CN110378150B

CN110378150B - Network anonymity method for modifying graph structure based on optimal grouping of degree sequence

Info

Publication number: CN110378150B
Application number: CN201910860277.4A
Authority: CN
Inventors: 张海涛; 于晨光; 韦伟; 胡栋; 朱少楠; 张建宇
Original assignee: Nanjing University of Posts and Telecommunications
Current assignee: Nanjing University of Posts and Telecommunications
Priority date: 2019-09-11
Filing date: 2019-09-11
Publication date: 2020-11-10
Anticipated expiration: 2039-09-11
Also published as: WO2021046950A1; CN110378150A

Abstract

The invention discloses a network anonymity method for modifying a graph structure based on optimal grouping of degree sequences

The anonymous optimal grouping problem is converted into the shortest path problem of a directed packet network; performing a sequence of network node values according to a shortest path of the directed packet network

Anonymity; according to said sequence of network node values

Modifying the network structure by anonymous information to achieve said network node values

Anonymous operation; the invention can effectively reduce the calculated amount in the network data anonymization process, and is suitable for large-scale network data anonymization processing.

Description

Network anonymity method for modifying graph structure based on optimal grouping of degree sequence

Technical Field

The invention belongs to the technical field of data mining, is applied to solving the privacy protection problem, and particularly relates to a network anonymization method for modifying a graph structure based on optimal grouping of degree sequences.

Background

With the increasing public distribution of network data, anonymization of network data has become an important issue.

Deleting the identifier of a node is the simplest anonymous method, but faces a node identification attack based on limited background knowledge. Network data generally has complex topological structure characteristics, and an anonymization method aiming at relationship data cannot be directly applied to the network data. In recent years, graph anonymization has become a mainstream method for network data anonymization. Node K anonymity is an important method in graph anonymity technology. The idea of the node K-anonymity technology is to cluster all nodes into a plurality of super points, wherein any super point must contain not less than K nodes. By reducing the probability of the node being identified to 1/K, corresponding privacy protection is achieved. Scholars at home and abroad successively propose a series of node K anonymization methods: the method comprises a graph anonymization method supporting the incremental weighting social network, a graph anonymization model of k-connection security grouping, a graph anonymization method supporting bipartite graphs, a graph anonymization method keeping node reachability, a personalized graph anonymization method based on node privacy attribute grading in the network, a graph anonymization method based on a combined map, a graph anonymization method preventing multi-community structured attack, a k-degree anonymization method based on an evolutionary algorithm and a community hierarchical structure, a graph anonymization method based on a hypergraph model and the like. However, these graph anonymization methods have the following common problems: the algorithm complexity is too high, and the method is only suitable for network data with thousands of nodes and edges at most, and is difficult to carry out anonymity processing on the network data in a larger scale.

Disclosure of Invention

The invention aims to provide a network anonymization method for modifying a graph structure based on optimal grouping of degree sequences aiming at the problem that an algorithm required by an anonymization process is too complex in the prior art, and the method can be applied to anonymization processing of large-scale network data; the specific technical scheme is as follows:

a network anonymity method for modifying a graph structure based on degree sequence optimal grouping converts the optimal grouping problem of anonymity of a network node degree value sequence k into the shortest path problem of a directed packet network; carrying out k anonymity on the network node value sequence according to the shortest path of the directed packet network; modifying a network structure according to the k anonymity information of the network node degree value sequence to realize the k anonymity operation of the network node degree value, which specifically comprises the following steps:

s1, specifying k-anonymity of the sequence of network node values in network G (V, E):

s11, arranging all nodes in the network G (V, E) in ascending order according to their values to obtain a first sequence of node values d, where d ═ d { (d)₁,d₂,···,d_nN denotes in said network G (V, E)The number of said nodes;

s12, setting a degree value anonymity parameter k, wherein k is an integer and is more than or equal to 1 and less than or equal to n;

s13, constructing a corresponding directional packet network H based on the anonymity parameter k and the first node degree value sequence d_k,nWherein the directed packet network H_k,nThe method comprises the following steps: { H_k,0,H_k,1,H_k,2,....,H_k,nN +1 nodes in total, and node H_k,0An additional node labeled 0;

s14, calculating the shortest path from node 0 to node n in the directional packet network, and obtaining the best packet g of the first node value sequence d based on the shortest path_opt；

S15, grouping g according to the best group_optCalculating to obtain a corresponding difference matrix M_p*2；

S16, based on heuristic method, obtaining the difference matrix M_p*2To select a specified item as an element to compose an optimal sequence P_opt；

S17, according to the optimal sequence P_optModifying the first node value sequence d to obtain a second node value sequence satisfying the k anonymity

S2, according to the second node value sequence

Modifying the structure of the network G (V, E):

s21, based on the first node value sequence d and the second node value sequence

Construction of a sequence of nodal-degree difference values

S22, obtaining the value of each element in the node value difference value sequenceObtaining a set of nodes in the original network G (V, E) that need to be increased in degree to satisfy k anonymity⁺And the set of nodes that need to be reduced in degrees to satisfy k anonymity^-；

S23, calculating the sum sigma (d) of all elements in the first node value sequence d, and calculating the second node value sequence

Sum of all elements in

S24, calculating the sum sigma (d) and the sum

And carrying out structural modification on the network G (V, E) based on the difference value to realize anonymous operation.

Preferably, the directional packet network H is calculated in the step S14_k,nThe shortest path from the middle node 0 to the node n is obtained, and the optimal grouping g of the node value sequence d is obtained based on the shortest path_optThe method comprises the following steps: computing the packet network H_k,nEach path from node 0 to node n

Length of (d):

i is more than or equal to 0 and less than or equal to w, u is more than or equal to j and less than or equal to n, and represents a packet network H_k,nWith directed edges in

The length of (a), wherein,

that is to say M_(i,j)Is d medium to a value of d_hH is not less than i +1 and not more than j; and

obtaining the path with the shortest length corresponds to an optimal k-anonymous grouping mode g_opt＝{g₁,g₂,···,g_pAnd (c) the step of (c) in which,

g₁＝{d₁,d₂,···,d_u}，g₂＝{d_u+1,d_u+2,···,d_v}， g_p＝{d_w+1,d_w+2,···,d_n}。

preferably, in the step S16, the difference matrix M is obtained based on a heuristic method_p*2All of which are the optimal P sequence of elements, including: given a difference matrix

From the difference matrix M based on a heuristic approach_p*2Corresponding sequence set Ps ═ P_i|1≤i≤2^pGet with minimum quickly

Optimal sequence of values P_optWherein P is_i＝{m₁,m₂,···,m_p}，m_j∈{m_j1,m_j2}，1≤j≤p。

Preferably, the optimal sequence P_optThe acquisition process comprises the following steps: sequentially selecting the difference matrix M_p*2As the optimal sequence P_optM of_i1And m_i2Formed corresponding item m_i(ii) a Wherein m is_i1、m_i2The calculation formula of the distribution probability is respectively

m_i1≠0，m_i2Not equal to 0, when m_i1＝0，m_i2When 0, m may be optionally present_i1、m_i2As the optimal sequence P_optThe corresponding item m in (1)_i。

Preferably, the step S24 of performing the structural modification on the network G (V, E) based on the difference value includes: computing the first nodeSum of elements in a sequence of values d

And calculating the second sequence of node values

Sum of the elements in

Calculating σ (d) and

determines the magnitude of the difference from a value of 0, wherein:

if it is

Performing an edge exchange on the network G (V, E): respectively from the node sets^-And the node set⁺In selecting node v_iAnd v_j，v_i∈^-,v_j∈⁺(ii) a Selecting a node V from V_kWherein k ≠ i, k ≠ j, and e_(i,k)E belongs to E; removing edge e_(i,k)Adding edge e_(k,l)；

If it is

Removing in said network G (V, E)

Side: from the node set^-Optionally two nodes v_iAnd v_j，v_i,v_j∈^-(ii) a Selecting two nodes V from V_k,v_lBelongs to V and satisfies the condition k, l is not equal to i, k, l is not equal to j, e_(i,k)∈E，e_(j,l)∈E，

Removing edge e_(i,k)And e_(j,l)Adding edge e_(k,l)；

If it is

Adding into the network G (V, E)

Side: from the node set⁺Optionally two nodes v_iAnd v_j，v_i,v_j∈⁺And meet the requirements

Increased edge e_(i,j)。

The invention relates to a network anonymity method for modifying a graph structure based on degree sequence optimal grouping, which comprises the steps of firstly carrying out anonymization processing on a node value sequence in a network, specifically converting an optimal grouping problem of anonymity of a first node value sequence of the network into a shortest path problem of a directed packet network, obtaining the optimal grouping of the node value sequence according to the shortest path of a node in the obtained directed packet network, calculating according to the optimal grouping to obtain a corresponding difference matrix, further obtaining the optimal sequence by a heuristic method, modifying the first node value sequence according to the optimal sequence to realize the first anonymization processing operation, and obtaining a second node value sequence; then, the sum of all elements in the first node value sequence and the second node value sequence is respectively obtained, the difference value between the first node value sequence and the second node value sequence is calculated, the network is modified according to the difference value, and finally the anonymous processing operation of the network data is realized; compared with the prior art, the method can effectively reduce the calculated amount in the network data anonymization process; meanwhile, the method is suitable for anonymous processing operation of large-scale network data, and improves the efficiency and speed of anonymity.

Drawings

FIG. 1 is a block diagram illustration of a given example network in an embodiment of the invention;

FIG. 2 is a block diagram illustration of a modified tag name sorted by value for a given example network in an embodiment of the invention;

FIG. 3 is a block diagram of a directed packet network constructed based on a given example network in an embodiment of the present invention;

FIG. 4 is a block diagram illustrating an exemplary network after performing edge pruning for sorted modified tag names for metric values in an embodiment of the present invention;

FIG. 5 is a block diagram illustrating an exemplary network re-performing edge pruning after sorting the magnitude values and modifying the tag names in accordance with an embodiment of the present invention;

FIG. 6 is a schematic structural diagram of satisfying anonymity of node degree K after performing edge deletion on a given example network according to an embodiment of the present invention;

FIG. 7 is a block diagram illustrating an exemplary network after performing edge switching after sorting label names according to metric values in an embodiment of the present invention;

FIG. 8 is a block diagram illustrating an example network after performing edge switching again after sorting the values and modifying the tag names in accordance with an embodiment of the present invention;

FIG. 9 is a schematic structural diagram of an example network after sorting degree values and modifying tag names according to an embodiment of the present invention, which satisfies anonymity of node degree values K after performing edge exchange;

FIG. 10 is a block diagram illustrating an exemplary network after performing edge addition after sorting values and modifying tag names in accordance with an embodiment of the present invention;

FIG. 11 is a block diagram illustrating an example network after performing edge addition again after sorting the values and modifying the tag names in accordance with an embodiment of the present invention;

FIG. 12 is a schematic structural diagram of an example network after sorting degree values and modifying tag names according to an embodiment of the present invention, which satisfies anonymity of node degree values K after edge addition is performed;

fig. 13 is a flowchart illustrating an implementation of the network anonymization method for modifying the graph structure based on the optimal grouping of the degree sequence in the embodiment of the present invention.

Detailed Description

In order to make the technical solutions of the present invention better understood, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention.

In the embodiment of the present invention, a network anonymization method for modifying a graph structure based on a degree sequence optimal grouping is provided, referring to fig. 13, the method specifically includes the steps of: firstly, converting the best grouping problem of anonymity of a network node value sequence k into the shortest path problem of a directed packet network; then, k anonymity is carried out on the network node value sequence according to the shortest path of the directed packet network; finally, modifying the network structure according to the k anonymity information of the network node degree value sequence to realize the k anonymity operation of the network node degree value; to illustrate the specific process of the present invention, the following basic definitions are combined:

definition 1: k-anonymity of network node degree values: given a network G (V, E), where V is the set of all nodes in the network and E is the set of all edges. d ═ d₁,d₂,···,d_nThe values of all nodes in V are arranged in ascending order, called the value sequence d for short, and n is the number of nodes in V. For any node v_iE is V (1 is more than or equal to i is less than or equal to n), and the value is d_i. If d ═ d₁,d₂,···,d_nThere is a subset

I-s is more than or equal to 1 and less than or equal to n, i + t is more than or equal to 1 and less than or equal to n, and the condition d is satisfied_i-s＝,···,＝d_i-1＝d_i＝d_i+1＝,···,＝d_i+tAnd (k-1) is less than or equal to (t + s), and k is less than or equal to 1 and less than or equal to n, the sequence d is called k anonymity, and the node degree value k of the network G (V, E) is also called anonymity.

Definition 2: k packet network of node value sequence: given a network G (V, E), its node value sequence is d ═ d₁,d₂,···,d_nAnd an integer k is set, wherein k is more than or equal to 1 and less than n, and a directed packet network can be generated

Wherein,

(1) for any one element d in d_i，1≤i≤n，H_k,nA node in which one tag is i corresponds to it. Furthermore, H_k,nThere is an additional node labeled 0. Therefore, the temperature of the molten metal is controlled,

(2) for the

Any node pair in

0≤i≤(n-k)，(i+k)≤j＜(i+2k)，j≤n， H_k,nAll have a slave node

To the node

Directed edge of

(3) Directed edge

Is defined as

Wherein,

that is to say M_(i,j)Is d medium to a value of d_hAnd h is more than or equal to i +1 and less than or equal to j.

(4) Network H_k,nThe path from node 0 to node n is:

the length of the utility model is as follows: l is_{(path(0，n))}＝L_(0,u)+L_(u,v)+,···,L_(w,n). A path_(0，n)Corresponding to a pair d ═ d₁,d₂,···,d_nThe grouping method g ═ g for k anonymity₁,g₂,···,g_pAnd (c) the step of (c) in which,

g₁＝{d₁,d₂,···,d_u}，g₂＝{d_u+1,d_u+2,···,d_v}，g_p＝{d_w+1,d_w+2,···,d_n}. The path with the shortest length corresponds to the best k-anonymous grouping method, denoted g_opt。

Definition 3: difference matrix M_p*2: giving the best k anonymous packet g_opt＝{g₁,g₂,···,g_pBased on g_optHeterogeneity among elements in the middle group can obtain a difference matrix

Wherein M is_p*2The values of the middle term are: g_optThe sum of the differences between the corresponding value of (a) and the arithmetic mean of all values of the set. The specific calculation is as follows:

(1) if g is_jAll of them are equal, i.e. m_j1＝m _j20. If not, then,

(2) calculating the sum of the differences downwards to obtain M_p*2The value of the 1 st column term in (1) is calculated by the formula:

wherein j is more than or equal to 1 and less than or equal to p, | g_jL is g_jThe number of the elements in (A) and (B),

that is to say that the first and second electrodes,

is g_jIs less than

And with

D having the smallest difference_o。m_j1The value is always 0Or a positive value, indicating the magnitude of the reduction value required in the set.

(3) Calculating the sum of the difference values upwards to obtain M_p*2The value of the middle 2 item, the calculation formula is:

that is to say that the first and second electrodes,

is g_jIs greater than

And with

D having the smallest difference_o。m_j2The value is always 0 or negative, indicating that the magnitude of the value needs to be increased in the set.

Definition 4: optimum sequence P_opt: given a difference matrix M_p*2One sequence set Ps ═ P can be obtained_i|1≤i≤2^pIn which P is_i＝{m₁,m₂,···,m_p},m_j∈{m_j1,m_j2J is more than or equal to 1 and less than or equal to p. Has the smallest among Ps

Value P_iSequence, called optimal sequence, denoted P_opt。

Calculating an optimal sequence P_optAn exhaustive approach may be used: first, all m is exhausted_j1,m_j2Combinations, the number of combinations is 2^p(ii) a Then, the absolute values of the elements in each combination are summed; finally, the optimal sequence is obtained according to the combination with the minimum value. The time complexity of the exhaustive method was analyzed: the computational overhead includes pair 2^pIn a combination of 2^pOperation of summing absolute values of x 2p elements, and sum of 2^pAnd comparing the sum value. According to the theory of algorithmic analysis, the time complexity of the exhaustive method is O (2)^p) I.e. of exponential order. Therefore, this method is not suitable for application on a large-scale network.

