack on a hypergraph in a real hypergraph network environment.

Description

Technical Field

[0001] The present invention relates to the technical field of hypergraph network attack evaluation, and more specifically to a method for predicting the network scale and reliability of a hypergraph network after a deliberate attack. Background Art

[0002] Network security usually refers to the security of computer networks, but in fact it can also refer to the security of computer communication networks.

[0003] A computer communication network is a system that interconnects several independently functioning computers through communication equipment and transmission media, enabling information transmission and exchange between them with the support of communication software. A computer network, on the other hand, is a system that uses communication methods to connect several geographically dispersed independent computer systems, terminal devices, and data devices for the purpose of resource sharing, exchanging data under protocol control. The fundamental purpose of a computer network is resource sharing, and communication networks are the means by which this sharing of network resources is achieved. Therefore, if a computer network is secure, then the corresponding computer communication network must also be secure and should enable information exchange and resource sharing for network users.

[0004] Cyberspace security has become particularly important in the new era, becoming a new battlefield for inter-state competition. Cyberattack methods have evolved from initially randomly selecting hosts or servers to targeting hosts or servers with specific attributes (typically high degree centrality). This deliberate attack method is clearly more destructive and harmful to networks. However, the aforementioned networks are simple networks with one-to-one connections between nodes, also known as pairwise interaction networks. However, with in-depth research, researchers have recently discovered that these pairwise interaction networks are insufficient to describe higher-order interactions. For example, in a scientific collaboration network, researchers abstract co-authors of the same article as multiple connected nodes, representing their collaboration one-to-one. Then, after the entire scientific collaboration network is constructed, we want to know which authors co-authored the article. This is impossible in a simple network. In other words, a simple network cannot express the high-order interactions between nodes. Therefore, the concept of hypergraph networks, as a representative of high-order interactions, has been proposed. Simply put, this approach successfully addresses this problem by topologically representing multiple authors in an article as a hyperedge containing multiple nodes.

[0005] At present, the attack methods based on hypergraph networks are limited to random attacks, that is, randomly removing a certain proportion of nodes on the hypergraph network to study the reliability of the network (usually expressed as the ratio of the node size in the largest connected subgraph to the node size in the initial network). A large number of experiments on simple networks have led to a conclusion: deliberate attacks are more destructive to the network than random attacks. Therefore, how to carry out deliberate attacks on hypergraph networks and analyze their system reliability after the attack and the network size composed of remaining functional nodes are currently urgent problems to be solved.

[0006] This issue currently faces the following challenges:

[0007] (1) The rapid growth of network devices in the Internet era and the complexity of counting the number of devices increase the difficulty of constructing hypergraph networks in real environments;

[0008] (2) When conducting a network attack, the question of which attributes of nodes to choose to destroy remains to be solved. Summary of the Invention

[0009] The purpose of the present invention is to address the above problems and provide an effective evaluation method for analyzing the network scale and reliability after a deliberate attack on a hypergraph in a real hypergraph network environment.

[0010] The method provided by the present invention for predicting the network scale and reliability of a hypergraph network after a deliberate attack comprises the following steps:

[0011] Step 1: Hypergraph network construction;

[0012] A sliding time window with a time interval of Δt is used to collect data from a known face-to-face contact dataset, and a hypergraph network is constructed by abstracting the nodes between the data. The largest connected subgraph is found in the hypergraph network composed of the data collected in each sliding time window, and all the largest connected subgraphs are deduplicated and aggregated to construct a hypergraph network model. Because the node numbers in each subgraph are different, aggregating different connected subgraphs into the hypergraph model is equivalent to different connected subgraphs slowly forming a large network, namely the hypergraph.

[0013] Specifically, the face-to-face contact dataset mainly consists of data collected during social activities, including data on face-to-face contact between different collected units in meetings, schools, and hospitals. The method for collecting this data is to assign a number to each collected unit and wear a sensor. The sensor collects data every Δt. The total number of collected units is the total number of nodes in the network. The data collected in the dataset is in the format of: time, number i, number j.

[0014] Furthermore, the maximum connected subgraph is to abstract the collected units that have face-to-face contact within the time Δt in each sliding time window into two nodes with an edge between them, thereby forming a network. Without considering repeated edges, the largest data cluster in the network is the giant branch in the network, that is, the maximum connected subgraph.

[0015] Preferably, the maximum connected subgraph is found by calculation using a depth-first traversal algorithm or a breadth-first traversal algorithm in common graph theory.

[0016] More preferably, the time interval Δt=20s.

[0017] Step 2, hypergraph conversion step;

[0018] In order to facilitate calculation and deduction, the hypergraph network constructed in the hypergraph network construction step needs to be converted into a set of non-overlapping variable nodes V (V1, V2, ..., V n ), a set of factor nodes U (e1, e2..., e n ), and a factor graph in the form of a bipartite graph G(V, U, E) consisting of an edge set E of pairwise interactions between the variable nodes V and the factor nodes U, wherein each pairwise interaction between the variable node V and the factor node U links a non-overlapping variable node to a factor node, and the factor graph is associated with the hypergraph by a simple mapping, that is, the nodes of the hypergraph network are mapped to the variable node set V of the factor graph, and each factor node U in the factor graph has a one-to-one correspondence with the hyperedge of the hypergraph network; the main difference between the hypergraph and the regular graph is the edge difference, the regular graph has an edge between the nodes, that is, there is a line between the two nodes, but the nodes contained in the hyperedge are greater than or equal to 2; that is, the variable node set V of the hypergraph and the factor graph = {V1, V2, ..., V n} are the same, the factor node set is represented by U, which is actually the abstract nodes e1, e2..., e n .

[0019] Step 3: Hypergraph target attack step;

[0020] In the factor graph transformed from the hypergraph, the degree of each variable node and factor node is traversed to obtain the degree distribution of the variable node and factor node, and the degree distribution generating function and the redundant degree distribution generating function of the variable node and factor node are obtained; based on the degree distribution generating function and the redundant degree distribution generating function, a target attack function cluster W is constructed, which includes both the influence of the degree of each node itself on the probability of the node being removed and the influence of different attack strategies on the probability of the node being removed. α (k i), through the general method of converting the targeted attack problem into a random attack problem and the mathematical tool of self-consistent equations, the network topology characteristics of the hypergraph network after responding to the targeted attack are obtained, and based on the network topology characteristics, the theoretical framework of the hypergraph network in the targeted attack based on the node excess size is obtained, so that the critical value of the hypergraph network collapse can be predicted.

[0021] Specifically, the degree of each variable node and factor node is traversed, specifically, the super-degree k of all nodes in the factor graph corresponding to the hypergraph network model is counted in turn, and the super-degree k is the number of nodes included in the hyperedge.

[0022] Preferably, the function cluster of target attack is constructed based on the degree of variable nodes. Among them, -∞<α<+∞, then:

[0023] When α is set to 0, the probability of each node being removed in the target attack is the same, which is equivalent to the random attack problem; when α is 1, the probability of each node being removed in the target attack is strictly related to the size of its overdegree. When α is +∞, the nodes in the hypergraph network model are removed strictly from large to small in the target attack according to their overdegree; when α is -∞, the nodes in the hypergraph network model are removed strictly from small to large in the target attack according to their overdegree.

[0024] More preferably, the general method of converting the target attack problem into a random attack problem described in step 3 above can be implemented by selecting various technical solutions in the existing technology used for network model testing and analysis, which can simulate network attacks using random selection methods.

[0025] More specifically, the self-consistent equation mathematical tool is to construct a random hypergraph network whose hyperdegree and hyperedge cardinality obey Poisson distribution, and define the probability of reaching a hyperedge from a variable node along the edge formed by the pairwise interaction between it and a factor node in the factor graph as The probability of reaching a variable node belonging to a hyperedge from a factor node along the edge formed by the pairwise interaction between it and a factor node is defined as s. According to the theoretical formula of the hypergraph network under random attack,

[0026] And the function value W of the node super calculation assignment step α (k i ), we can get the self-consistent equation of the equivalent network of the hypergraph network under deliberate attack:

[0027] as well as

[0028] Where p is the proportion of nodes retained in the network during random attacks, G eq0() is the equivalent network G eq The generating function of is the generating function of the redundancy distribution of the hyperedge cardinality, G eq1 () is the equivalent network G eq The generating function of the redundancy distribution is given by R, which is the order parameter of the probability that a node in the hypergraph network belongs to a hyperedge. The intentional attack problem on the hypergraph network based on node excess can be mapped into a random attack problem on the hypergraph network, thereby converting the intentional attack problem based on excess in the hypergraph network into a random attack problem on the network G. eq The random attack problem.

[0029] More preferably, the network topology characteristics of the hypergraph network after responding to the target attack include the hypergraph network under different parameter values, the network's percolation threshold, the change in degree distribution of the two types of nodes after the attack is implemented, etc.

[0030] Beneficial effects

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] The method of the present invention converts a hypergraph network into a factor graph, uses a deliberate attack method to change the probability of node removal to judge and calculate the scale of the network, introduces a self-consistent equation in the calculation, and finally calculates the number of nodes in the factor graph as the final scale of the network. Compared with the previous aimless random removal of nodes, the method can cause the hypergraph network to collapse more quickly, and the method can accurately predict the critical point of the hypergraph network collapse through rigorous mathematical deduction. By understanding the process of implementing the deliberate attack, some important nodes can be protected in a targeted manner during the network protection process.

[0033] In addition, this method has a certain compatibility effect. The attack strategy is selected according to the different values ​​of the index α. By adjusting the parameter = 0, the intentional attack problem can be reduced to a random attack problem: logically speaking, when α is set to 0, the probability of each node being deleted is 1 / N, that is, the probability of being removed is the same, which is equivalent to a random attack problem; when α is 1, the probability of each node being removed is strictly related to the size of its overdegree (the larger the overdegree, the larger the value of the probability in the formula, which is not difficult to see). When α is +∞, the nodes in the hypergraph network model are strictly removed from large to small according to the overdegree; when α is -∞, the nodes in the hypergraph network model are strictly removed from small to large according to the overdegree, and the final scale is equal to the value of R in the theoretical derivation, which can predict the network scale and reliability of the hypergraph network after a deliberate attack. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] The foregoing and following detailed description of the present invention will become more apparent when read in conjunction with the following drawings, in which:

[0035] Figure 1 It is a schematic diagram of a hypergraph network;

[0036] Figure 2 It is a schematic diagram of converting a hypergraph network into a factor graph;

[0037] Figure 3 It is a schematic diagram of the probability circuit in the step of introducing the self-consistent equation;

[0038] Figure 4 It is a schematic diagram of the steps for implementing a target attack;

[0039] Figure 5 This is a schematic diagram of the algorithm for constructing a randomly generated hypergraph network in the step of introducing the self-consistent equation;

[0040] Figure 6 This is a schematic diagram of the algorithm for calculating the maximum connected subgraph in a hypergraph network under certain conditions in the step of introducing the self-consistent equation;

[0041] Figure 7 This is a schematic diagram of the deliberate attack process based on the hypergraph network model;

[0042] Figure 8 It is a simulated three-dimensional graph of intentional attacks based on the hypergraph network model with different parameter values. DETAILED DESCRIPTION

[0043] The technical solutions for achieving the purpose of the present invention are further described below through specific examples. It should be noted that the technical solutions claimed in the present invention include but are not limited to the following examples.

[0044] As a specific embodiment of the present invention, Figure 6 This embodiment discloses a method for predicting the network scale and reliability of a hypergraph network after a deliberate attack, comprising the following steps:

[0045] Step 1: Hypergraph network construction. Data is collected from a known face-to-face contact dataset using a sliding time window with a time interval of Δt. A hypergraph network is constructed by abstracting the nodes between the data. The largest connected subgraph is found in the hypergraph network formed by the data collected in each sliding time window. All the largest connected subgraphs are deduplicated and aggregated to construct a hypergraph network model. Because the nodes in each subgraph are uniquely numbered, aggregating different connected subgraphs into the hypergraph model is equivalent to the connected subgraphs gradually forming a large network, namely the hypergraph.

[0046] Furthermore, the face-to-face contact dataset mainly consists of data collected during social activities, including data on face-to-face contact between different collected units in meetings, schools, and hospitals. The method for collecting this data is to have the collected units wear sensors and collect data every Δt. Before collection, a number is assigned to each collected unit. The total number of collected units is the total number of nodes in the network. The data format collected in the dataset is: time, number i, number j.

[0047] Specifically, the maximum connected subgraph is to abstract the collected units that have face-to-face contact within the time Δt in each sliding time window into two nodes with an edge between them, thereby forming a network. Duplicate edges are not considered. The largest data cluster is the giant branch in the network, that is, the maximum connected subgraph.

[0048] Preferably, the maximum connected subgraph is found by calculation using a depth-first traversal algorithm or a breadth-first traversal algorithm in common graph theory, and more preferably, the time interval Δt=20s.

[0049] Step 2, hypergraph transformation step. In order to facilitate calculation and derivation, as Figure 1 and 2 As shown, the hypergraph network constructed in the hypergraph network construction step needs to be converted into a set of non-overlapping variable nodes V (V1, V2, ..., V n ), a set of factor nodes U (e1, e2..., e n ), and a factor graph in the form of a bipartite graph G(V, U, E) consisting of a set of edge sets E of pairwise interactions between the variable nodes V and the factor nodes U, where each pairwise interaction between the variable node V and the factor node U links a non-overlapping variable node to a factor node, and the factor graph is associated with the hypergraph through a simple mapping, that is, the nodes of the hypergraph network are mapped to the variable node set V of the factor graph, and each factor node U in the factor graph has a one-to-one correspondence with the hyperedge of the hypergraph network; the main difference between the hypergraph and the regular graph is the edge. There is an edge between the nodes of the regular graph, that is, there is a line between the two nodes, but the nodes contained in the hyperedge are greater than or equal to 2, such as Figure 1 The hyperedge e1 contains two variable nodes V1 and V2; the hyperedge e5 contains five variable nodes V1, V6, V7 and V8. Figure 1 There are eight variable nodes V1 to V8, and the corresponding factors are Figure 2 There are also eight nodes, one-to-one correspondence. The hyperedge e1 on the left contains two variable nodes V1 and V2, so the corresponding right graph e1 is connected to these two variable nodes V1 and V2; that is, the variable node set V of the hypergraph and factor graph is V = {V1, V2, ..., V n} are the same, the factor node set is represented by U, which is actually the abstracted nodes e1, e2..., e n .like Figure 1 As shown in the figure, the hypergraph network consists of 8 vertices and 5 hyperedges, where the hyperdegree is represented by k and the cardinality of the hyperedge is represented by m, then m1=2, m2=3, m3=5, m4=2, m5=4, k1=2; k2=2; k3=2; k4=2; K5=2; K6=3; k7=2; k8=1, Figure 2 It is a factor graph transformed from a hypergraph network. The small circles represent nodes, and their sizes are positively correlated with the hyperdegree. The polygons represent factor nodes, where the small dots represent that the cardinality of the hyperedge is 2, and the number of edges of the polygon represents the number of nodes contained in the corresponding hyperedge.

[0050] Step 3: Hypergraph target attack step;

[0051] In the hypergraph network, we traverse the hyperdegree of each node k and the number of nodes contained in each hyperedge m, and then calculate the degree distribution P(k) and P(m) of the two. According to the definition of the generating function, we can get the generating function of the degree distribution of the two types of nodes: And the generating function of the redundancy distribution

[0052] Construct the target attack function cluster W based on the node's excess k α (k i ). The node super-degree calculation and assignment step is to count the degree k of all nodes in the factor graph corresponding to the hypergraph network model in turn. The degree k is the number of edges directly connecting the node and the factor node, and assign a function value W to each node i with a degree ki. α (k i ), considering W α (k i ) cannot be 0, so, Among them, -∞<α<+∞.

[0053] In order to obtain the size of the network after a deliberate attack, a self-consistent equation needs to be introduced; the probability of reaching a hyperedge from a variable node along the edge formed by the pairwise interaction between it and a factor node in the factor graph is defined as The probability of reaching a variable node belonging to a hyperedge from a factor node along the edge formed by the pairwise interaction between it and a factor node is defined as s, and s are shown in Figure 3 In (a) and (b), circles represent nodes, polygons represent factor nodes, triangles, squares, and pentagons represent factor nodes with cardinality of 3, 4, and 5, respectively. According to the theoretical formula of the hypergraph network under random attack, as well as

[0054] The function cluster W of the node over-computation assignment step is calculated based on the node over-computation α (k i ), after removing (1-p) nodes from the hypergraph network, the self-consistent equation of the hypergraph network under deliberate attack can be obtained as

[0055] as well as

[0056] Where p is the proportion of nodes retained in the network during random attacks, G eq0 () is the equivalent network G eq The generating function of is the generating function of the redundancy distribution of the hyperedge cardinality, G eq1 () is the equivalent network G eq The generating function of the redundant degree distribution is , and R is the order parameter of the probability that a node belongs to a hyperedge in the hypergraph network. Since the factor node is never deleted from the beginning to the end, in the self-consistent equation, the generating function of the cardinality of the hyperedge remains unchanged, but the equivalent generating function of the redundant degree distribution and the redundant degree distribution after the deliberate attack satisfies the formula G0() and Therefore, the intentional attack problem based on node overdegree on the hypergraph network can be mapped into the random attack problem on the hypergraph network, thereby converting the intentional attack problem based on overdegree in the hypergraph network into a random attack problem on the network G. eq Random attack problems, such as Figure 4 shown.

[0057] The above theoretical derivation steps are as follows:

[0058] First, a random hypergraph network is constructed in which both the degree and the edge cardinality obey the Poisson distribution. The specific construction algorithm is as follows: Figure 5 As shown in the figure, the average hyperdegree is defined as k, the average hyperedge cardinality is defined as m, and the theoretical formula of the hypergraph network under random attacks is as follows:

[0059]

[0060] Where p is the proportion of nodes retained in the network during random attacks, and the percolation problem is characterized by using the probability of finding a node belonging to a giant branch in the hypergraph network as the order parameter R.

[0061] In a random hypergraph, the order parameter R is expressed as:

[0062]

[0063] In addition, the generating function of the excess degree distribution of the initial network is defined as

[0064]

[0065] Where P(k) is the excess degree distribution of the network, and the generating function of the co-excess degree distribution is

[0066]

[0067] The average excess of the network is

[0068]

[0069] Similarly, the generating function of the hyperedge cardinality distribution of the initial network is defined as

[0070]

[0071] Where P(m) is the degree distribution of the network's hyperedge cardinality, and the generating function of the redundant degree distribution of the hyperedge cardinality is

[0072]

[0073] The average cardinality of the network's hyperedges is

[0074]

[0075] According to (3)-(8), equations (1) and (2) can be transformed into

[0076]

[0077] as well as

[0078]

[0079] Without loss of generality, the generating function of the node excess degree distribution in the random hypergraph network after the deliberate attack is obtained. Then, the size of the giant branch of the random hypergraph network after the deliberate attack is calculated by generating the corresponding factor graph and using the self-consistent equation. The main idea is to find the equivalent network G of the initial network excess degree distribution. eq The generating function of , thus transforming the problem of intentional attack based on hyper-degree in the hypergraph network into an attack on the network G eq Specifically, for each random attack problem with k degrees of excess i Node i is assigned a function value W α (k i ):

[0080]

[0081] According to formula (11), after removing (1-p) nodes in the hypergraph network, the degree distribution P of the remaining nodes is calculated p (k), but retain the edges leading to the remaining nodes of the removed node;

[0082] Let G p (k) is the number of nodes with degree k,

[0083]

[0084] When another node is deleted, Gp(k) becomes

[0085]

[0086] When N is →∞, Equation (13) can be expressed by the derivative of Gp(k) with respect to p,

[0087]

[0088] By taking the derivative of p in equation (12) and combining it with equation (14), we can get

[0089]

[0090] This is exact for N→∞. To solve Equation (15), we define a function And introduce a new variable Right now

[0091]

[0092] Then the solution of formula (15) is

[0093]

[0094] as well as

[0095]

[0096] This can be shown to satisfy Equation (15);

[0097] After removing a fraction (1-p) of nodes from the network according to (11), the generating function of the remaining nodes in the network is:

[0098]

[0099] Because the hypergraph network is randomly connected, the probability that an edge ends at a remaining node is equal to the ratio of the number of edges emanating from the remaining nodes to the number of edges emanating from all nodes of the initial network:

[0100]

[0101] in <k>is the average degree of the initial hypergraph network, and the average degree of the remaining nodes is

[0102]

[0103] Removing edges that end at deleted nodes in a randomly connected network is equivalent to randomly removing the remaining nodes. Part of the edge. At this time, randomly remove The generating function of the remaining nodes after some edges is equal to

[0104]

[0105] If we find a generator function G eq0 The network Geq is such that after removing the random attacks of (1-p) nodes, the generating function of the remaining nodes in Geq is the same as G c (x) are the same, then we get

[0106] G eq0 (x)≡G c (1-p+px), (23)

[0107] According to formula (23), we can get

[0108]

[0109] The generating function of the excess degree distribution is

[0110]

[0111] Since the factor nodes are never deleted from the beginning to the end, in the self-consistent equation, the generating function of the hyperedge cardinality remains unchanged, but the equivalent generating functions of the excess degree distribution and the excess degree distribution after the deliberate attack satisfy equations (24) and (25). Therefore, the deliberate attack problem on the hypergraph network based on node excess degree can be mapped to the random attack problem on the hypergraph network. According to equations (9) and (25), the self-consistent equation of the equivalent network of the hypergraph network under deliberate attack can be obtained as follows:

[0112]

[0113] as well as

[0114]

[0115] The specific implementation is as follows:

[0116] Assuming α = 0, the probability of each node being removed is 1 / N. When using C++ language for simulation in the vs2019 software tool, first generate a vector container of length N, and assign values ​​1, 2, ..., N to the container. When the network removal ratio is p, use the random function random to select a number in the container and delete it, reduce the container length by one, and remove the node with the corresponding number in the hypergraph network, repeating pN times.

[0117] When α=1, the probability of each node being removed is positively correlated with its over-degree size. When using C++ language to simulate in the vs2019 software tool, a vector container is first generated with a length of The values ​​in the container are 1, 1, ..., 1 (k1+1 1s in total), 2, 2, ..., 2 (k2+1 2s in total), ..., N, N, ..., N (k N +1 N); when the network removal ratio is p, the random function random is used in turn to select a number i in the container, delete all the numbers i in the container, and reduce the container length by (k i +1), and remove the nodes with the corresponding number in the hypergraph network, repeating pN times in total.

[0118] Assuming that α is positive or negative infinite, the effect is logical. In actual operation, a relatively large number is taken and the same method as above is used. The effect is that the order of node removal is strictly from the largest excess to the smallest excess, because the larger the excess, the greater the proportion it occupies in the container.

[0119] In this way, we can get the relationship between the degree of each node and the total number of nodes in the hypergraph network, and adopt different deliberate attack strategies by adjusting the value of the parameters.

[0120] like Figure 7 The flowchart of a deliberate attack based on the hypergraph network model is shown. Through the deliberate attack method, not only can the hypergraph network be damaged more effectively than a random attack, but the scale of the remaining nodes after the attack can also be calculated, which has a certain predictive effect.

[0121] More specifically, for example, in VS2019 software, a random hypergraph network with hyperdegree and hyperedge cardinality obeying Poisson distribution is constructed using C++ language. Figure 8 Here is a 3D diagram of how this method works on a random hypergraph network:

[0122] Among them, (a) to (d) are fixed ( <k>=3), and set <m>=2, 3, 4, 5 and 6, α takes -1, 0, 1 and 2 respectively; it can be seen that the robustness of the network increases with <m>The network becomes more robust with the increase of , and the giant branches of the network become larger. Moreover, as the value of α increases, the network threshold becomes higher and higher, and the robustness of the network becomes more and more fragile.

[0123] (e)~(h) are fixed ( <m>=3), and set <k>= 2, 3, 4, 5 and 6, α is -1, 0, 1 and 2 respectively. It can also be seen that the robustness of the network increases with <k>As the value of α increases, the network becomes more robust, the giant branch type of the network becomes larger, and, as the value of α increases, the network threshold becomes higher and higher, and the robustness of the network becomes more and more fragile.

[0124] In order to further verify the intentional attack situation of the present invention in a real network, four real-world datasets are used:

[0125] Contacts in the Workplace (Workplace): This dataset contains a temporal network of contacts between individuals measured in an office building in France between June 24 and July 3, 2013. Nodes are employees of the company. Wearable sensors were used to construct a network of close contacts between individuals. Contacts were clustered in 20-second time windows. Each hyperedge is the largest clique in each layer (i.e., each interval) of the temporal contact network.

[0126] Primary School Temporal Network Data (Primary School): This dataset contains the temporal network of contacts between children and teachers used in a study published in BMC Infectious Diseases 2014, 14:695. The nodes are primary school students. Wearable sensors are used to construct a close contact network between students. Contacts are clustered in 20-second time windows. Each hyperedge is the largest clique in each layer (i.e., each interval) of the temporal contact network.

[0127] High School Contact and Friendship Networks (HS): This dataset represents the connections and friendships among students at a high school in Marseille, France, in December 2013, measured using several techniques. Nodes are students at a single high school. Wearable sensors are used to construct a network of close contacts between students. Contacts are clustered in 20-second time windows. Each hyperedge is the largest clique in each layer (i.e., each interval) of the temporal contact network.

[0128] SFHH Conference Dataset (Conference): This dataset describes the face-to-face interactions of 405 attendees of the 2009 SFHH conference held in Nice, France (June 4–5, 2009). Nodes are participants in the conference. Wearable sensors are used to construct a network of close contacts between people. Contacts are aggregated within 20-second time windows. Each hyperedge is the largest clique in each layer (i.e., each interval) of the temporal contact network.

[0129] This method proposes an analytical framework for analyzing the robustness of random hypergraphs whose excess degree distribution and hyperedge cardinality follow arbitrary degree distributions under deliberate attacks, and discovers the giant branches and percolation thresholds of single-layer random hypergraph networks. In addition, when the excess degree and cardinality of hyperedges in a hypergraph network follow a Poisson distribution and the expected value of the excess degree and cardinality of hyperedges is constant, the average degree of the entire network can be obtained by multiplying the two expected values. Therefore, this method further analyzes the impact of the average degree in a hypergraph network on the robustness of the system and finds that the average degree has a certain impact on the robustness of the network: when <k>or <m>When α is fixed and is a certain value, the robustness of the system increases with the increase of the average degree; when the average degree remains unchanged, <k>The larger is the more robust the system is. <k>and <m> When the value of α is fixed, the robustness of the hypergraph network becomes more fragile. Experiments are conducted on hypergraph networks with Poisson distribution and power-law distribution of hyperdegree and hyperedge cardinality, as well as real networks, to verify the effectiveness of these equations under different topological structures.< / m> < / k> < / k> < / m> < / k> < / k> < / k> < / m> < / m> < / m> < / k> < / k>

Claims

1. A method for predicting the network size and reliability of a hypergraph network after a deliberate attack, characterized in that: The following steps are involved: Step 1: Hypergraph network construction Using a sliding event window with a time interval of Δt, we collect data from a known face-to-face contact dataset and construct a hypergraph network based on the nodes between the data. We then find the largest connected subgraph in the hypergraph network constructed by the data collected in each sliding time window, remove duplicates from all the largest connected subgraphs, and aggregate them to construct a hypergraph network model. The face-to-face contact dataset includes data on face-to-face contact between different collected units in conferences, schools, and hospitals. Specifically, the data collection method for the face-to-face contact dataset is to assign a number to each collected unit and to wear a sensor. The sensor collects data every Δt. The total number of collected units is the total number of nodes in the network. The data collected in the dataset is in the format of: time, number i, number j. Step 2: Hypergraph conversion step The hypergraph network constructed in the hypergraph network construction step is converted into a set of non-overlapping variable nodes V (V1, V2, ..., V n ), a set of factor nodes U(e1,e2,…,e n ), and a factor graph formed by a bipartite graph G(V,U,E) consisting of an edge set E of pairwise interactions between the variable nodes V and the factor nodes U, wherein each pairwise interaction between the variable node V and the factor node U links a non-overlapping variable node to a factor node, the nodes of the hypergraph network are mapped to the variable node set V of the factor graph, and each factor node U in the factor graph has a one-to-one correspondence with a hyperedge of the hypergraph network; Step 3: Hypergraph Target Attack Step In the factor graph transformed from the hypergraph, the degree of each variable node and factor node is traversed to obtain the degree distribution of the variable node and factor node, and the degree distribution generating function and the redundant degree distribution generating function of the variable node and factor node are obtained; based on the degree distribution generating function and the redundant degree distribution generating function, a target attack function cluster W is constructed, which includes both the influence of the degree of each node itself on the probability of the node being removed and the influence of different attack strategies on the probability of the node being removed. α (k i ), by transforming the targeted attack problem into a general method of a random attack problem and using the mathematical tool of self-consistent equations, the network topology characteristics of the hypergraph network after responding to the targeted attack are obtained, and based on the network topology characteristics, a theoretical framework for the hypergraph network to carry out targeted attacks based on the node excess size is obtained; The self-consistent equation data tool constructs a random hypergraph network in which both the hyperdegree and hyperedge cardinality obey the Poisson distribution. The probability of reaching a hyperedge from a variable node along the edge formed by the pairwise interaction between it and a factor node in the factor graph is defined as , and the probability of reaching a variable node belonging to the hyperedge from a factor node along the edge formed by the pairwise interaction between it and a factor node is defined as s. Then, according to the theoretical formula of the hypergraph network under random attack: , and the function value W of the node super-computation assignment step α (k i ), we can get the self-consistent equation of the equivalent network of the hypergraph network under deliberate attack: ,as well as, , in, p is the proportion of nodes that remain in the network during random attacks, G eq0 () is the equivalent network Geq The generating function of is the generating function of the redundancy distribution of the hyperedge cardinality, G eq1 () is the equivalent network G eq The generating function of the redundancy distribution is R is the order parameter of the probability that a node in the hypergraph network belongs to a hyperedge. The intentional attack problem on the hypergraph network based on node overdegree can be mapped into a random attack problem on the hypergraph network, thereby converting the intentional attack problem based on overdegree in the hypergraph network into a random attack problem on the network. G eq The random attack problem.

2. The method for predicting the network scale and reliability of a hypergraph network after a deliberate attack according to claim 1, characterized in that: The maximum connected subgraph is to abstract the collected units that have face-to-face contact within the time Δt in each sliding time window into two nodes with an edge between them, thereby forming a network. The largest data cluster in the network is the giant branch in the network, that is, the maximum connected subgraph.

3. The method for predicting the network scale and reliability of a hypergraph network after a deliberate attack according to claim 1 or 2, characterized in that: The maximum connected subgraph is found by calculation using a depth-first traversal algorithm or a breadth-first traversal algorithm.

4. The method for predicting the network scale and reliability of a hypergraph network after a deliberate attack according to claim 1 or 2, characterized in that: The time interval Δt=20 s.

5. The method for predicting the network scale and reliability of a hypergraph network after a deliberate attack according to claim 1, characterized in that: In step 3, the degree of each variable node and factor node is traversed, specifically, the hyperdegree of all nodes in the factor graph corresponding to the hypergraph network model is counted in turn. k , transcendence k is the number of nodes included in the hyperedges.

6. The method for predicting the network scale and reliability of a hypergraph network after a deliberate attack according to claim 1 or 5, characterized in that: The function cluster , where -∞< α <+∞, then when α If set to 0, the probability of each node being removed in the target attack is the same, which is equivalent to the random attack problem; when α When it is 1, the probability of each node being removed in the target attack is strictly related to its overload size. α When +∞ is selected, the nodes in the hypergraph network model are strictly removed from the largest to the smallest in the target attack; when α When -∞ is selected, the nodes in the hypergraph network model are removed strictly from small to large according to the degree of hyperdegree in the target attack.

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