A dynamic differential privacy synthetic social network graph acquisition method and device

Abstract

The present invention provides a dynamic differential privacy synthetic social network graph acquisition method and device. The method includes: inputting a real social network graph; obtaining a node degree sequence and a node similarity matrix after noise processing and constraint reasoning; constructing an adjacency list; traversing the node degree sequence from the tail to the head to obtain the edge set of the differential privacy synthetic social network graph, and when traversing to node i: determining the candidate connection node list of node i; obtaining the common neighbor information of node i and the nodes in the candidate connection node list; calculating the edge generation probability of node i and the nodes in the candidate connection node list according to the common neighbor information, the node degree sequence and the node similarity matrix; generating candidate edges according to the edge generation probability; merging the candidate edges that meet the preset conditions into the edge set of the differential privacy synthetic social graph, updating the adjacency list; generating the differential privacy synthetic social graph through the edge set and the node set. The present invention improves the privacy protection level and the utility of the differential privacy synthetic social network graph.

Description

Technical Field

[0001] The present invention relates to the technical field of social privacy security protection, and in particular to a method and device for obtaining a dynamic differential privacy synthetic social network graph. Background Art

[0002] A social network graph is a graphical representation used to show the social relationships between people. It consists of nodes (vertices) and edges connecting nodes. Each person is a node, and an edge indicates that there is a direct relationship between the two nodes (two people) it connects (such as family relationships, work relationships, social relationships, or communication relationships, or friend relationships on chat platforms such as WeChat). If there is an edge between two nodes, it means that the corresponding two people have a direct relationship. A synthetic social network graph refers to a virtual social network graph generated by computer programs and algorithms that has similar network characteristics to a real social network graph. It is used to study social network structure and behavior patterns to protect the privacy of sensitive information in a real social network graph.

[0003] To improve the level of privacy protection, differential privacy is used to generate synthetic social network graphs. Differential privacy is a technology that analyzes and shares data while protecting personal privacy. In differential privacy, by adding a certain amount of noise, attackers cannot infer what the sensitive information of an individual is. However, the added noise may cause deviation and inaccuracy in the data analysis results, that is, the differential privacy synthetic social network graph has poor usability.

[0004] In order to solve the problem of poor usability of differential privacy synthetic social network graphs, the applicant's prior application for a Chinese patent with publication number CN115878906 A provides a social graph generation method and system for protecting personal similarity, which uses the definition of differential privacy and protects similarity based on noise processing and post-processing methods, making node similarity available but invisible, avoiding attribute inference between related nodes through similarity, improving the protection strength of social graphs, and minimizing damage to data utility. However, the patent only considers the node attribute similarity of the real social network graph, and does not consider the differences between the differential privacy synthetic social network graph and the real social network graph in node degree distribution and clustering coefficient indicators, which limits the usability of differential privacy synthetic social network graphs. Summary of the invention

[0005] The present invention aims to solve the technical problem that the existing differential privacy synthetic social network graph generation technology does not take into account the differences in node degree distribution and clustering coefficient indicators between the differential privacy synthetic social network graph and the real social network graph, which limits the availability of the differential privacy synthetic social network graph, and provides a dynamic differential privacy synthetic social network graph acquisition method and device.

[0006] In order to achieve the above-mentioned purpose of the present invention, according to the first aspect of the present invention, the present invention provides a dynamic differential privacy synthetic social network graph acquisition method, comprising: inputting a real social network graph; obtaining a node degree sequence and a node similarity matrix after noise processing and constraint reasoning based on the real social network graph, wherein the node degree sequence is arranged in non-descending order; constructing an adjacency list, wherein the adjacency list is used to record the real-time neighbor node information of each node in the differential privacy synthetic social network graph; initializing the adjacency list and the edge set of the differential privacy synthetic social network graph, and using the node set of the real social network graph as the node set of the differential privacy synthetic social network graph; traversing the node degree sequence from tail to head to obtain the edge set of the differential privacy synthetic social network graph, and traversing to the node When point i is reached, the following is executed: determine the candidate connection node list of node i based on the node similarity matrix, 1<i≤n, n represents the total number of nodes in the node degree sequence; obtain the common neighbor information of node i and the nodes in the candidate connection node list in the current differential privacy synthetic social network graph according to the current adjacency table; calculate the edge generation probability between node i and the nodes in the candidate connection node list according to the common neighbor information, the node degree sequence and the node similarity matrix; generate candidate edges between node i and the nodes in the candidate connection node list according to the corresponding edge generation probability; after merging the candidate edges that meet the preset conditions into the edge set of the differential privacy synthetic social graph, update the adjacency table; generate the differential privacy synthetic social graph through the edge set and node set of the differential privacy synthetic social graph obtained after the traversal is completed.

[0007] In order to achieve the above-mentioned purpose of the present invention, according to the second aspect of the present invention, the present invention provides a dynamic differential privacy synthetic social network graph acquisition device, which is used to implement a dynamic differential privacy synthetic social network graph acquisition method described in the first aspect of the present invention, including: an input module, which inputs a real social network graph; a noisy constraint reasoning module, which obtains a node degree sequence and a node similarity matrix after noise processing and constraint reasoning based on the real social network graph, wherein the node degree sequence is arranged in non-descending order; a construction module, which constructs an adjacency list, and the adjacency list is used to record the real-time neighbor node information of each node in the differential privacy synthetic social network graph; an initialization module, which initializes the adjacency list and the edge set of the differential privacy synthetic social network graph, and uses the node set of the real social network graph as the node set of the differential privacy synthetic social network graph; an edge set generation module, which generates nodes from the tail to the top. The head sequentially traverses the node degree sequence to obtain the edge set of the differential privacy synthetic social network graph, and when traversing to node i, executes: determining the candidate connection node list of node i based on the node similarity matrix, 1<i≤n, n represents the total number of nodes in the node degree sequence; obtaining the common neighbor information of node i and the nodes in the candidate connection node list in the current differential privacy synthetic social network graph according to the current adjacency table; calculating the edge generation probability of node i and the nodes in the candidate connection node list according to the common neighbor information, the node degree sequence and the node similarity matrix; generating candidate edges between node i and the nodes in the candidate connection node list according to the corresponding edge generation probability; merging the candidate edges that meet the preset conditions into the edge set of the differential privacy synthetic social graph, and updating the adjacency table; a synthesis module generates a differential privacy synthetic social graph through the edge set and node set of the differential privacy synthetic social graph obtained after the traversal is completed.

[0008] In the process of generating a differentially private synthetic social network graph, the present invention performs noise processing on the original node degree sequence and the original similarity matrix of the real social network graph, thereby improving the privacy protection level; in order to improve the utility, i.e., usability, of the generated differentially private synthetic social network graph, constraint reasoning is performed on the original node degree sequence and the original similarity matrix after the noise processing, respectively, so that they respectively satisfy the preset distribution rules of the original node degree sequence and the original similarity matrix, thereby ensuring that the node similarity of the originally large node is still large after the noise is added, and the node similarity of the originally large probability of generating an edge is still large after the noise is added, so that the node degree distribution of the differentially private synthetic social network graph is consistent with the real social network graph The difference is reduced and the accuracy is higher; in the process of obtaining the edge set of the differential privacy synthetic social network graph, the edge generation probability between nodes is calculated through the common neighbor information, node degree sequence and node similarity matrix between nodes in the current differential privacy synthetic social network graph. The more common neighbors between nodes, the greater the probability of edge generation between nodes, which increases the number of triangles in the differential privacy synthetic social network graph, thereby improving the clustering coefficient of the differential privacy synthetic social network graph, reducing the difference in clustering coefficient indicators with the real social network graph, and further improving the utility of the differential privacy synthetic social network graph; in addition, during the traversal process, the adjacency table is updated in real time, and the common neighbor information between nodes is obtained according to the adjacency table, which improves the processing speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Figure 1 It is a flowchart of a method for obtaining a dynamic differential privacy synthetic social network graph in a preferred embodiment of the present invention;

[0010] Figure 2 This is an overall flow chart of the server generating a differentially private synthetic social network graph in an example of the present invention. DETAILED DESCRIPTION

[0011] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be understood as limiting the present invention.

[0012] In the description of the present invention, it is necessary to understand that the terms "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention.

[0013] In the description of the present invention, unless otherwise specified and limited, it should be noted that the terms "installed", "connected" and "connected" should be understood in a broad sense. For example, it can be a mechanical connection or an electrical connection, or it can be the internal connection between two components. It can be a direct connection or an indirect connection through an intermediate medium. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to the specific circumstances.

[0014] The execution subject of the dynamic differential privacy synthetic social network graph acquisition method includes but is not limited to at least one of the electronic devices such as the server and the terminal that can be configured to execute the method provided in the embodiment of the present application. In other words, the dynamic differential privacy synthetic social network graph acquisition method can be executed by software or hardware installed on the terminal device or the server device, and the software can be a blockchain platform. The server includes but is not limited to: a single server, a server cluster, a cloud server or a cloud server cluster, etc. The server can be an independent server, or it can be a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communications, middleware services, domain name services, security services, content delivery networks (Content Delivery Network, CDN), and big data and artificial intelligence platforms.

[0015] The present invention discloses a dynamic differential privacy synthetic social network graph acquisition method. In a preferred implementation, Figure 1 As shown, including:

[0016] Step S1, input a real social network graph. The real social network graph is an undirected graph, which can be represented by G(V,E), where V represents a set of nodes in the real social network graph, each node represents a person, and E represents an edge set in the real social network graph. There is an edge connecting nodes with direct relationships. The direct relationship preferably includes, but is not limited to, relatives, communication relationships in mobile terminal communication records, and friend relationships on chat platforms such as WeChat or QQ. Preferably, the node degree privacy budget ∈1 and the similarity privacy budget ∈2 are also input for subsequent noise processing. The real social network graph, ∈1 and ∈2 can be input through a server (such as a social network software platform server) that stores social network graph data or pre-stored in the execution body of the method.

[0017] Step S2, obtaining a node degree sequence and a node similarity matrix after noise addition and constraint reasoning based on a real social network graph, wherein the node degree sequence is arranged in non-descending order.

[0018] The node degree represents the number of edges connected to the node. If the number of edges connected to node i is x, then the node degree of node i is x. The node degrees of all nodes are extracted from the real social network graph to form a sequence, namely the original node degree sequence. The original node degree sequence is subjected to the first noisy constraint reasoning to obtain the node degree sequence. The first noisy constraint reasoning includes two parts: noise addition and constraint reasoning. The privacy of the node degree value is protected by noise addition. The node degree sequence is made to retain as much real original node degree sequence information and characteristics as possible through constraint reasoning, such as value distribution, so as to increase the availability and accuracy of the differential privacy synthetic social network graph. In the first noisy constraint reasoning, the constraint reasoning preferably adopts, but is not limited to, the non-descending distribution constraint reasoning, proportional constraint reasoning or average value constraint reasoning disclosed in the Chinese patent with publication number CN118095417A, which will not be repeated here.

[0019] Calculate the similarity between nodes in the real social network graph to obtain the original similarity matrix. The similarity between nodes can be the weighted sum of the number of common neighbor nodes, the number of common edges, the number of common neighbor nodes and the number of common edges of the two nodes. Generate a differential privacy synthetic social network graph in combination with the original similarity matrix, which can further improve the availability of the differential privacy synthetic social network graph. Perform a second noise-added constraint reasoning on the original similarity matrix to obtain a node similarity matrix. In order to improve the level of privacy protection, noise is added to each similarity in the second noise-added constraint reasoning, and constraint reasoning is performed on the noise similarity after adding noise, so that the obtained node similarity matrix retains as much real information and characteristics of the original similarity matrix as possible, such as numerical range or numerical distribution. The constraint reasoning in the second noise-added constraint reasoning is preferably, but not limited to, the non-descending distribution constraint reasoning, proportional constraint reasoning or average constraint reasoning disclosed in the Chinese patent with publication number CN118095417A, which will not be repeated here.

[0020] Step S3, construct an adjacency table, which is used to record the real-time neighbor node information of each node in the differential privacy synthetic social network graph. The adjacency table adj is dynamically updated during the generation process of the differential privacy synthetic social network graph, which includes the real-time neighbor node information of all nodes. The neighbor node information adj[n] of node i includes the neighbor node ID of node i, the number of neighbor nodes, and the degree of each neighbor node.

[0021] Step S4, initialize the adjacency list and the edge set of the differential privacy synthetic social network graph, and use the node set of the real social network graph as the node set of the differential privacy synthetic social network graph. The adjacency list is initialized to an empty set. The node set V1 of the differential privacy synthetic social network graph G1 is V1 = V, and the edge set E1 of the differential privacy synthetic social network graph G1 is initialized to an empty set.

[0022] Step S5, traverse the node degree sequence from the end to the beginning to obtain the edge set of the differential privacy synthetic social network graph, and execute when traversing to node i:

[0023] Step S51, determining a candidate connection node list of node i based on the node similarity matrix, 1<i≤n, n represents the total number of nodes in the node degree sequence.

[0024] Preferably, step S51 includes: taking node i as the starting node, selecting nodes with non-zero similarity to node i from the i-1, i-2, ..., 1 nodes in the node degree sequence (i.e., the nodes before node i) and adding them to the candidate connection node list of node i, which is recorded as can(i). In this way, while ensuring that the expected degree of the nodes in the differentially private synthetic social network graph is equal to the degree of the nodes in the real graph, node i only attempts to generate edges with nodes with non-zero similarity, and divides the probability of nodes with zero similarity in the original CL model to nodes with non-zero similarity, thereby increasing the probability of the differentially private synthetic social network graph retaining edges in the real graph, so that the differentially private synthetic social network graph retains more information and characteristics of the real graph, and improving the availability and accuracy of the differentially private synthetic social network graph.

[0025] Step S52, obtaining the common neighbor information of node i and the nodes in the candidate connection node list in the current differential privacy synthetic social network graph according to the current adjacency table. The common neighbor information is preferably, but not limited to, the number of common neighbor nodes of the two nodes in the current differential privacy synthetic social network graph or the expected node degree information of the common neighbor nodes. The expected node degree of a node in the differential privacy synthetic social network graph is the node degree of the node in the node degree sequence.

[0026] Preferably, to improve the calculation speed, in step S51, when a node is added to the candidate connection node list of node i, the common neighbor information is calculated according to the current adjacency table at the same time, and only one intersection operation is required for the common neighbor information of two nodes in the current adjacency table.

[0027] Step S53, calculate the edge generation probability between node i and the nodes in the candidate connection node list based on the common neighbor information, node degree sequence and node similarity matrix. Suppose the node in the candidate connection node list is j, then p(i,j) represents the edge generation probability between node i and node j.

[0028] Step S54: Node i and the nodes in the candidate connection node list generate candidate edges according to the corresponding edge generation probabilities.

[0029] Step S55: After merging the candidate edges that meet the preset conditions into the edge set of the differentially private synthetic social graph, the adjacency list is updated.

[0030] Preferably, the preset condition is that the candidate edge is not in the edge set E1 of the differentially private synthetic social graph, that is, if the candidate edge is not in the edge set E1 of the differentially private synthetic social graph, the candidate edge is added to E1, and if the candidate edge is already in the edge set E1, the candidate edge is discarded.

[0031] Step S1, generating a differentially private synthetic social graph by traversing the edge set and node set of the differentially private synthetic social graph obtained after completion.

[0032] In a preferred embodiment, in step S2, obtaining a node degree sequence and a node similarity matrix after noise processing and constraint reasoning based on a real social network graph includes:

[0033] Step S21, obtaining an original node degree sequence based on a real social network graph, and performing a first noisy constraint reasoning on the original node degree sequence to obtain a node degree sequence.

[0034] The first noisy constraint reasoning includes:

[0035] Step S211, arranging the node degrees in the original node degree sequence in non-descending order to obtain a first node degree sequence.

[0036] Extract the nodes and corresponding node degrees of the real social network graph G(V,E) to obtain the original node degree sequence, sort the node degrees in the original node degree sequence in non-descending order to obtain the sorted first node degree sequence D. Calculate the number of edges in the real social network graph G(V,E), denoted as M. Let p be both the first node degree sequence D and the noise node degree sequence The position index of the element in the graph, assuming that the number of nodes in the real social network graph is P, then 1≤p≤P, satisfying D[p]≤D[p+1].

[0037] Step S212: adding noise to each node degree in the first node degree sequence to obtain a noise node degree sequence

[0038] For the degree d of node j in the first node degree sequence D j Add independent Laplace noise, preferably, the Laplace noise is generated by Laplace distribution:

[0039]

[0040] Among them, x1 is the added noise value, b1 is the first scale parameter, and it is set as follows: b1 = 2 / ∈1, 2 is the sensitivity. Under edge differential privacy, the sensitivity of node degree is always 2. The sensitivity of degree is 2, which has a smaller sensitivity, so that a smaller privacy budget can be used when adding Laplace noise, which has a stronger protection effect on node degree privacy.

[0041] Therefore, the noise adding process is expressed as: Noisy node degree sequence after adding Laplace noise Non-descending order may no longer be satisfied.

[0042] Step S213: Perform a first non-descending order constraint on the noise node degree sequence to obtain a node degree sequence The first non-descending order constraint is to adjust the values ​​of the node degrees in the node degree sequence so that the nodes in the node degree sequence are arranged in non-descending order, that is, satisfying:

[0043]

[0044] In one example, step S213 of this implementation specifically includes:

[0045] p is both the first node degree sequence D and the noise node degree sequence The position index of the element in, q is the node degree sequence The position index of the element in, 1≤q≤P.

[0046] Calculate M between all nodes [i”,j”] , Index variable p1∈[i”,j”].

[0047] Traverse the index q, that is, q takes 1 to P in sequence, and execute the following steps to obtain the node degree sequence The qth element value of Let p take [1,q] in turn, extract M [P,p] To M [P,P] Get the minimum value min corresponding to index p p ; The minimum value min corresponding to the index p that satisfies 1≤o≤q p Select the largest one as

[0048] In another example, step S213 of this implementation specifically includes:

[0049] p is both the first node degree sequence D and the noise node degree sequence The position index of the element in, q is the node degree sequence The position index of the element in, 1≤q≤P.

[0050] Calculate M between all nodes [i”,j”] , Index variable p1∈[i”,j”].

[0051] Traverse the index q, that is, q takes 1 to P in sequence, and execute the following steps to obtain the node degree sequence The qth element value of Let p take [q,P] in turn and extract M [1,1] To M [1,p] The maximum value in the index p is obtained. p ; From the maximum value max corresponding to the index p that satisfies q≤p≤P p Select the smallest one as

[0052] Step S22, calculating the similarities between nodes in the real social network graph to obtain an original similarity matrix, and performing a second noise-added constraint reasoning on the original similarity matrix to obtain a node similarity matrix.

[0053] Preferably, in order to improve the calculation efficiency, in step S22, calculating the similarity between nodes in the real social network graph includes:

[0054] Step S221, calculate the similarity S between node i and node j in the real social network graph [i][j] .

[0055] Step S222: If nodes i and j in the real social network graph have no common neighbor nodes and are not directly connected, the similarity between nodes i and j is assigned a value of 0, that is, S [i][j] =0; otherwise, the similarity between node i and node j is calculated by the node degree, connection relationship and shortest path length of the common neighbor nodes of node i and node j. When node i and node j are directly connected, the shortest path length is 1, when node i and node j are connected with one node apart, the shortest path length is 2, and when there are y nodes on the shortest path between node i and node j, the shortest path length between node i and node j is y+1.

[0056] In this embodiment, preferably, the similarity S between node i and node j is calculated by the node degree, connection relationship and shortest path length of the common neighbor nodes of node i and node j according to the following formula: [i][j] :

[0057]

[0058] Where N(i) represents the set of neighbor nodes of node i; N(j) represents the set of neighbor nodes of node j; node u is the common neighbor node of node i and node j; d u is the node degree of node u; a represents the connection relationship between node i and node j. When there is an edge between node i and node j, a=1, and when there is no edge between node i and node j, a=0; L represents the shortest path length between node i and node j. i, j, and z are all node indexes, all positive integers. It represents the impact of the shortest path length between node i and node j on the similarity. The closer the two nodes are, the greater the similarity.

[0059] When calculating the similarity between nodes, this implementation not only takes into account the common neighbor nodes between nodes, but also takes into account the connection relationship and the shortest path length between nodes, so that the similarity can reflect the characteristics of whether there is a direct edge between the nodes. In addition, only the similarity between the node and the neighbor node, and the similarity between the node and the neighbor node of the neighbor node is calculated, without traversing all nodes, thereby speeding up the calculation efficiency.

[0060] In a preferred embodiment, in step S22, the second noisy constraint reasoning includes:

[0061] Step B1: extract similarities with non-repeating values ​​from the original similarity matrix S and arrange them in non-descending order to obtain a similarity list SL. [j][i] With S [i][j] Only one of them is taken out for sorting, because the two are completely equivalent) and sorted in non-descending order according to the similarity to obtain a list SL. Let the position index of the element in the similarity list SL be p', the number of elements be P', 1≤p'≤P'. Satisfy SL[p']≤SL[p'+1].

[0062] Step B2: Add noise to each similarity in the similarity list SL to obtain a noise similarity list

[0063] An independent Laplace noise is added to each similarity in the similarity list SL. Preferably, the Laplace noise is generated by a Laplace distribution:

[0064]

[0065] Among them, x2 is the added noise value, b2 is the first scale parameter, and it is set as: b2 = 2 / ∈2, 2 is the sensitivity. Under edge differential privacy, the sensitivity of node degree is always 2. The sensitivity of node degree is 2, which has a smaller sensitivity, so that a smaller privacy budget can be used when adding Laplace noise, and it has a stronger protection effect on similarity privacy.

[0066] Therefore, the noise adding process is expressed as: Add Laplace noise to the noise similarity list Non-descending order may no longer be satisfied.

[0067] Step B3: noise similarity list Perform the second non-descending sort constraint to obtain the inference similarity list Among them, the second non-descending sort constraint is to adjust the inference similarity list The value of the inference similarity in makes the inference similarity list The inference similarity is arranged in non-descending order, that is, it satisfies:

[0068]

[0069] In one example, step B3 of this implementation specifically includes:

[0070] p' is both the similarity list SL and the noise similarity list The position index of the element in , q' is the inference similarity list The position index of the element in, 1≤q'≤P'.

[0071] Calculate M1 between all nodes [i”,j”] , 1≤i”≤j”≤P', Index variable p2∈[i”,j”].

[0072] Traverse the index q', that is, q' takes 1 to P' in sequence, and execute the following steps to obtain the inference similarity list The q'th element value Let p' take [1,q'] in turn, extract M1 [p',p'] To M1 [p',P'] Get the minimum value of index p' p' ; The minimum value min corresponding to the index p that satisfies 1≤p'≤q' p' Select the largest one as

[0073] In another example, step B3 of this embodiment specifically includes:

[0074] p' is both the similarity list SL and the noise similarity list The position index of the element in , q' is the inference similarity list The position index of the element in, 1≤q'≤P'.

[0075] Calculate M1 between all nodes [i”,j”] , 1≤i”≤j”≤P', Index variable p2∈[i”,j”].

[0076] Traverse the index q', that is, q' takes 1 to P' in sequence, and execute the following steps to obtain the inference similarity list The q'th element value Let p' take [q',P'] in turn, extract M1 [1,1] To M1 [1,p'] The maximum value in the index p' is obtained. p'; From the maximum value max corresponding to the index p' that satisfies q'≤p'≤P' p' Select the smallest one as

[0077] Step B4: Using the inference similarity list The inferred similarity in replaces the corresponding similarity in the original similarity matrix to obtain the node similarity matrix.

[0078] Preferably, in step B1, the row and column positions of each similarity in the similarity list SL in the original similarity matrix are recorded. Each similarity in the similarity list SL may record more than one row and column position, and the row and column position of each similarity record is associated with the position index of the similarity in the similarity list SL. Finally, the inferred similarity of each position index is used to replace the similarity of the row and column positions associated with the position index in the original similarity matrix, and the node similarity matrix is ​​obtained after replacement.

[0079] In a preferred embodiment, in step S53, the edge generation probability between node i and node j in the candidate connection node list is calculated according to the common neighbor information, node degree sequence and node similarity matrix of node i and node j in the current differential privacy synthetic social network graph, i≠j, including:

[0080] Step S531 : Obtain the allocation weight W(i, j) of node j based on the node similarity matrix and the common neighbor information between node i and node j.

[0081] Step S532: Combine the node degree sequence to obtain the edge generation probability p(i, j) between node i and node j according to the following formula:

[0082]

[0083] in, represents the node degrees of node i, node j, and node z in the node degree sequence; node j and node z both belong to the candidate connection node list can(i) of node i; M represents the number of edges in the real social network graph, and 2M is the total node degrees of the real social network graph.

[0084] In this embodiment, the allocation weight W(i, j) of node j is obtained based on the common neighbor information between node i and node j in the current differential privacy synthetic social network graph, which is conducive to improving the clustering coefficient of the differential privacy synthetic social network graph. Since the clustering coefficient is related to the number of triangles in the differential privacy synthetic social network graph (three points have edges between each other), if there are more common neighbor nodes between the two nodes and the two nodes generate edges, the number of triangles in the differential privacy synthetic social network graph will increase, so the clustering coefficient will increase more, and thus its allocation weight will be increased.

[0085] In this embodiment, preferably, obtaining the allocation weight W(i, j) of node j based on the node similarity matrix and the common neighbor information between node i and node j includes:

[0086] Step 1, add the similarity and common neighbor information of node i and the nodes in the candidate connection node list to obtain the candidate information of the node in the candidate connection node list, which can be recorded as C(i,j);

[0087] Step 2: Calculate the ratio of the candidate information of node j in the candidate connection node list to the cumulative value of the candidate information of all nodes in the candidate connection node list, and use the ratio as the allocation weight W(i,j) of node j:

[0088]

[0089] in, Represents the similarity between node i and node j in the node similarity matrix; represents the similarity between node i and node z in the node similarity matrix; C(i,j) represents the common neighbor information of node i and node j; C(i,z) represents the common neighbor information of node i and node z.

[0090] In this embodiment, when the node degree sequence is traversed for the first time, the adjacency list is empty, C(i,j)=0, and the weight assigned to the edge generated by node i and node j is:

[0091]

[0092] The edge generation probability between node i and node j is:

[0093]

[0094] It can be seen that when the last node of the node degree sequence is selected as the starting node for the first round of cycle, because there is no edge in the current differential privacy synthetic social network graph, its allocation weight is only related to the similarity.

[0095] In this embodiment, when it is not the first time to traverse the degree sequence, the adjacency list is not empty, and the weight assigned to the edge generated by node i and node j is:

[0096]

[0097] The edge generation probability between node i and node j is:

[0098]

[0099] In a preferred embodiment, the common neighbor information C(i,j) of node i and node j is:

[0100]

[0101] The common neighbor information C(i,z) of node i and node z is:

[0102]

[0103] Among them, com(i,j) represents the number of common neighbors of node i and node j in the current differential privacy synthetic social network graph, represents the maximum expected node degree of node i and node j in the common neighbor nodes of the current differential privacy synthetic social network graph (that is, the maximum value of the node degrees corresponding to the common neighbor nodes of node i and node j in the node degree sequence of the current differential privacy synthetic social network graph); β represents the first heuristic parameter, α represents the second heuristic parameter; com(i,z) represents the number of common neighbors of node i and node z in the current differential privacy synthetic social network graph, It represents the maximum expected node degree of node i and node z in the common neighbor nodes of the current differential privacy synthetic social network graph (that is, the maximum value of the node degrees corresponding to the common neighbor nodes of node i and node z in the node degree sequence of the current differential privacy synthetic social network graph). α>0, β>0.

[0104] In this embodiment, preferably, β and α are used to control the number of common neighbors and the importance of the maximum expected node degree of the common neighbor nodes in the common neighbor information, respectively. To reduce the number of parameters, preferably, β=1.

[0105] In this implementation, in order to better increase the utility of the differentially private synthetic social network graph, the values ​​of β and α are set according to the characteristics of the real social network graph, including:

[0106] Get the uniformity of the node degree in the real social network graph. If the uniformity is less than or equal to the preset uniformity threshold, set β>α; if the uniformity is greater than the preset uniformity threshold, set β<α. The uniformity of the node degree in the real social network graph can be the standard deviation of the node degree, or the difference between the maximum node degree and the minimum node degree. For a real social network graph with uniform node degrees, the importance of the maximum expected node degree in the common neighbor nodes becomes smaller, which can increase the importance of the number of common neighbors. For a real social network graph with uneven node degrees and large differences, the importance of the maximum expected node degree in the common neighbor nodes is increased, which can better improve the clustering coefficient.

[0107] In addition, the numerical values ​​of β and α are positively correlated with the clustering coefficient of the real social network graph. The larger the clustering coefficient of the real social network graph, the larger the values ​​of β and α, because larger β and α can synthesize a real social network graph with a larger clustering coefficient.

[0108] In an example of this implementation, the overall process of synthesizing a social network graph with differential privacy is as follows: Figure 2 shown.

[0109] In a preferred embodiment, to simplify calculation, the common neighbor information C(i, j) of node i and node j is:

[0110]

[0111] The common neighbor information C(i,z) of node i and node z is:

[0112]

[0113] in, represents the sum of the expected node degrees of the common neighbor nodes of node i and node j in the current differential privacy synthetic social network graph, represents the sum of the expected node degrees of the common neighbor nodes of node i and node z in the current differential privacy synthetic social network graph; γ represents the third heuristic parameter.

[0114] In a preferred embodiment, in order to improve the clustering coefficient of the final differential privacy synthetic social network graph and retain more degree distribution characteristics of the real social network graph, it also includes:

[0115] In step S5, before traversing the node degree sequence from the end to the beginning, the following steps are further included: constructing the remaining node degree sequence D copy , the initial state of the node residual degree sequence is the node degree sequence. The residual node degree sequence D copy Includes the residual node degree of each node, which is dynamically updated (reduced) during the generation of edge set E1.

[0116] When traversing to node i, after merging the candidate edges that meet the preset conditions into the edge set of the differential privacy synthetic social graph, it also includes: reducing the remaining node degrees of the two nodes connected by the candidate edge in the remaining node degree sequence by 1 respectively, so as to update the remaining node degree sequence.

[0117] The differentially private synthetic social graph generated after the traversal is completed is post-processed to obtain the final differentially private synthetic social graph. The utility of the final differentially private synthetic social network graph is further improved through post-processing.

[0118] In this embodiment, step S5 specifically includes:

[0119] Construct the remaining node degree sequence D copy , the initial state of the node residual degree sequence is the node degree sequence, let Traverse the node degree sequence from the end to the beginning to obtain the edge set of the differential privacy synthetic social network graph. When traversing to node i, execute:

[0120] Step S51, determining a candidate connection node list of node i based on the node similarity matrix.

[0121] Step S52, obtaining the common neighbor information of node i and the nodes in the candidate connection node list in the current differential privacy synthetic social network graph according to the current adjacency table.

[0122] Step S53, calculate the edge generation probability between node i and the nodes in the candidate connection node list based on the common neighbor information, node degree sequence and node similarity matrix. Suppose the node in the candidate connection node list is j, then p(i,j) represents the edge generation probability between node i and node j.

[0123] Step S54: Node i and the nodes in the candidate connection node list generate candidate edges according to the corresponding edge generation probabilities.

[0124] Step S55: After the candidate edges that meet the preset conditions are merged into the edge set of the differentially private synthetic social graph, the adjacency table is updated, and at the same time, the remaining node degrees of the two nodes of the candidate edges added to the edge set of the differentially private synthetic social graph in the remaining node degree sequence are reduced by 1 respectively.

[0125] In this embodiment, preferably, the post-processing includes performing a first post-processing step, and executing the first post-processing step includes:

[0126] For each isolated node in the differentially private synthetic social graph, a node is selected to connect with the isolated node to generate a candidate edge according to the selection probability corresponding to each node in the differentially private synthetic social graph. If the residual node degree of the selected node (set as node j) in the node residual degree sequence is greater than or equal to 1, and the candidate edge meets the preset conditions, the candidate edge is added to the edge set of the differentially private synthetic social graph, the adjacency list is updated, and the residual node degrees of the isolated node and the selected node (node ​​j) are reduced by 1 in the residual node degree sequence respectively.

[0127] In this implementation, let the isolated node be i, then the selection probability corresponding to node j in the differential privacy synthetic social graph is: represents the node degree of node j in the node degree sequence, Represents the sum of the node degrees of all nodes in the node degree sequence.

[0128] In this embodiment, it is further preferred that after executing the first post-processing step, the post-processing further executes a second post-processing step, and the second post-processing step is to loop through the following sub-steps until the remaining node degree of each node in the remaining node degree sequence is equal to 0:

[0129] For node u whose remaining node degree is greater than or equal to 1 in the remaining node degree sequence, search the node in the current differential privacy synthetic social graph that has the largest number of common neighbor nodes with node u and has no direct connection edge with node u according to the current adjacency list. Let the found node be node j, connect the found node j with node u to generate an edge, add the generated edge to the edge set of the differential privacy synthetic social graph, update the adjacency list, and reduce the remaining node degrees of the found node j and node u in the remaining node degree sequence by 1 respectively.

[0130] In this embodiment, the nodes whose remaining node degrees in the remaining node degree sequence are greater than or equal to 1 can be added to the list list, and the nodes in the list list are traversed in sequence. If the traversed node is u, the node with the largest number of common neighbor nodes with node u and no direct connection edge with node u is found from the current differential privacy synthetic social graph, recorded as node j, and the found node j is connected to node u to generate an edge, and the generated edge is added to the edge set of the differential privacy synthetic social graph, and the adjacency table is updated. At the same time, the remaining node degrees of the found node j and node u in the remaining node degree sequence are respectively reduced by 1, and then the next node of node u in the list list is traversed. If the remaining node degree of each node in the remaining node degree sequence is equal to 0 after traversing the list list, the process ends. If there are still nodes with remaining node degrees greater than or equal to 1 in the remaining node degree sequence, the list list is re-established, and the list list is traversed to perform the above steps, and the cycle is repeated until the remaining node degree of each node in the remaining node degree sequence is equal to 0.

[0131] In this embodiment, if all D copy [i] are all equal to 0, then the degree distribution of the differentially private synthetic social network graph will be well preserved. Therefore, in this implementation, all nodes with a degree greater than 0 are found out, so that they generate edges with the nodes with the most common neighbors and currently have no direct edges. This can contribute to preserving the degree distribution and improving the clustering coefficient.

[0132] The present invention also discloses a dynamic differential privacy synthetic social network graph acquisition device, which is used to implement a dynamic differential privacy synthetic social network graph acquisition method improved by the present invention. In a preferred embodiment, it includes:

[0133] Input module, input the real social network graph;

[0134] A noisy constraint reasoning module is used to obtain a node degree sequence and a node similarity matrix after noise processing and constraint reasoning based on a real social network graph, wherein the node degree sequence is arranged in non-descending order;

[0135] A construction module is used to construct an adjacency table, where the adjacency table is used to record the real-time neighbor node information of each node in the differential privacy synthetic social network graph;

[0136] An initialization module initializes the adjacency list and the edge set of the differential privacy synthetic social network graph, and uses the node set of the real social network graph as the node set of the differential privacy synthetic social network graph;

[0137] The edge set generation module traverses the node degree sequence from the end to the beginning to obtain the edge set of the differential privacy synthetic social network graph. When traversing to node i, it executes:

[0138] Determine the candidate connection node list of node i based on the node similarity matrix, 1<i≤n, n represents the total number of nodes in the node degree sequence;

[0139] According to the current adjacency table, obtain the common neighbor information of node i and the nodes in the candidate connection node list in the current differential privacy synthetic social network graph;

[0140] The edge generation probability between node i and the nodes in the candidate connection node list is calculated based on the common neighbor information, node degree sequence and node similarity matrix;

[0141] Node i generates candidate edges with the nodes in the candidate connection node list according to the corresponding edge generation probability;

[0142] After merging the candidate edges that meet the preset conditions into the edge set of the differentially private synthetic social graph, the adjacency table is updated;

[0143] The synthesis module generates a differentially private synthetic social graph by using the edge set and node set of the differentially private synthetic social graph obtained after the traversal is completed.

[0144] In this embodiment, the input module, the noisy constraint reasoning module, the construction module, the initialization module, the edge set generation module, and the synthesis module respectively correspond to step S1, step S2, step S3, step S4, step S5, and step S6 in the above-mentioned dynamic differential privacy synthetic social network graph acquisition method, and will not be repeated here.

[0145] The present invention provides a dynamic differential privacy synthetic social network graph acquisition method and device, which has the following advantages:

[0146] High degree of privacy protection: In the present invention, the sensitivity of node degree and node similarity are 2 and 2 respectively, which has a smaller sensitivity. It allows a smaller privacy budget to be used when adding Laplace noise, and has a stronger privacy protection effect.

[0147] Availability and accuracy: The new node degree sequence obtained through constraint reasoning retains the existence information of the edges of the graph as much as possible when synthesizing the social network graph with differential privacy. While ensuring that the expected node degree of the nodes of the differential privacy synthesized social network graph is equal to the nodes of the real graph, it only attempts to generate edges with nodes whose similarity is not 0, and divides the probability of nodes with similarity of 0 in the original CL model to nodes with similarity of not 0, which improves the probability of the differential privacy synthesized social network graph retaining the edges in the real graph, so that the differential privacy synthesized social network graph retains more information and characteristics of the real graph, and improves the availability and accuracy of the differential privacy synthesized social network graph. In addition, when generating edges, the common neighbors between nodes in the current graph and the maximum expected node degree in the common neighbor nodes are also considered to better restore the clustering coefficient in the original graph, and the synthesis effect can be improved by adjusting the heuristic parameters α, β, and γ. Constrained reasoning on similarity ensures that the original large similarity is still large in the similarity after noise addition, so that the probability of generating edges between nodes with a large probability of generating edges is still large, making the accuracy of the differential privacy synthesized social network graph higher.

[0148] High computational efficiency: Because when calculating the similarity between nodes, only the similarity between the node and its neighbor nodes and the neighbor nodes of its neighbor nodes is needed, there is no need to traverse all nodes. When looking for common neighbors, only one intersection operation is needed, which speeds up the computational efficiency.

[0149] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", "an implementation", "a preferred implementation" or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0150] Although the embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the claims and their equivalents.

Claims

1. A dynamic differential privacy synthetic social network graph acquisition method, characterized in that: include: Input a real social network graph; Based on a real social network graph, a node degree sequence and a node similarity matrix are obtained after noise processing and constraint reasoning, wherein the node degree sequence is arranged in non-descending order; Constructing an adjacency table, wherein the adjacency table is used to record the real-time neighbor node information of each node in the differential privacy synthetic social network graph; Initialize the adjacency list and the edge set of the differential privacy synthetic social network graph, and use the node set of the real social network graph as the node set of the differential privacy synthetic social network graph; Traverse the node degree sequence from the end to the beginning to obtain the edge set of the differential privacy synthetic social network graph. When traversing to node i, execute: Determine the candidate connection node list of node i based on the node similarity matrix, 1<i≤n, n represents the total number of nodes in the node degree sequence; Obtain the common neighbor information of node i and the nodes in the candidate connection node list in the current differential privacy synthetic social graph according to the current adjacency table; The edge generation probability between node i and the nodes in the candidate connection node list is calculated based on the common neighbor information, node degree sequence and node similarity matrix; Node i generates candidate edges with the nodes in the candidate connection node list according to the corresponding edge generation probability; After merging the candidate edges that meet the preset conditions into the edge set of the differentially private synthetic social graph, the adjacency table is updated; Generate a differentially private synthetic social graph by using the edge set and node set of the differentially private synthetic social graph obtained after traversal; Among them, the edge generation probability between node i and node j in the candidate connection node list is calculated according to the common neighbor information, node degree sequence and node similarity matrix, i≠j, including: Obtain the allocation weight W(i, j) of node j based on the node similarity matrix and the common neighbor information between node i and node j; Combined with the node degree sequence, the edge generation probability p(i,j) between node i and node j is obtained according to the following formula: in, represents the node degrees of node i, node j, and node z in the node degree sequence; node j and node z both belong to the candidate connection node list can(i) of node i; M represents the number of edges in the real social network graph.

2. A dynamic differential privacy synthetic social network graph acquisition method as described in claim 1, characterized in that: The step of obtaining the allocation weight W(i, j) of node j based on the node similarity matrix and the common neighbor information between node i and node j includes: Add the similarity and common neighbor information of node i and the nodes in the candidate connection node list to obtain the candidate information of each node in the candidate connection node list; Calculate the ratio of the candidate information of node j in the candidate connection node list to the accumulated value of the candidate information of all nodes in the candidate connection node list, and use the ratio as the allocation weight W(i,j) of node j: in, Represents the similarity between node i and node j in the node similarity matrix; represents the similarity between node i and node z in the node similarity matrix; C(i,j) represents the common neighbor information of node i and node j; C(i,z) represents the common neighbor information of node i and node z.

3. A dynamic differential privacy synthetic social network graph acquisition method as described in claim 1 or 2, characterized in that: The common neighbor information C(i,j) of node i and node j in the current differential privacy synthetic social network graph is: The common neighbor information C(i,z) of node i and node z is: Among them, com(i,j) represents the number of common neighbors of node i and node j in the current differential privacy synthetic social network graph, represents the maximum expected node degree of node i and node j in the common neighbor nodes of the current differential privacy synthetic social network graph; β represents the first heuristic parameter, α represents the second heuristic parameter; com(i,z) represents the number of common neighbors of node i and node z in the current differential privacy synthetic social network graph, represents the maximum expected node degree that node i and node z have in the common neighbor nodes of the current differential privacy synthetic social network graph; or, The common neighbor information C(i,j) of node i and node j is: The common neighbor information C(i,z) of node i and node z is: in, represents the sum of the expected node degrees of the common neighbor nodes of node i and node j in the current differential privacy synthetic social graph, represents the sum of the expected node degrees of the common neighbor nodes of node i and node z in the current differential privacy synthetic social graph; γ represents the third heuristic parameter.

4. A dynamic differential privacy synthetic social network graph acquisition method as described in claim 3, characterized in that: Also includes: Before traversing the node degree sequence from the end to the beginning, the method further includes: constructing a remaining node degree sequence, wherein the initial state of the remaining node degree sequence is the node degree sequence; When traversing to node i, after merging the candidate edges that meet the preset conditions into the edge set of the differential privacy synthetic social graph, it also includes: reducing the remaining node degrees of two nodes connected by the candidate edge in the remaining node degree sequence by 1 respectively; The differentially private synthetic social graph generated after the traversal is completed is post-processed to obtain the final differentially private synthetic social graph.

5. A dynamic differential privacy synthetic social network graph acquisition method as described in claim 4, characterized in that: Performing a first post-processing step, the first post-processing step comprising: For each isolated node in the differentially private synthetic social graph, a node is selected to connect with the isolated node to generate a candidate edge according to the selection probability corresponding to each node in the differentially private synthetic social graph. If the remaining node degree of the selected node in the remaining node degree sequence is greater than or equal to 1, and the candidate edge meets the preset conditions, the candidate edge is added to the edge set of the differentially private synthetic social graph, the adjacency list is updated, and the remaining node degrees of the isolated node and the selected node in the remaining node degree sequence are reduced by 1 respectively.

6. A dynamic differential privacy synthetic social network graph acquisition method as described in claim 5, characterized in that: After executing the first post-processing step, a second post-processing step is also executed, wherein the second post-processing step is to loop through the following sub-steps until the remaining node degree of each node in the remaining node degree sequence is equal to 0: For node u whose remaining node degree is greater than or equal to 1 in the remaining node degree sequence, search the node in the current differential privacy synthetic social graph that has the largest number of common neighbor nodes with node u and has no direct connection edge with node u according to the current adjacency list, connect the found node with node u to generate an edge, add the generated edge to the edge set of the differential privacy synthetic social graph, update the adjacency list, and reduce the remaining node degrees of the found node and node u in the remaining node degree sequence by 1 respectively.

7. A method for obtaining a dynamic differential privacy synthetic social network graph as described in claim 1 or 2 or 5 or 6, characterized in that: The method of obtaining the node degree sequence and node similarity matrix after noise addition and constraint reasoning based on the real social network graph includes: An original node degree sequence is obtained based on a real social network graph, and a first noise-added constraint reasoning is performed on the original node degree sequence to obtain a node degree sequence, wherein the first noise-added constraint reasoning includes: Arrange the node degrees in the original node degree sequence in non-descending order to obtain a first node degree sequence; Adding noise to each node degree in the first node degree sequence to obtain a noisy node degree sequence; Performing a first non-descending arrangement constraint on the noise node degree sequence to obtain a node degree sequence, wherein the first non-descending arrangement constraint is to adjust the values ​​of the node degrees in the node degree sequence so that the nodes in the node degree sequence are arranged in a non-descending order; Calculate the similarity between nodes in the real social network graph to obtain an original similarity matrix, and perform a second noise-added constraint reasoning on the original similarity matrix to obtain a node similarity matrix, wherein the second noise-added constraint reasoning includes: Take out the similarities with non-duplicate values ​​from the original similarity matrix and arrange them in non-descending order to obtain a similarity list; Add noise to each similarity in the similarity list to obtain a noise similarity list; Performing a second non-descending arrangement constraint on the noise similarity list to obtain an inference similarity list, wherein the second non-descending arrangement constraint is to adjust the values ​​of the inference similarities in the inference similarity list so that the inference similarities in the inference similarity list are arranged in a non-descending order; The inferred similarities in the inferred similarity list are used to replace the corresponding similarities in the original similarity matrix to obtain the node similarity matrix.

8. A method for obtaining a dynamic differential privacy synthetic social network graph as described in claim 7, characterized in that: The calculating of the similarity between nodes in the real social network graph includes: Designed to calculate the similarity between node i and node j in a real social network graph; If nodes i and j in the real social network graph have no common neighbor nodes and are not directly connected, the similarity between nodes i and j is assigned to 0; otherwise, the similarity between nodes i and j is calculated by the node degree, connection relationship and shortest path length of the common neighbor nodes of nodes i and j.

9. A dynamic differential privacy synthetic social network graph acquisition device, used to implement a dynamic differential privacy synthetic social network graph acquisition method according to any one of claims 1-8, characterized in that: include: Input module, input the real social network graph; A noisy constraint reasoning module is used to obtain a node degree sequence and a node similarity matrix after noise processing and constraint reasoning based on a real social network graph, wherein the node degree sequence is arranged in non-descending order; A construction module is used to construct an adjacency table, where the adjacency table is used to record the real-time neighbor node information of each node in the differential privacy synthetic social network graph; An initialization module initializes the adjacency list and the edge set of the differential privacy synthetic social network graph, and uses the node set of the real social network graph as the node set of the differential privacy synthetic social network graph; The edge set generation module traverses the node degree sequence from the end to the beginning to obtain the edge set of the differential privacy synthetic social network graph. When traversing to node i, it executes: Determine the candidate connection node list of node i based on the node similarity matrix, 1<i≤n, n represents the total number of nodes in the node degree sequence; Obtain the common neighbor information of node i and the nodes in the candidate connection node list in the current differential privacy synthetic social graph according to the current adjacency table; The edge generation probability between node i and the nodes in the candidate connection node list is calculated based on the common neighbor information, node degree sequence and node similarity matrix; Node i generates candidate edges with the nodes in the candidate connection node list according to the corresponding edge generation probability; After merging the candidate edges that meet the preset conditions into the edge set of the differentially private synthetic social graph, the adjacency table is updated; The synthesis module generates a differentially private synthetic social graph by traversing the edge set and node set of the differentially private synthetic social graph obtained after completion; Among them, the edge generation probability between node i and node j in the candidate connection node list is calculated according to the common neighbor information, node degree sequence and node similarity matrix, i≠j, including: Obtain the allocation weight W(i, j) of node j based on the node similarity matrix and the common neighbor information between node i and node j; Combined with the node degree sequence, the edge generation probability p(i,j) between node i and node j is obtained according to the following formula: in, represents the node degrees of node i, node j, and node z in the node degree sequence; node j and node z both belong to the candidate connection node list can(i) of node i; M represents the number of edges in the real social network graph.

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