Based on this, the method based on heuristic method of the invention calculates and obtains the optimal sequence P_opt: selecting difference matrix in sequence

M with larger selection probability_i1、m_i2As the optimal sequence P_optCorresponding item m in_i. Wherein m is_i1、m_i2The calculation formulas of the distribution probability are respectively as follows:

m_i1≠0，m_i2not equal to 0, when m_i1＝0，m_i2When 0, m may be optionally present_i1、m_i2As the optimal sequence P_optCorresponding item m in_i。

The time complexity of the invention adopting a heuristic method is analyzed: the computational overhead includes the pair of difference matrices M_p*2The operation of 2p times of distribution probability calculation and the operation of p times of comparison of 2p probability values are performed. According to the theory of algorithmic analysis, the time complexity of the heuristic method is O (p) and is also linear order. Compared with the existing exhaustion method, the method has the advantages that the time complexity of processing the network data is lower, namely the network data is processed with higher efficiency; and when the time complexity is reduced from the corresponding exponential order to the linear order, the improvement of the network data processing efficiency is combined, so that the method can be ensured to be effective and have good calculation efficiency when being applied to larger-scale network data.

Definition 5: k-anonymity node degree value sequence

Given a network G (V, E), its corresponding sequence of node values d, the best k anonymous packet G_optAnd the optimal sequence P_optAre respectively d ═ d₁,d₂,···,d_n}， g_opt＝{g₁,g₂,···,g_p}，P_opt＝{m₁,m₂,···,m_pAnd (c) the step of (c) in which,

g₁＝{d₁,d₂,···,d_u}， g₂＝{d_u+1,d_u+2,···,d_v}，g_p＝{d_w+1,d_w+2,···,d_nget the k anonymous node value sequence of network G (V, E)

Wherein,

u+1≤i≤v，...，

w+1≤i≤n。

definition 6: sequence of nodal value difference values: given a network G (V, E), the corresponding sequence of node values d ═ d₁,d₂,···,d_n}, k anonymous node degree value sequence

Then the sequence of node value differences is

That is to say that the first and second electrodes,

wherein,

1≤i≤n。

respectively representing the node sets which need to increase and decrease degrees to satisfy the anonymity of the node degree value k.

Definition 7: modifying the network structure with anonymous node value k: given a network G (V, E), the corresponding sequence of node values d ═ d₁,d₂,···,d_n}, k anonymous node degree value sequence

The sequence of the node value difference values is

Node set with degree needing to be increased and decreased to meet anonymity of node degree k

Sum of elements in d

Sum of the elements in

Then a structure modification operation with a constant number of nodes is performed on the network G (V, E):

(1) if it is

Edge switching is performed for the network G (V, E). First, respectively from^-And⁺to select two nodes v_i,v_jI.e. v_i∈^-,v_j∈⁺. Then, a node is selected from Vv_kWherein k ≠ i, k ≠ j, and e_(i,k)E.g. E. Finally, remove edge e_(i,k)Adding edge e_(k,l)。

(2) If it is

Removing in network G (V, E)

An edge. First, from^-To select two nodes v_i,v_jI.e. v_i,v_j∈^-. Then, two nodes V are selected from V_k,v_lBelongs to V and satisfies the condition k, l is not equal to i, k, l is not equal to j, e_(i,k)∈E，e_(j,l)∈E，

Finally, remove edge e_(i,k)And e_(j,l)Adding edge e_(k,l)。

(3) If it is

Adding to network G (V, E)

An edge. First subordinate to the ren⁺Select two nodes v_i,v_jI.e. v_i,v_j∈⁺And require

Adding edge e again_(i,j)。

With reference to the above definitions 1 to 7, the detailed process of the network anonymity method for modifying the graph structure based on the optimal grouping of degree sequences according to the present invention is described by using a specific embodiment, which specifically includes:

s11, arranging all nodes in the network G (V, E) according to the degree values in an ascending order to obtain a first node degree valueSequence d, wherein d ═ d₁,d₂,···,d_nN denotes the number of all nodes in the network G (V, E).

In the present embodiment, an example network G (V, E) is given, in which:

V＝{v_A,v_B,v_C,v_D,v_E,v_F,v_G,v_H,v_I,v_J}，

concrete structure

Referring to fig. 1, node labels and correspondence values for an example network are shown in table 1:

A	B	C	D	E	F	G	H	I	J
										4	6	3	3	4	2	3	2	2	1

TABLE 1

The example network is arranged in ascending order according to its degree and the tag name is modified to obtain the node information shown in table 2, and correspondingly, the network structure signed by the modification table is obtained, specifically referring to fig. 2, for the modified network structure, where V and E are respectively:

V＝{v₈,v₁₀,v₅,v₆,v₉,v₂,v₇,v₃,v₄,v₁}，

v₁

v₂

v₃

v₄

v₅

v₆

v₇

v₈

v₉

v₁₀

J

F

H

I

C

D

G

A

E

B

1

2

3

4

6

TABLE 2

Finally, the first node degree value sequence of the example network can be obtained as d ═ 1,2,2,2,3,3,3,4,4,6} based on the modified node information.

S12, setting a degree value anonymity parameter k, wherein k is an integer and is more than or equal to 1 and less than or equal to n; and an anonymous parameter k exists that satisfies the condition: k < n; specifically, in the present embodiment, n is 10, and the setting value anonymity parameter k is 2.

S13, constructing a corresponding directional packet network H based on the anonymity parameter k and the first node degree value sequence d_k,nWherein there is a directed packet network H_k,nThe method comprises the following steps: { H_k,0,H_k,1,H_k,2,....,H_k,nN +1 nodes in total, and node H_k,0An additional node labeled 0.

In this embodiment, based on the first node value sequence d ═ {1,2,2,2,3,3,3,4,4,6} and the anonymity parameter k ═ 2, the directional packet network is constructed as a directional packet network

Wherein:

node removing device

Are additional nodes, and the other 10 nodes correspond to the elements in d, as shown in fig. 3.

The conditions are required to be met when a packet network is constructed: any node pair

0≤i≤(n-k)， (i+k)≤j＜(i+2k)，j≤n，H_k，nAll have a slave node

To the node

Directed edge of

Thus, when i is 0, (0+2) ≦ j < (0+4), i.e., the node pair

In the network H_2,10In which there is a corresponding edge

When i is equal to 1, (1+2) is less than j and less than (1+4), namely the node pair

In the network H_2,10In which there is a corresponding edge

Similarly, when i is valued at 2-8, the corresponding obtained edges are respectively:

that is, H_2,10The edges in (1) are:

finally, a directed packet network H is constructed_2,10The structure of (1).

S14, calculating the shortest path from node 0 to node n in the directional packet network, and obtaining the best packet g of the first node value sequence d based on the shortest path_opt。

Referring again to FIG. 3, in the present embodiment, based on the network path search, it can be seen from H_2,10Node in

To

The nodes have 7 paths, which are respectively:

(1)

(2)

(3)

(4)

(5)

(6)

(7)

directed edge

Is defined as

Wherein,

is d medium to a value of d_hAverage value of (a). That is, L_(i,j)Is d_hThe sum of the squared differences from the mean.

In this example, there are directed edges

Length of (2)

As can be seen from the first sequence of node values d ═ {1,2,2,2,3,3,3,4,4,6}, d₁、d₂Respectively 1 and 2. Therefore, the temperature of the molten metal is controlled,

L_(0,2)＝(1-1.5)²+(2-1.5)²＝0.5。

for the same reason, for directed edges

Corresponding d thereof₃、d₄Respectively 2 and 2.

Therefore, the temperature of the molten metal is controlled,

L_(2,4)＝(2-2)²+(2-2)²＝0。

calculating edges in sequence

Are respectively obtained

L_(4,6)＝(3-3)²+(3-3)²＝0，

L_(6,8)＝(3-3.5)²+(4-3.5)²＝0.5，

L_(8,10)＝(4-5)²+(6-5)²＝2。

Thus, path₁Length of (2)

Similarly, the following can be obtained in turn:

for the shortest path, the corresponding best packet is g_opt＝{g₁,g₂,g₃,g₄,g₅In which g is₁＝{d₁,d₂}，g₂＝{d₃,d₄}， g₃＝{d₅,d₆}，g₄＝{d₇,d₈}，g₄＝{d₉,d₁₀}, that is: g_opt＝{{d₁,d₂},{d₃,d₄},{d₅,d₆},{d₇,d₈},{d₉,d₁₀}}。

S15, grouping g according to the best_optCalculating to obtain a corresponding difference matrix M_p*2。

In the present embodiment, the optimal grouping g is based on the above definition 3_optHeterogeneity among elements in the middle group, and calculating to obtain a difference matrix M_p*2。

In this example, g_opt＝{{d₁,d₂},{d₃,d₄},{d₅,d₆},{d₇,d₈},{d₉,d₁₀} that is to say: g_optThe corresponding difference matrix is {1,2}, {2,2}, {3,3}, {4,4}, {4,6} }

For packet g ₁1,2, the constituent items are not identical:

wherein

g₁Less than {1,2}

And the term having the smallest difference is d₁And therefore, the first and second electrodes are,

wherein | g₁|＝2，

g₁Greater than {1,2}

And the term having the smallest difference is d₂And therefore, the first and second electrodes are,

for packet g₂＝{2,2}，g₃(iii) 3, the constituent items are identical, and m is₂₁＝m₂₂＝0，m₃₁＝m₃₂＝0。

For packet g₄1, {3,4}, whose constituent items are not identical:

for packet g₅1, {4,6}, whose constituent items are not identical:

finally, a difference matrix is obtained as

S16, based on heuristic method, from difference matrix M_p*2To select a specified item as an element to compose an optimal sequence P_opt。

In particular according to the formula

Calculate m_jSelection of m_j1,m_j2Selecting elements with larger probability values to construct an optimal sequence P_opt。

In the present example, it is shown that,

due to P (m)₁＝m₁₂)＝P(m₁＝m₁₁) Thus, P_optThe first element of the sequence may be m₁₁Or m₁₂。

Similarly, the following can be calculated:

furthermore, m₂₁＝m₂₂＝0，m₃₁＝m ₃₂0, therefore, P_optMay be { m }₁₁,m₂₁,m₃₁,m₄₁,m₅₁}、 {m₁₁,m₂₁,m₃₁,m₄₁,m₅₂}、{m₁₁,m₂₁,m₃₁,m₄₂,m₅₁}、{m₁₁,m₂₁,m₃₁,m₄₂,m₅₂}、 {m₁₂,m₂₁,m₃₁,m₄₁,m₅₁}、{m₁₂,m₂₁,m₃₁,m₄₁,m₅₂}、{m₁₂,m₂₁,m₃₁,m₄₂,m₅₁}、{m₁₂,m₂₁,m₃₁,m₄₂,m₅₂Any sequence of {1,0,0,1,2}, {1,0,0,1, -2}, {1,0,0, -1, -2}, { -1,0,0,1, -2}, { -1,0,0, -1, -2 }. In this embodiment, P is selected_opt＝{1,0,0,1,2}。

In practice, if the exhaustion method is adopted, it is necessary to first pair { m }₁₁,m₂₁,m₃₁,m₄₁,m₅₁}、 {m₁₁,m₂₁,m₃₁,m₄₁,m₅₂}、{m₁₁,m₂₁,m₃₁,m₄₂,m₅₁}、{m₁₁,m₂₁,m₃₁,m₄₂,m₅₂}、{m₁₁,m₂₁,m₃₂,m₄₁,m₅₁}、 {m₁₁,m₂₁,m₃₂,m₄₁,m₅₂}、{m₁₁,m₂₁,m₃₂,m₄₂,m₅₁}、{m₁₁,m₂₁,m₃₂,m₄₂,m₅₂}、{m₁₁,m₂₂,m₃₁,m₄₁,m₅₁}、 {m₁₁,m₂₂,m₃₁,m₄₁,m₅₂}、{m₁₁,m₂₂,m₃₁,m₄₂,m₅₁}、{m₁₁,m₂₂,m₃₁,m₄₂,m₅₂}、{m₁₁,m₂₂,m₃₂,m₄₁,m₅₁}、 {m₁₁,m₂₂,m₃₂,m₄₁,m₅₂}、{m₁₁,m₂₂,m₃₂,m₄₂,m₅₁}、{m₁₁,m₂₂,m₃₂,m₄₂,m₅₂}、{m₁₂,m₂₁,m₃₁,m₄₁,m₅₁}、 {m₁₂,m₂₁,m₃₁,m₄₁,m₅₂}、{m₁₂,m₂₁,m₃₁,m₄₂,m₅₁}、{m₁₂,m₂₁,m₃₁,m₄₂,m₅₂}、{m₁₂,m₂₁,m₃₂,m₄₁,m₅₁}、 {m₁₂,m₂₁,m₃₂,m₄₁,m₅₂}、{m₁₂,m₂₁,m₃₂,m₄₂,m₅₁}、{m₁₂,m₂₁,m₃₂,m₄₂,m₅₂}、 {m₁₂,m₂₂,m₃₁,m₄₁,m₅₁}、{m₁₂,m₂₂,m₃₁,m₄₁,m₅₂}、{m₁₂,m₂₂,m₃₁,m₄₂,m₅₁}、 {m₁₂,m₂₂,m₃₁,m₄₂,m₅₂}、{m₁₂,m₂₂,m₃₂,m₄₁,m₅₁}、{m₁₂,m₂₂,m₃₂,m₄₁,m₅₂}、 {m₁₂,m₂₂,m₃₂,m₄₂,m₅₁}、{m₁₂,m₂₂,m₃₂,m₄₂,m₅₂}, that is: {1,0,0,1,2}, {1,0,0,1, -2}, {1,0,0, -1, -2}, {1,0,0,1, -2}, {1,0,0,0, -1,0,0, -2}, {1,0, 2}, {1, -2}, {1,0,0,1,2}, and {1,0, 1,2}, and {1,0,0,1,2}, { -1,0,0,1, -2}, { -1,0,0, -1, -2}, { -1,0,0,1, -2}, { -1,0,0, -1,2}, and { -1,0,0, -1,2}The absolute value summation calculation is carried out on items in 32 sequences in total, namely { -1,0,0, -1, -2}, { -1,0,0, -1, -2}, { -1,0,0,1, -2}, { -1,0,0, -1, -2}, and { -1,0,0, -1, -2}, so as to obtain corresponding values, wherein the corresponding values are: 4. thus, the optimal sequence P_optCan be any of the 32 sequences.

In fact, the analysis found: the 32 sequences, wherein the corresponding element values in the 24 sequences are all the same, that is: and performing sum of absolute values calculation on the terms in 24 sequences, wherein all the calculation is repeated. The heuristic method provided by the invention can effectively avoid the repeated calculation, and a user only needs to select among 8 non-repeated sequences; further, the method of the invention can effectively improve the processing efficiency of the network data.

S17 according to the optimal sequence P_optModifying the first node value sequence d to obtain a second node value sequence d which meets the k anonymity; specifically, in the embodiment of the present invention, according to P_opt＝{m₁,m₂,···,m_p}， g_opt＝{g₁,g₂,···,g_p}，

g₁＝{d₁,d₂,···,d_u}，g₂＝{d_u+1,d_u+2,···,d_v}， g_p＝{d_w+1,d_w+2,···,d_nAnd obtaining a k-anonymous second node value sequence of the network G (V, E):

wherein,

1≤i≤u，

u+1≤i≤v，...，

w +1 is not less than i and not more than n. In this example, d ═ {1,2,2,2,3,3,3,4,4,6}, P_opt＝{1,0,0,1,2}， g_opt＝{{1,2},{2,2},{3,3},{4,4},{4,6}}。

For packet g₁＝{1,2}，

m₁1, therefore

1≤i≤2。

For packet g₂＝{2,2}，m₂The requirement value does not need to be changed when being equal to 0, and therefore

Also for packet g₃＝{3,3}，m₃The requirement value does not need to be changed when being equal to 0, and therefore

For packet g₄＝{3,4}，

m₄1, therefore

7≤i≤8。

For packet g₅＝{4,6}，

m

₅2, therefore

9≤i≤10。

Therefore, the second node value sequence is finally obtained as:

s2, according to the second node value sequence

Modifying the structure of the network G (V, E):

Construction of a sequence of nodal-degree difference values

In particular, d ═ d for a given first sequence of node values₁,d₂,···,d_nAnd anonymized second node value sequenceCorresponding node value difference value sequence can be obtained

That is to say

Wherein,

1≤i≤n。

in this embodiment, the first node value sequence is: d ═ 1,2,2,2,3,3,3,4,4,6, and the second node value sequence is given by

Therefore, the final sequence of the node value difference values obtained by calculation is as follows: 0, -1,0,0,0,0, -1,0, -2 }.

S22, obtaining the node set of the original network G (V, E) needing degree increase to satisfy k anonymity according to the value of each element in the node value difference value sequence⁺And the set of nodes that need to be reduced in degrees to satisfy k anonymity^-(ii) a Specifically, according to the above definition 6, there are:

then in this embodiment, one can obtain: 0, -1,0,0,0,0, -1,0, -2 }. And because of

Therefore, the temperature of the molten metal is controlled,

^-＝{v₂,v₈,v₁₀}。

Sum of all elements in

Specifically, in this embodiment, the first node value sequence is d ═ 1,2,2,2,3,3,3,4,4,6, and the second node value sequence is d ═ 1,2,2,2,3,3, 4,4,6

Thus, it is possible to provide

S24, calculating sum sigma (d) sum

And modifying the structure of the network G (V, E) based on the difference value to realize anonymous operation.

In this embodiment, since the first node value sequence is d ═ 1,2,2,2,3,3,3,4,4,6, the second node value sequence is d ═ 1,2,2,2,3,3, 4,4,6

Thus, σ (d) and

the difference between them is

In combination with the above definition 7, the edge removal operation needs to be performed on the network structure after the tag names are sorted and modified according to the value, and specifically includes the following processes:

first, from^-＝{v₂,v₈,v₁₀Select node v₂,v₁₀Selecting a node V from V_m,v_nSatisfies the conditions m, n ≠ 2, m, n ≠ 10, and e_(2,m)∈E,e_(10,n)E.g. E. Thus, v_m∈{v₇}，v_n∈{v₃,v₄,v₇,v₈,v₉}. When v is selected_m＝v₇,v_n＝v₉When, the operation is executed: removing e_(2,7),e_(10,9)Increase e_(7,9)At removal of e_(2,7),e_(10,9)And increase e_(7,9)The network structure obtained can be referred to fig. 4.

In conjunction with FIG. 4, at this time, d₂＝1，d₇＝3，d₉＝4，d₁₀When 5, i.e., d ═ 1,1,2,2,3,3,3,4,4,5,

according to definition 6, {0,0,0,0,0,0, -1,0, -1},

^-＝{v₈,v₁₀}。

then, from^-＝{v₈,v₁₀Select node v₈,v₁₀And selecting a node V from V_m,v_nSatisfies the conditions m, n ≠ 8, m, n ≠ 10, and e_(8,m)∈E,e_(10,n)E.g. E. Thus, v_m∈{v₃,v₆,v₉}，v_n∈{v₃,v₄,v₇}。When v is selected_m＝v₆,v_n＝v₇When, the operation is executed: removing e_(8,6),e_(10,7)Increase e_(6,7)Then remove e_(8,6),e_(10,7)And increase e_(6,7)The network structure obtained can be specifically referred to fig. 5; at this time, d₆＝3，d₇＝3，d₈＝3，d₁₀As a result, the first node value sequence d is {1,1,2,2,3,3,3,3, 4,4} and the second node value sequence d is 4

＝{0,0,0,0,0,0,0,0,0,0}，

Stopping the network structure modification.

And finally, labeling the nodes of the network structure shown in fig. 5, and finally obtaining the K-degree anonymous network structure by combining fig. 6.

In the embodiment of the present invention, in order to describe the process of modifying the network structure through the edge switching operation, it is assumed that the selected P is_optIs { -1,0,0, -1,2}, and then sequentially available

To obtain {1,0,0,0,0,0,1,0, 0, -2}, to obtain⁺＝{v₁,v₇}、^-＝{v₁₀Get it

To obtain

According to definition 7, at this time, the network structure after the label names are sorted and modified according to the value needs to be executed with edge switching operation; the specific process is as follows:

first, from⁺＝{v₁,v₇And^-＝{v₁₀select node v₁,v₁₀Selecting a node V from V_mSatisfies the conditions m.noteq.1, m.noteq.10, and

e_(10,m)e.g. E. Thus, v_m∈{v₂,v₃,v₄,v₇,v₈,v₉}. When v is selected_m＝v₄When, the operation is executed: removing e_(10,4)Increase e_(1,4)The final result can be seen in FIG. 7; at this time, d₁＝2，d₄＝2，d₁₀That is, d is 5 {2,2,2,2,3,3,3,4,4,5},

according to definition 6, {0,0,0,0,0, 1,0,0, -1},⁺＝{v₇}，^-＝{v₁₀}。

then, from⁺＝{v₇And^-＝{v₁₀select node v₇,v₁₀And selecting a node V from V_mSatisfies the conditions m.noteq.7, m.noteq.10, and

e_(10,m)e.g. E. Thus, v_m∈{v₂,v₃,v₈,v₉}. When v is selected_m＝v₃When, the operation is executed: removing e_(10,3)Increase e_(7,3)The final result can be seen in FIG. 8; at this time, d₃＝3，d₇＝4，d₁₀4, i.e., d ═ 2,2,2,3,3,4,4,4,4},

＝{0,0,0,0,0,0,0,0,0,0}，

stopAnd (5) modifying the network structure.

Finally, label labeling is performed on the nodes of the network structure shown in fig. 8, and a K-degree anonymous network is finally obtained, and a specific network structure can be referred to as 9.

Similarly, to describe the process of network fabric modification by edge add operation, assume that the derived P is selected_optWhen { -1,0,0, -1, -2}, the subsequent sequences will give

Yield {1,0,0,0,0, 1,0,2,0}, yielding:⁺＝{v₁,v₇,v₉}、

to obtain

Obtaining:

according to definition 7, at this time, edge adding operation is performed on the network structure after the label names are sorted and modified according to the value; the specific process is as follows:

first, from⁺＝{v₁,v₇,v₉Select node v₁,v₉Satisfies the conditions

And (3) executing the operation: increase of e_(1,9)The final result can be seen in FIG. 10; at this time, d₁＝2，d₉That is, the first node value sequence is d ═ 2,2,2,3,3,3,4,5,6, and the second node value sequence is d ═ 2,2,2,3,3,4, 5,6

Then according to definition 6: (0, 0,0,0,0,1,0,1,0},⁺＝{v₇,v₉}，

then, from⁺＝{v₇,v₉Select node v₇,v₉Satisfies the conditions

And (3) executing the operation: increase of e_(7,9)The network structure at this time is shown in fig. 11; at this time, d₇＝4,d₉That is, the first node value sequence is d ═ 2,2,2,3,3,4,4,6,6}, and the second node value sequence is d ═ 2,2,2,3,3,4,4,6,6}

＝{0,0,0,0,0,0,0,0,0,0}，

At this point, the network structure modification operation is stopped.

Finally, label labeling is performed on the nodes of the network structure shown in fig. 11, and a K-degree anonymous network is finally obtained, and a specific network structure can be referred to in fig. 12.

Although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that modifications may be made to the embodiments described in the foregoing detailed description, or equivalent changes may be made in some of the features of the embodiments described above. All equivalent structures made by using the contents of the specification and the attached drawings of the invention can be directly or indirectly applied to other related technical fields, and are also within the protection scope of the patent of the invention.

Claims

1. A network anonymity method for modifying a graph structure based on degree sequence optimal grouping is characterized in that the method converts the optimal grouping problem of anonymity of a network node degree value sequence k into the shortest path problem of a directed packet network; carrying out k anonymity on the network node value sequence according to the shortest path of the directed packet network; modifying a network structure according to the k anonymity information of the network node degree value sequence to realize the k anonymity operation of the network node degree value, which specifically comprises the following steps:

s11, arranging all nodes in the network G (V, E) in ascending order according to their values to obtain a first sequence of node values d, where d ═ d { (d)₁,d₂,···,d_nN represents the number of all said nodes in said network G (V, E);

s13, constructing a corresponding directional packet network H based on the anonymity parameter k and the first node degree value sequence d_k,nWherein the directed packet network H_k,nThe method comprises the following steps: { H_k,0,H_k,1,H_k,2,....,H_k,nN +1 nodes in total, and node H_k,0For additional section labeled 0Point;

s14, calculating the length of each path from node 0 to node n of the packet network by the length of the directed edge of the directed packet network and the average value of the values in the first node value sequence, and obtaining the best k-anonymous grouping mode corresponding to the path with the shortest length, namely obtaining the best grouping g of the first node value sequence d_opt；

S15, obtaining the best group g according to the previous step_optBased on the best packet g_optHeterogeneity between elements in the middle group, grouping the best g_optThe sum of the differences between the middle corresponding value and the arithmetic mean of all the values in the group is collected to obtain a difference matrix M_p*2；

S16, based on heuristic method, obtaining the difference matrix M_p*2Sequentially selecting items with larger selection probability as corresponding items in the optimal sequence, and using the items as elements to form the optimal sequence P_opt；

The node value sequence d ═ { d } corresponding to the network G (V, E) obtained in the above-described step₁,d₂,···,d_nH, best k anonymous packet g_opt＝{g₁,g₂,···,g_pAnd the best sequence P_opt＝{m₁,m₂,···,m_pAnd (c) the step of (c) in which,

g₁＝{d₁,d₂,···,d_u}，g₂＝{d_u+1,d_u+2,···,d_v}，g_p＝{d_w+1,d_w+2,···,d_nget the k anonymous node value sequence of the network G (V, E)

Wherein,

s2, according to the second node value sequence

Modifying the structure of the network G (V, E):

Construction of a sequence of nodal-degree difference values

S22, obtaining a node set which needs degree increase in the original network G (V, E) to meet k anonymity according to the numerical value of each element in the node value difference value sequence⁺And the set of nodes that need to be reduced in degrees to satisfy k anonymity^-；

Sum of all elements in

S24, calculating the sum sigma (d) and the sum

The difference between them, if

Performing edge switching on the network G (V, E); if it is

Removing in network G (V, E)

A side; if it is

Adding to network G (V, E)

A side; anonymous operation is achieved by the above-described structural modification of the network G (V, E).

2. The method for network anonymity of claim 1, wherein the step S14 of computing a directed packet network H is based on graph structure modification of degree sequence optimized packets_k,nThe shortest path from the middle node 0 to the node n is obtained, and the optimal grouping g of the node value sequence d is obtained based on the shortest path_optThe method comprises the following steps: computing the packet network H_k,nEach path from node 0 to node n

Length of (d): l is_{(path(0，n))}＝L_(0,u)+L_(u,v)+,···,L_(w,n)，

The length of (a), wherein,

g₁＝{d₁,d₂,···,d_u}，g₂＝{d_u+1,d_u+2,···,d_v}，g_p＝{d_w+1,d_w+2,···,d_n}。

3. the method for anonymizing networks according to claim 2, wherein the step S16 is based on heuristic method to obtain the difference matrix M_p*2All of which are the optimal P sequence of elements, including: given a difference matrix

4. The network anonymizing method for graph structure modification based on degree sequence optimal grouping of claim 3, wherein the optimal sequence P_optThe acquisition process comprises the following steps:sequentially selecting the difference matrix M_p*2As the optimal sequence P_optM of_i1And m_i2Formed corresponding item m_i(ii) a Wherein m is_i1、m_i2The calculation formula of the distribution probability is respectively

m_i1≠0，m_i2Not equal to 0, when m_i1＝0，m_i2When not greater than 0, optionally m_i1、m_i2As the optimal sequence P_optThe corresponding item m in (1)_i。

5. The network anonymizing method according to claim 1, wherein the step S24 of modifying the structure of the network G (V, E) based on the difference comprises: calculating the sum of the elements in the first sequence of node values d