A k-Anonymization Method for Social Network Data
with Link Prediction
Risa Sugai, Yuichi Sei
a
, Yasuyuki Tahara
b
and Akihiko Ohsuga
c
Graduate School of Informatics and Engineering, The University of Electro-Communications, Tokyo, Japan
Keywords:
Social Network, Link Prediction, Data Mining, Privacy Protection Technique.
Abstract:
Recently, social networking services have come to pervade every aspect of our lives, increasing the demand
for the utilization of social network data. However, since the utilization of social network data has the risk
of personal identification, k-anonymization methods have been proposed to protect privacy as a solution.
In addition, the actual data contains missing values, which may reduce the utility of the data by applying
conventional methods. In this paper, we propose a method for k-anonymization of social network data with
link prediction, with the aim of improving the utility of anonymized data. Based on evaluation experiments on
real data, we examine the utility of anonymized data.
1 INTRODUCTION
Recently, social networking services have come to
pervade every aspect of our lives, increasing the de-
mand for the utilization of social network data (Siva-
ganesan, 2021)(Rahmayani and Nofrialdi, 2022).
However, since social network data contains personal
information, the risk of personal identification arises
(Liu and Terzi, 2008).
To take an example, data includes not only iden-
tifiers such as name, but also quasi-identifiers such
as age and profession. Usually, the identifiers are re-
moved when the data is provided to data providers. In
this situation, however, there is a possibility that indi-
viduals can be identified from the personal informa-
tion of quasi-identifiers provided, and sensitive per-
sonal information such as income and disease can be
revealed. Therefore, it is necessary to consider the
personal information when protecting privacy (Oishi,
2020).
In the case of social network data, structural
information is also included such as friendships.
For this reason, privacy-preserving methods focus-
ing on structural information have been studied for
anonymization of social network data.
In addition, the actual social network data may
contain missing data. For example, Facebook, which
a
https://orcid.org/0000-0002-2552-6717
b
https://orcid.org/0000-0002-1939-4455
c
https://orcid.org/0000-0001-6717-7028
is one of the most influential social networking ser-
vices, allows users to set friendships such to private.
Therefore, when dealing with real data, it is effec-
tive to consider the missing friendships in the data
and supplement links by link prediction (Zareie and
Sakellariou, 2020). In this situation, it is important
to suppress the information loss of anonymized data
with link prediction.
In general, missing data is not considered during
data anonymization. However, the presence of miss-
ing data increases the amount of information lost after
anonymization, so the missing data should be consid-
ered when applying anonymization to real data.
This paper focuses on an anonymization method
for social network data with link prediction, and aim
to improve the utility of anonymized data.
In this study, we proposed a new indicator k-
maximum degree and an anonymization algorithm
using the indicator for social network data with link
prediction. In addition, we assumed that an attacker
can estimate a node, and added an analysis algo-
rithm for node estimation. Then, we conducted ex-
periments adapting the proposed method to two ac-
tual social network data and evaluated the utility of
the anonymized data. Experimental results showed
that the anonymized data generated by the proposed
method had the highest link match rate with the origi-
nal data compared to those of other existing methods,
indicating that it is superior in terms of data utility.
This paper is organized as follows. In Section 2,
we describe the assumed environment in this study.
Sugai, R., Sei, Y., Tahara, Y. and Ohsuga, A.
A k-Anonymization Method for Social Network Data with Link Prediction.
DOI: 10.5220/0011676800003405
In Proceedings of the 9th International Conference on Information Systems Security and Privacy (ICISSP 2023), pages 493-500
ISBN: 978-989-758-624-8; ISSN: 2184-4356
Copyright
c
 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)
493

We explain some background knowledge related to
this study in Section 3. Section 4 introduces the new
indicator and algorithm for anonymization of social
network data with link prediction. Then, we present
the experiments and discuss the results in Section 5.
Finally, we present the conclusions and the future
work in Section 6.
2 ASSUMPTION
In this section, we show an assumed environment and
an attack scenario in the situation. In this study, the
notations used is shown in Table 1.
Table 1: Table of Notation.
G(V, E) Graph G with node set V and edge
set E
G
0
(V
0
,E
0
) Graph G
0
obtained by link predic-
tion.
|V | = n The number of nodes in G
|E| = m The number of edges in G
deg(v) The degree of node v.
k The anonymization requirement pa-
rameter.
add The total number of links added by
link prediction.
add
i
The number of links added by link
prediction of v
i
.
2.1 Assumed Environment
In general, it is difficult for data analysts to voluntar-
ily collect vast amounts of social network data, so it
is very meaningful to analyze the data provided by
data owners. In this paper, the case that data own-
ers such as providers of social networking services
provide the social network data to data analysts is as-
sumed as shown in Figure 1.
Data owners know which links users have set as
private, but no information related to these private
links should be released to the outside. In case of
such restrictions, it is necessary to anonymize so-
cial network data without using the private informa-
tion. In this case, it is acceptable to infer private
links only from public information (non-private links
and nodes). Therefore, data owners may provide
anonymized social network data after link prediction
of public information.
In addition, the case where social network data
contains missing links is assumed, and the following
link prediction and anonymization is performed. The
data flow is shown in Figure 2.
Figure 1: Assumed Environment.
Figure 2: Data Flow.
2.2 Attacker’s Background Knowledge
The following knowledge is set as the attacker’s back-
ground knowledge.
• The degree of a node
• Total number of links added by link prediction
If the attacker knows the total number of links added
by link prediction, the degree of node v will be at most
the degree before link prediction plus the total number
of links added.
deg(v) 5 deg
0
(v) 5 deg(v) + add (1)
In this case, the attacker cannot determine which
links have been added by link prediction.
3 BACKGROUND
3.1 Social Network Data
Social network data includes profiles such as name
and profession, posts and friendships. Social network
data consists of a set of nodes V and a set of edges E,
which can be expressed as graph G = (V, E). In this
situation, the degree of a node indicates the number
of friends.
3.2 Anonymization Techniques
Social network data contains personal privacy infor-
mation. Therefore, data providers are required to pro-
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494

tect the personal privacy information contained in the
data before providing it.
k-anonymization (Sweeney, 2002) was proposed
as one of the privacy protection methods. k-
anonymization is a method to reduce the risk of re-
identification to 1/k by processing data so that there
are k or more data with the same attributes. How-
ever, social network data includes structural informa-
tion such as friendships as well as attribute informa-
tion (Beigi and Liu, 2020). For this reason, it may not
be safe to only anonymize attribute information.
Privacy preserving methods for network data can
be divided into three main categories. The first
method is graph modification. The approach is a
method of anonymization by adding and deleting
nodes and edges in the graph. The second method is
generalization.The approach is a generalized method
of grouping nodes and edges by clustering (Campan
and Truta, 2008a)(Yu et al., 2017). The third method
is uncertain graphs (Yan et al., 2018). The approach
is based on uncertain graphs, which adds probabilities
of existence to the edges of the graphs to add uncer-
tainty to the graphs.
Among them, the k-anonymization method, which
uses the degree of a vertex as a quasi-identifier,
has been widely studied as graph modification ap-
proach (Casas-Roma et al., 2017a)(Casas-Roma et al.,
2017b)(Casas-Roma et al., 2019).
A typical anonymity metric of social network data
is k-degree (Liu and Terzi, 2008). k-degree guaran-
tees the existence of at least k nodes with the same de-
gree, and Liu et al. propose an anonymization method
that uses k-degree to add or remove edges. k-degree
is defined as follows.
Definition 1. An integer vector v satisfies k-
anonymity if every value of v appears at least k times.
Example: v = [5,5,3,3,2,2,2] satisfies 2-anonymity.
Definition 2. Let V be the degree sequence of the
input graph and W be the degree sequence of the
anonymized graph. In this case, Equation (2), v
i
∈ V
and w
i
∈ W hold.
∆(V,W ) =
n
∑
i=1
|v
i
− w
i
| (2)
For example, suppose that in the situation shown
in Figure 3, an attacker has background knowledge of
the degree of a particular user, and wants to identify a
node of degree 2.
The degree of each node in Figure 3 is {’Ada’:2,
’Bob’:1, ’Cathy’:1}. Since there is only one node
with degree 2, Ada can be uniquely identified from
the graph in Figure 3.
CathyBob
Ada
Figure 3: Social Network Graph.
CathyBob
Ada
Figure 4: 3–degree Graph.
In Figure 4, the degree of each user becomes
{’Ada’:2, ’Bob’:2, ’Cathy’:2} by adding a new edge
for Bob and Cathy. As a result, the risk of identifica-
tion can reduce to 1/3. At this point, we can say that
the graph in Figure 4 satisfies 3-degree.
However, it is clear that there is a trade-off be-
tween data utility and anonymity in anonymization
(Majeed and Lee, 2020). For the reason, it is neces-
sary to apply anonymization methods with the needs
of both data owners and data analysts depending on
the characteristics of the data.
3.3 Problem in Link Prediction
In social network analysis, link prediction methods
that use graph theory to predict the likelihood of the
existence of links have been studied (Ahmad et al.,
2020)(Campan and Truta, 2008b)(Lorrain and White,
1971)(Liben-Nowell and Kleinberg, 2003). Finding
hidden relationships through link prediction is ex-
pected to increase the utility of social network data.
Common Neighbor and Centrality based Param-
eterized Algorithm (CCPA) was proposed in 2020.
CCPA score is calculated based on common neigh-
bors and centrality, and is defined as follows (Ah-
mad et al., 2020). In addition, the performance of the
CCPA algorithm has been shown to be consistently
better on some datasets than other algorithms (Sharma
and Rai, 2022).
CCPAscore = α · (|Γ(u) ∩ Γ(v)|) + (1 − α) ·
N
d
uv
(3)
In this case, Γ(u) and Γ(v) are the set of neigh-
boring nodes of each node, N is the total number of
nodes, and d
uv
is the shortest distance between nodes.
A k-Anonymization Method for Social Network Data with Link Prediction
495

The higher the score, the more likely it is that a link
between nodes exists.
In this way, missing links in social network data
can be predicted by link prediction. However, the
question of an anonymization method for social net-
work data with link prediction is still open in previous
researches.
4 PROPOSED ALGORITHM
In this section, we propose k-maximum degree as an
anonymity metric for social network data with link
prediction, and risk of node re-identification as a pos-
sible attacker’s method of attack in the situation.
4.1 Definition of k-maximum degree
In the situation of anonymized data after link pre-
diction, we propose an anonymization indicator k-
maximum degree.
Definition 1. A vector of integers V is k-anonymous,
if every distinct value v
i
∈ V appears at least k times.
Definition 2. An undirected network G = (V,E) sat-
isfies k-maximum degree anonymous, if the maximum
degree in the degree sequence of G appears at least k
times.
When there are at least k nodes with the maximum
degree, the anonymized data after link prediction sat-
isfies k-maximum degree. For example, if the degree
sequence of G is [5,5,3,2,2,2,2,1], the graph G sat-
isfies 2-maximum degree.
4.2 Risk of Node Re-Identification
In this situation, the attack is assumed as shown in
Figure 5.
Figure 5: Data Attack Flow.
The degree of a node may be inferred from the
total number of additions by link prediction. In this
time, the risk of re-identification in a node is calcu-
lated by the Equation (4). The Equation (4) indicates
the probability that a node is of a possible degree be-
fore link prediction.
deg probability =
deg(v
i
)
C
add
i
×
m−deg(v
i
)
C
add−add
i
m
C
add
(4)
The total number of links added by link prediction
is add, the total number of edges in graph is m, the
degree of v
i
is deg(v
i
), and the number of links added
by link prediction of v
i
is add
i
.
For example, suppose we have a social network
data with link prediction as shown in Figure 6.
Figure 6: Social network data with link prediction.
This graph consists of 6 nodes and 9 edges, and
the edges contain 2 additional links by link prediction.
In this time, node A is the a-th node and the degree of
A is 5 in the social network data with link prediction
G
0
.
The probability that add
a
= 0 and deg(A) = 5 is:
5
C
0
×
9−5
C
2−0
9
C
2
=
6
36
=
1
6
The probability that add
a
= 1 and deg(A) = 4 is:
5
C
1
×
9−5
C
2−1
9
C
2
=
20
36
=
5
9
The probability that add
a
= 2 and deg(A) = 3 is:
5
C
2
×
9−5
C
2−2
9
C
2
=
10
36
=
5
18
From the results, it is inferred that node A was
likely of degree 4 before link prediction.
4.3 Analysis Algorithm
Since it is assumed that attackers estimate the degree
of users from the link prediction results and attempts
to identify the nodes, an analysis algorithm estimates
the pre-link prediction degree of each node from the
total number of links added, which is one of the link
prediction results.
An analysis algorithm that estimates the pre-link
prediction degree of each node is shown in Algorithm
1.
ICISSP 2023 - 9th International Conference on Information Systems Security and Privacy
496

Algorithm 1: Analysis Protocol.
1: Input: G
0
(V
0
,E
0
), add
2: Output: Predicted degree sequence D
i
(i =
0,··· ,n −1)
3: function ESTIMATION DEGREE(G
0
,add)
4: D ← [0] ∗ n
5: for all i = 0,··· ,n − 1 do
6: max ← 0
7: for all s = 0,··· ,add − 1 do
8: /* Calculate degree probability */
9: x
s
← calDegProbability(dev(v
i
),s)
10: if x
s
> max then
11: max ← x
s
12: D
i
← dev(v
i
) − s
13: end if
14: end for
15: end for
16: return D
i
(i = 0,··· , n − 1)
17: end function
In calDegProbability(dev(v
i
),s), it receives the
degree sequence deg(v
i
) and the number of links
added by link prediction s at v
i
. Then, it estimates
the probability that the degree before link prediction
for v
i
is dev(v
i
) − s.
It is possible to find the most likely value as the
degree before link prediction from the total number of
links added by link prediction by using this analysis
algorithm, and determine if a node with the degree
satisfies k-anonymity.
4.4 Anonymization Protocol
In the next, an anonymization algorithm that satisfies
the k-maximum degree defined. In this algorithm, a
method of adding edges for anonymization is adopted.
In the conventional method, the amount of mod-
ification of the graph is enormous, so the amount
of modification is suppressed by adding and delet-
ing graphs to maintain the quality of the anonymized
graph. However, the proposed method is expected
to suppress the amount of modification of graphs by
anonymizing only the graph structure of some nodes,
and to generate high-quality anonymized graphs even
with only additions.
This anonymization algorithm is shown in Algo-
rithm 2.
If any node has less than k nodes with the same
degree in the predicted degree sequence D, then
estimationDegreeAdd(D,list) is performed. In
estimationDegreeAdd(D,list), it receives a list list1
of nodes with fewer than k nodes having the same de-
gree in the predicted degree sequence D. Starting with
Algorithm 2: Anonymization Algorithm.
1: Input:G
0
(V
0
,E
0
), add, k
2: Output: Anonymized graph G”
3: function ANONYMIZATION(G
0
,add,k)
4: G” ← empty graph
5: vd ← [0] ∗ n
6: D ← ESTIMAT ION DEGREE(G
0
,add)
7: list1 ← []
8: for all i = 0,··· ,n − 1 do
9: if D.count(D[i]) < k then
10: list1.append(i)
11: end if
12: end for
13: if list1.size > 0 then
14: vd ← estimationDegreeAdd(D,list1)
15: end if
16: vd ← degreeAnonymization(G
0
,vd)
17: G” ← graphConstruction(G
0
,vd)
18: /* Graph Construction */
19: return G”
20: end function
the smallest degree, add to each degree until there are
at least k nodes with the same degree. When there are
no more nodes with the same degree less than the k
value, a list of changes for each node is returned.
In degreeAnonymization(G
0
,vd), it receives a
graph G
0
obtained by link prediction and a list vd
of changes for each node, and finds the minimum
amount of additions required to have at least k nodes
with k-maximum degree.
In graphConstruction(G
0
,vd), it receives a graph
G
0
obtained by link prediction and a list vd of
changes for each node. In addition, it adds edges
so that the graph changes minimally and satisfies k-
maximum degree.
5 EVALUATION EXPERIMENT
5.1 Experimental Setup
In this experiment, we evaluated the usefulness of
anonymization methods for link prediction. In this
experiment, we prepared missing social network data
with 20% or 50% of edges removed, and anonymized
the social network data using the following method.
A k-Anonymization Method for Social Network Data with Link Prediction
497

 
(a) Anonymization by k-degree
(b) CCPA + k-degree
(c) CCPA + k-maximum degree
 
In recent years, many anonymization methods for
social network data have been studied, but k-degree
algorithm, which uses only structural information and
is widely used, was used for comparison.
In this study, k-degree and k-maximum degree
were used for anonymization and CCPA was used for
link prediction.
For link prediction, the CCPA parameter was set
to the default value, α = 0.8, and additional links were
set as links with a normalized CCPA score of 0.9 or
higher.
5.2 Evaluation Index
As an evaluation index, we used the link match rate.
To evoluate the utility of degree-anonymous graph
Gb(V, Eb), the link match rate with the original data
G(V, E) before edge removed was used. The link
match rate is defined in the study as the edge inter-
section as EI(E, Eb) = |Eb ