CN115277156B - User identity privacy protection method for resisting neighbor attack in social network - Google Patents
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Abstract
The invention relates to a user identity privacy protection method for resisting neighbor attack in a social network, which comprises the following steps: when graph data of the social network is subject to 1-neighbor attack, the protection of privacy information of the user privacy identity is realized by adopting a graph modification technology; modifying the 1-neighbor graphs in the same cluster according to the graph editing distance to make the graphs indistinguishable in probability; the usability of the graph data is improved while the privacy protection of the user identity in the social network is realized.
Description
Technical Field
The invention relates to the field of social network privacy protection, in particular to a user identity privacy protection method for resisting neighbor attack in a social network.
Background
In the social network, users fill in information such as names, professions, telephone numbers, emails, identification card numbers and the like and store the information in a database, however, certain social relations are also reflected in the data besides personal information. The data contains privacy information of many users, so that anonymity technology must be used to protect the privacy of users before the social network data is published.
The naive user privacy protection method is to remove the identity, attribute and the like of the user, but Backstrom and the like indicate that the naive privacy protection technology can re-identify the identity of the user when facing a 1-neighbor attack, and cannot well protect the privacy of the user. The graph structure modification can effectively protect the privacy of users, and the purpose of user identity privacy or attribute privacy is achieved in the modified graph (called anonymous graph) by changing the structure of the graph through a method of adding or deleting nodes and edges in the original graph before data release. User privacy protection using graph modification techniques, first partitioning nodes, where the partitioning accuracy directly affects the amount of graph information lost may result in reduced graph data availability, and more accurate partitioning criteria must be sought.
Disclosure of Invention
Therefore, the invention aims to provide a user identity privacy protection method for resisting neighbor attack in a social network, and the modified anonymity graph reaches k-anonymity through modifying the graph structure, so that the identity privacy of a user can be effectively protected.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a user identity privacy protection method for resisting neighbor attack in a social network comprises the following steps:
step 1) establishing a social network model, and representing the social network model as a graph G= (V, E), wherein V is a top point set of the graph and represents users in the social network; e is an edge set representing relationships between users in the social network;
according to a measure d (v), lc (v) divides the user nodes into T clusters, wherein d (v) represents the degree of the user nodes v and the meaning is the number of users connected with the user in the social network; lc (v) represents a local clustering coefficient of the user node v in the network, which means that the connection between neighbors of the node v is tight, and after the division is finished, the clusters are arranged in descending order according to the maximum node degree of each cluster;
step 2) presetting a user privacy requirement threshold k, if a certain cluster C i If the number of users in the cluster is less than the threshold k, calculating the average degree of the cluster and the adjacent front and rear clusters C i-1 ,C i+1 Combining the clusters into clusters with small differences, repeating the process until the number of users in all clusters is greater than k;
step 3), after the cluster merging is completed, carrying out cluster splitting operation on clusters with the number of user nodes being more than 2k so that the number of users in each cluster is a certain value of [ k,2 k); the method comprises the following steps:
s3-1, for user nodes in each cluster, sorting according to a degree descending order, and constructing a 1-neighbor graph of the user nodes;
s3-2, constructing a 1-neighbor structure feature matrix of the user node
Wherein the method comprises the steps of
Respectively representing the degree distribution, the internal degree distribution, the external degree distribution and the gap degree distribution of the node v of the user in the social network;
s3-3, according to the formula
Calculating the structural similarity between any two nodes in the same cluster, wherein +.>
Respectively representing the uncorrelated degree, k of the user node degree distribution, the internal degree distribution, the external degree distribution and the gap degree distribution 1 、k 2 、k 3 、k 4 Respectively represent the proportion of each similarity and satisfy k 1 +k 2 +k 3 +k 4 ＝1；
S3-4, dividing the nodes into T clusters by using a K-means clustering algorithm;
step 4), calculating the similarity between each pair of nodes of the user according to the 1-neighbor graph of the user node in each cluster, constructing a weighted bipartite graph according to the similarity, calculating graph editing distances on the bipartite graph, and finding a target graph editing path P according to the graph editing distances;
step 5), editing the path P according to the diagram found in the step 4), and modifying the 1-neighbor diagram of the nodes in the cluster so that the nodes are isomorphic.
2. A method for protecting privacy of user identities against a 1 x-neighbor attack according to claim 1, characterized by: the 1 x-neighbor graph is a subgraph of the original graph G, defined as:
G(v)＝(V(v),E(v),D(v))
where V (V) is a set comprising the user node V itself and its neighbors, E (V) is the relationship between the edges of the nodes in V (V), i.e. the neighbors, and D (V) is the set of the number of neighbors of the node V in the social network, i.e. the set of the degrees of all the nodes in V (V).
Further, the step 2) specifically includes:
s2-1, for clusters with node number less than k, it is noted as
Wherein the superscript 1 indicates that the cluster is the result obtained after the first division, and the average degree of the nodes in the cluster is marked as +.>
Calculate->
Two clusters adjacent to each other in front of and behind the same->
Is respectively marked as +.>
S2-2, if
Satisfy the formula->
Will->
Added to->
In, otherwise will->
Added to->
In (a) and (b);
s2-3, repeatedly executing the steps until the number of nodes in all clusters exceeds k.
Further, the step 4) specifically includes:
s4-1, if the number of neighbor nodes in the l-neighbor graphs of the two user nodes is not equal, adding the user nodes in the graph with few user neighbor nodes so that the number of nodes in the two graphs is equal;
s4-2, constructing a matching cost matrix of the user nodes, and constructing a weighted bipartite graph by taking the matching cost of the user nodes as an edge weight;
s4-3, calculating graph editing distances among the user nodes by utilizing the bipartite graph to obtain matched nodes and graph editing paths.
Further, the step 5) specifically includes:
s5-1, the adjacency matrix of the structural diagram G is denoted as A= (a) ij ) n×n Wherein when node v i And v j When there is an edge between a ij =1, otherwise, a ij ＝0；
S5-2, calculation A 2 A is a 3 ，
Is->
If->
Order of principle
If->
Make->
Calculate->
S5-3, for each user node v in the social network, calculating the obtained matches according to S4-3Matching the node u, calculating the degree of the node v needing to be modified and recording as
The degree of each user node in the social network to be modified is arranged according to descending order, and the obtained degree modification sequence is marked as +.>
Wherein d v Representing the number of neighbors of the user node v;
s5-4 according to D M The graph structure is modified.
Further, the S3-2 specifically comprises the following steps:
s3-2-1, calculating the degree distribution of neighbor nodes in the 1-neighbor graph G (v) of the user node v
Is user node v i The degree of (v) represents v i The number of neighbors in the original graph G,
N(v i ) A set of all neighbors of the user node v;
s3-2-2, calculating the internal degree distribution of the neighbor nodes in the 1-neighbor graph G (v) of the user node v
Is the user node's internal degree, representing user node v i The number of neighbors in the 1 x-neighbor graph G (v), the +.>
Step 3-2-3, calculating the degree distribution of neighbor nodes in the 1 x-neighbor graph G (v) of the user node v
Is v i Is indicative of the degree of egress of the user node v i The number of neighbors outside 1 x-neighbor graph G (v), the +.>
Step 3-2-4, calculating the gap degree distribution of the neighbor nodes in the 1-neighbor graph G (v) of the user node v
Wherein->
S3-2-5, marking the characteristic matrix of each user node in the social network as
Is the number of neighbors of user node v in the social network.
Further, the S3-3 specifically comprises the following steps:
s3-3-1, for user nodes v and u in the same cluster, calculating the uncorrelated degree of the degree distribution, the internal degree distribution, the output degree distribution and the gap degree distribution by using JS divergences, wherein the uncorrelated degree is respectively recorded as:
the JS divergence is defined as:
wherein p= { P 1 ,p 2 ,…,p t }，Q＝{q 1 ,q 2 ,…,q t Respectively two probability distributions in the same probability space,
s3-3-2, calculating similarity vectors of user nodes v and u
The similarity of user nodes u and v is +.>
k 1 +k 2 +k 3 + k 4 ＝1。
Further, the S4-2 specifically comprises the following steps:
s4-2-1, for any pair of vertices V and u, G (V) = (V) in the same cluster 1 ,E 1 ) And G (u) = (V) 2 ,E 2 ) Respectively their 1-neighbor graphs, for any node v i E G (v), calculating the matching cost of E G (v) and all nodes in G (u)
S4-2-2, constructing the cost matrix
S4-2-3, constructing a weighted bipartite graph
V 1 、V 2 Vertex sets with equal number of nodes, denoted as x, < >>
For edge set, add>
Is an edge weight matrix, w ij ＝c ij 。
Further, the S4-3 specifically comprises the following steps:
s4-3-1, selecting a node with the maximum degree as a matched seed node pair;
s4-3-2, utilizing a Monte Carlo method to obtain the optimal matching of the bipartite graph B;
s4-3-3, finding a graph editing path P= { v corresponding to the optimal matching 1 →u t1 ,v 2 →u t2 ,…,v x → u tx }, where u t1 、u t2 、u tm V respectively 1 、v 2 、v m Is a matching node of (c).
Further, the S5-4 specifically comprises the following steps:
s5-4-1, if
Representing user node v i Add->
The edges are respectively found between two-hop neighbor nodes and three-hop neighbor nodes of the node, the nodes needing to be added with edges are connected, and if the number of the connected edges is less than +.>
Then add the dummy node and associate with v i The edges are finally such that the total number of edges is equal to +.>
The method comprises the following steps:
s5-4-1-1 at node v i Two-hop node search of (a) requiresThe node to be added is preset as i If (if)
Then at v i And v j An edge is added between the two parts, and the part is added with->
S5-4-1-2, if there is no two-hop node needing to be added, searching the node needing to be added in the three-hop node, and presetting as i If (if)
Then at v i And v j An edge is added between the two parts, and the part is added with->
S5-4-1-3, repeating the above steps until
Or there is no two-hop and three-hop node requiring an increase in the degree;
s5-4-1-4, if
Terminating;
s5-4-1-5, if
If there are no two-hop and three-hop nodes requiring increasing degree, then the corresponding number of false nodes is increased and the false nodes are matched with v i Are connected;
s5-4-2, if
Representing user node v i Deletion of strip->
Edges, searching neighbors needing to delete the edges in the neighbors, deleting the edges connected between the neighbors, and when the number of the deleted edges is equal to +.>
Stopping when deleting the edges, if the number of deleted edges is insufficient +.>
Deleting the adjacent edges of the nodes from low to high according to the edge medium centrality until the total edge deletion number is equal to +.>
The method comprises the following steps:
s5-4-2-1 at node v i Sequentially searching nodes needing to be reduced in degree, adding the nodes into a candidate set CS, and arranging the nodes in descending order according to the degree of the user node;
s5-4-2-2, deleting nodes and v in CS in turn i A connecting edge between the two;
s5-4-2-3, if
Terminating;
s5-4-2-4, if
At v i Corresponding edges are deleted from small to large in turn according to the edge median centrality among the remaining adjacent edges of (1) until +.>
The edge betweenness centrality is the ratio of the number of paths of the shortest paths among all users in the social network passing through the edge to the number of the short paths among all the nodes in the network.
Compared with the prior art, the invention has the following beneficial effects:
when the graph data of the social network is subject to 1-neighbor attack, the protection of the privacy information of the user privacy identity is realized by adopting the graph modification technology; modifying the 1-neighbor graphs in the same cluster according to the graph editing distance to make the graphs indistinguishable in probability; the usability of the graph data is improved while the privacy protection of the user identity in the social network is realized. The user identity privacy protection method for resisting the 1-neighbor attack in the social network has better application and popularization effects.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a schematic diagram of the 1-neighbor of the node labeled 1 in the original karate diagram in accordance with one embodiment of the present invention;
FIG. 3 is a two-part pictorial representation of one embodiment of the present invention.
Detailed Description
The invention will be further described with reference to the accompanying drawings and examples.
Referring to fig. 1, the present invention provides a user identity privacy protection method for resisting 1 x-neighbor attack in a social network, comprising the following steps:
step 1), for a given graph g= (V, E), according to the metric: d (v), lc (v) divides the node into several clusters, where d (v), lc (v) represent the degree of the node v and its local cluster coefficients, respectively. After the division is finished, arranging the clusters in descending order according to the maximum node degree of each cluster;
step 2), after the coarse division of the nodes, the number of the nodes in some clusters is less than a given privacy requirement k, and the clusters are combined into clusters with small differences according to the difference between the average degree of the clusters and the average degree of two adjacent clusters so as to ensure that the sizes of all groups are greater than k;
the specific method of the step 2) is as follows:
s2-1, we mark it as a cluster with node number less than k
Wherein the superscript 1 indicates that the cluster is the result obtained after the first division, and the average degree of the nodes in the cluster is marked as +.>
Calculate->
Two clusters adjacent to each other in front of and behind the same->
Is respectively marked as +.>
S2-2, if
Satisfy the formula->
Will->
Added to->
In, otherwise will->
Added to->
In (a) and (b);
s2-3, repeatedly executing the steps until the number of nodes in all clusters exceeds k.
Step 3), after cluster merging is completed, the number of nodes in some clusters is more than 2k, and cluster splitting operation is needed to be carried out on the nodes so that the size of each cluster is [ k,2 k);
the step 3) is specifically as follows:
s3-1, for user nodes in each cluster, sorting according to a degree descending order, and constructing a 1-neighbor graph of the user nodes;
s3-2, constructing a 1-neighbor structure feature matrix of the user node
Wherein the method comprises the steps of
Respectively representing the degree distribution, the internal degree distribution, the external degree distribution and the gap degree distribution of the node v of the user in the social network; s3-2-1, calculating the degree distribution of neighbor nodes in the 1-neighbor graph G (v) of the user node v
Is user node v i The degree of (v) represents v i Number of neighbors in original graph G, < >>
N(v i ) A set of all neighbors of the user node v;
s3-2-2, calculating the internal degree distribution of the neighbor nodes in the 1-neighbor graph G (v) of the user node v
Is the user node's internal degree, representing user node v i The number of neighbors in the 1 x-neighbor graph G (v), the +.>
Step 3-2-3, calculating the degree distribution of neighbor nodes in the 1 x-neighbor graph G (v) of the user node v
Is v i Is indicative of the degree of egress of the user node v i The number of neighbors outside 1 x-neighbor graph G (v), the +.>
Step 3-2-4, calculating the gap degree distribution of the neighbor nodes in the 1-neighbor graph G (v) of the user node v
S3-2-5, each user in the social networkThe characteristic matrix of the node is marked as
Is the number of neighbors of user node v in the social network.
S3-3, according to the formula
Calculating the structural similarity between any two nodes in the same cluster, wherein +.>
Respectively representing the uncorrelated degree, k of the user node degree distribution, the internal degree distribution, the external degree distribution and the gap degree distribution 1 、k 2 、k 3 、k 4 Respectively represent the proportion of each similarity and satisfy k 1 +k 2 +k 3 +k 4 ＝1；
S3-3-1, for user nodes v and u in the same cluster, calculating the uncorrelated degree of the degree distribution, the internal degree distribution, the output degree distribution and the gap degree distribution by using JS divergences, wherein the uncorrelated degree is respectively recorded as:
the JS divergence is defined as:
Wherein p= { P 1 ,p 2 ,…,p t }，Q＝{q 1 ,q 2 ,…,q t Two probability distributions in the same probability space, +.>
S3-3-2, calculating user sectionSimilarity vector of points v and u
The similarity of user nodes u and v is +.>
k 1 +k 2 +k 3 + k 4 ＝1。
S3-4, dividing the nodes into T clusters by using a K-means clustering algorithm.
Step 4), calculating the similarity between nodes according to the 1-neighbor graph of the nodes in each cluster, constructing a weighted bipartite graph, calculating graph editing distance on the bipartite graph, and finding a graph editing path P;
the specific method of the step 4 is as follows:
s4-1, if the number of neighbor nodes in the l-neighbor graphs of the two user nodes is not equal, adding the user nodes in the graph with few user neighbor nodes so that the number of nodes in the two graphs is equal;
s4-2, constructing a matching cost matrix of the nodes, and constructing a weighted bipartite graph by taking the matching cost of the nodes as an edge weight;
s4-2-1, for any pair of vertices V and u, G (V) = (V) in the same cluster 1 ,E 1 ) And G (u) = (V) 2 ,E 2 ) Respectively their 1-neighbor graphs, for any node v i E G (v), calculating the matching cost of E G (v) and all nodes in G (u)
S4-2-2, constructing the cost matrix
S4-2-3, constructing a weighted bipartite graph
V 1 、V 2 Respectively vertex sets and in bothThe number of nodes is equal, and is marked as x,>
for edge set, add>
Is an edge weight matrix, w ij ＝c ij 。
S4-3, calculating the graph editing distance of the nodes by utilizing the bipartite graph, and obtaining the matched nodes and graph editing paths.
S4-3-1, selecting a node with the maximum degree as a matched seed node pair;
s4-3-2, utilizing a Monte Carlo method to obtain the optimal matching of the bipartite graph B;
s4-3-3, finding a graph editing path P= { v corresponding to the optimal matching 1 →u t1 ,v 2 →u t2 ,…,v x →
u tx }, where u t1 、u t2 、u tm V respectively 1 、v 2 、v m Is a matching node of (c).
Step 5), editing the path P according to the diagram found in the step 4), and modifying the 1-neighbor diagram of the nodes in the cluster so that the nodes are isomorphic.
The method of the step 5) comprises the following steps:
s5-1, the adjacency matrix of the structural diagram G is denoted as A= (a) ij ) n×n Wherein when node v i And v j When there is an edge between a ij =1, otherwise, a ij ＝0；
S5-2, calculation A 2 A is a 3 ，
Is->
If->
Make->
If->
Make->
Calculate->
S5-3, for each user node v in the social network, calculating the degree of modification required by the node v according to the matched node u calculated in the S4-3 and recording as
The degree of each user node in the social network to be modified is arranged according to descending order, and the obtained degree modification sequence is marked as +.>
Wherein d v Representing the number of neighbors of the user node v;
s5-4 according to D M The graph structure is modified.
S5-4-1, if
Representing user node v i Add->
The edges are respectively found between two-hop neighbor nodes and three-hop neighbor nodes of the node, the nodes needing to be added with edges are connected, and if the number of the connected edges is less than +.>
Then add the dummy node and associate with v i The edges are finally such that the total number of edges is equal to +.>
S5-4-1-1 at node v i To search the nodes requiring the degree of increase, preset as i If (if)
Then at v i And v j An edge is added between the two parts, and the part is added with->
S5-4-1-2, if there is no two-hop node needing to be added, searching the node needing to be added in the three-hop node, and presetting as i If (if)
Then at v i And v j An edge is added between the two parts, and the part is added with->
S5-4-1-3, repeating the above steps until
Or there is no two-hop and three-hop node requiring an increase in the degree;
s5-4-1-4, if
Terminating;
s5-4-1-5, if
If there are no two-hop and three-hop nodes requiring increasing degree, then the corresponding number of false nodes is increased and the false nodes are matched with v i Are connected.
S5-4-2, if
Representing user node v i Deletion of strip->
Edges, searching neighbors needing to delete the edges in the neighbors, deleting the edges connected between the neighbors, and when the number of the deleted edges is equal to +.>
Stopping when deleting the edges, if the number of deleted edges is insufficient +.>
Deleting the adjacent edges of the nodes from low to high according to the edge medium centrality until the total edge deletion number is equal to +.>
S5-4-2-1 at node v i Sequentially searching nodes needing to be reduced in degree, adding the nodes into a candidate set CS, and arranging the nodes in descending order according to the degree of the user node;
s5-4-2-2, deleting nodes and v in CS in turn i A connecting edge between the two;
s5-4-2-3, if
Terminating;
s5-4-2-4, if
At v i Corresponding edges are deleted from small to large in turn according to the edge median centrality among the remaining adjacent edges of (1) until +.>
The edge betweenness centrality is the ratio of the number of paths of the shortest paths among all users in the social network passing through the edge to the number of the short paths among all the nodes in the network.
The foregoing description is only of the preferred embodiments of the invention, and all changes and modifications that come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.
Claims (9)
1. A user identity privacy protection method for resisting neighbor attack in a social network is characterized by comprising the following steps:
step 1) establishing a social network model, and representing the social network model as a graph G= (V, E), wherein V is a top point set of the graph and represents users in the social network; e is an edge set representing relationships between users in the social network;
according to a measure d (v), lc (v) divides the user nodes into T clusters, wherein d (v) represents the degree of the user nodes v and the meaning is the number of users connected with the user in the social network; lc (v) represents a local clustering coefficient of the user node v in the network, which means that the connection between neighbors of the node v is tight, and after the division is finished, the clusters are arranged in descending order according to the maximum node degree of each cluster;
step 2) presetting a user privacy requirement threshold k, if a certain cluster C i If the number of users in the cluster is less than the threshold k, calculating the average degree of the cluster and the adjacent front and rear clusters C i-1 ,C i+1 Combining the clusters into clusters with small differences, repeating the process until the number of users in all clusters is greater than k;
step 3), after the cluster merging is completed, carrying out cluster splitting operation on clusters with the number of user nodes being more than 2k so that the number of users in each cluster is a certain value of [ k,2 k); the method comprises the following steps:
s3-1, for user nodes in each cluster, sorting according to a degree descending order, and constructing a 1-neighbor graph of the user nodes;
s3-2, constructing a 1-neighbor structure feature matrix of the user node
Wherein the method comprises the steps of
Respectively representing the degree distribution, the internal degree distribution, the external degree distribution and the gap degree distribution of the node v of the user in the social network;
s3-3, according to the formula
Calculating the structural similarity between any two nodes in the same cluster, wherein +.>
Respectively representing the uncorrelated degree, k of the user node degree distribution, the internal degree distribution, the external degree distribution and the gap degree distribution 1 、k 2 、k 3 、k 4 Respectively represent the proportion of each similarity and satisfy k 1 +k 2 +k 3 +k 4 ＝1；
The S3-3 specifically comprises the following steps:
s3-3-1, for user nodes v and u in the same cluster, calculating the uncorrelated degree of the degree distribution, the internal degree distribution, the output degree distribution and the gap degree distribution by using JS divergences, wherein the uncorrelated degree is respectively recorded as:
the JS divergence is defined as:
wherein p= { P 1 ,p 2 ,…,p t }，Q＝{q 1 ,q 2 ,…,q t Respectively two probability distributions in the same probability space,
s3-3-2, calculating similarity vectors of user nodes v and u
The similarity of user nodes u and v is +.>
k 1 +k 2 +k 3 +k 4 ＝1；
S3-4, dividing the nodes into T clusters by using a K-means clustering algorithm;
step 4), calculating the similarity between each pair of user nodes according to the 1-neighbor graph of the user nodes in each cluster, constructing a weighted bipartite graph according to the similarity, calculating graph editing distances on the bipartite graph, and finding a target graph editing path P according to the similarity;
step 5), editing the path P according to the diagram found in the step 4), and modifying the 1-neighbor diagram of the nodes in the cluster so that the nodes are isomorphic.
2. The method for protecting privacy of user identity against neighbor attack according to claim 1, wherein: the 1 x-neighbor graph is a subgraph of the original graph G, defined as:
G(v)＝(V(v),E(v),D(v))
where V (V) is a set comprising the user node V itself and its neighbors, E (V) is the relationship between the edges of the nodes in V (V), i.e. the neighbors, and D (V) is the set of the number of neighbors of the node V in the social network, i.e. the set of the degrees of all the nodes in V (V).
3. The method for protecting user identity privacy against neighbor attack according to claim 1, wherein the step 2) specifically comprises:
s2-1, for clusters with node number less than k, it is noted as
Wherein the superscript 1 indicates that the cluster is the result obtained after the first division, and the average degree of the nodes in the cluster is marked as +.>
Calculate->
Two clusters adjacent to each other in front of and behind the same->
Is of (2)Point average degree, respectively marked as +.>
S2-2, if
Satisfy the formula->
Will->
Added to
In, otherwise will->
Added to->
In (a) and (b);
s2-3, repeatedly executing the steps until the number of nodes in all clusters exceeds k.
4. The method for protecting privacy of user identity against neighbor attack according to claim 1, wherein: the step 4) is specifically as follows:
s4-1, if the number of neighbor nodes in the l-neighbor graphs of the two user nodes is not equal, adding the user nodes in the graph with few user neighbor nodes so that the number of nodes in the two graphs is equal;
s4-2, constructing a matching cost matrix of the user nodes, and constructing a weighted bipartite graph by taking the matching cost of the user nodes as an edge weight;
s4-3, calculating graph editing distances among the user nodes by utilizing the bipartite graph to obtain matched nodes and graph editing paths.
5. The method for protecting privacy of user identity against neighbor attack according to claim 1, wherein: the step 5) specifically comprises the following steps:
s5-1, the adjacency matrix of the structural diagram G is denoted as A= (a) ij ) n×n Wherein when node v i And v j When an edge exists between the two adjacent layers,
a ij =1, otherwise, a ij ＝0；
S5-2, calculation A 2 A is a 3 ，
Is->
If->
Order of principle
If->
Make->
Calculate->
S5-3, for each user node v in the social network, calculating the degree of modification required by the node v according to the matched node u calculated in the S4-3 and recording as
The degree of each user node in the social network to be modified is arranged according to descending order, and the obtained degree modification sequence is marked as +.>
Wherein d v Representing the number of neighbors of the user node v;
s5-4 according to D M The graph structure is modified.
6. The method for protecting privacy of user identity against neighbor attack according to claim 1, wherein: the S3-2 specifically comprises the following steps:
s3-2-1, calculating the degree distribution of neighbor nodes in the 1-neighbor graph G (v) of the user node v
Is user node v i The degree of (v) represents v i Number of neighbors in original graph G, < >>
N (v) is a set of all neighbors of the user node v;
s3-2-2, calculating the internal degree distribution of the neighbor nodes in the 1-neighbor graph G (v) of the user node v
Is the user node's internal degree, representing user node v i The number of neighbors in the 1 x-neighbor graph G (v), the +.>
Step 3-2-3, calculating the degree distribution of neighbor nodes in the 1 x-neighbor graph G (v) of the user node v
Is v i Is indicative of the degree of egress of the user node v i In 1 x-oNumber of neighbors outside graph G (v), +.>
Step 3-2-4, calculating the gap degree distribution of the neighbor nodes in the 1-neighbor graph G (v) of the user node v
Wherein->
S3-2-5, marking the characteristic matrix of each user node in the social network as
N v Is the number of neighbors of user node v in the social network.
7. The method for protecting privacy of user identity against neighbor attack according to claim 4, wherein: the S4-2 specifically comprises the following steps:
s4-2-1, for any pair of vertices V and u, G (V) = (V) in the same cluster 1 ,E 1 ) And G (u) = (V) 2 ,E 2 ) Respectively their 1-neighbor graphs, for any node v i E G (v), calculating the matching cost of E G (v) and all nodes in G (u)
S4-2-2, constructing the cost matrix
S4-2-3, constructing a weighted bipartite graph
V 1 、V 2 Vertex sets with equal number of nodes, denoted as x, < >>
For edge set, add>
W＝(w ij ) m×m Is an edge weight matrix, w ij ＝c ij 。
8. The method for protecting privacy of user identity against neighbor attack according to claim 4, wherein: the S4-3 specifically comprises the following steps:
s4-3-1, selecting a node with the maximum degree as a matched seed node pair;
s4-3-2, utilizing a Monte Carlo method to obtain the optimal matching of the bipartite graph B;
s4-3-3, finding a graph editing path P= { v corresponding to the optimal matching 1 →u t1 ,v 2 →u t2 ,…,v x →u tx }, where u t1 、u t2 、u tx V respectively 1 、v 2 、v x Is a matching node of (c).
9. The method for protecting user identity privacy against neighbor attack according to claim 5, wherein: the S5-4 specifically comprises the following steps:
s5-4-1, if
Representing user node v i Add->
The edges are respectively found between two-hop neighbor nodes and three-hop neighbor nodes of the node, the nodes needing to be added with edges are connected, and if the number of the connected edges is less than +.>
Then add the dummy node and associate with v i The edges are finally such that the total number of edges is equal to +.>
The method comprises the following steps:
s5-4-1-1 at node v i Searching nodes needing increasing degree by two-hop nodes, and presetting as u i If (if)
Then at v i And v j An edge is added between the two parts, and the part is added with->
S5-4-1-2, if there is no two-hop node needing to be added, searching the node needing to be added in the three-hop node, and presetting as u i If (if)
Then at v i And v j An edge is added between the two parts, and the part is added with->
S5-4-1-3, repeating the above steps until
Or there is no two-hop and three-hop node requiring an increase in the degree;
s5-4-1-4, if
Terminating;
s5-4-1-5, if
If there are no two-hop and three-hop nodes requiring increasing degree, then the corresponding number of false nodes is increased and the false nodes are matched with v i Are connected;
s5-4-2, if
Representing user node v i Deletion->
Strip edge, find the neighbors needing deleting edge too in its neighbors, delete the edge connecting between them, when delete edge number equal to +.>
Stopping when deleting the edges, if the number of deleted edges is insufficient +.>
Deleting the adjacent edges of the nodes from low to high according to the edge medium centrality until the total edge deletion number is equal to +.>
The method comprises the following steps:
s5-4-2-1 at node v i Sequentially searching nodes needing to be reduced in degree, adding the nodes into a candidate set CS, and arranging the nodes in descending order according to the degree of the user node;
s5-4-2-2, deleting nodes and v in CS in turn i A connecting edge between the two;
s5-4-2-3, if
Terminating;
s5-4-2-4, if
At v i Corresponding edges are deleted from small to large in turn according to the edge median centrality among the remaining adjacent edges of (1) until +.>
The edge betweenness centrality is the number of paths of the shortest path among all users in the social network passing through the edge and all nodes in the networkThe ratio of the number of short paths. />
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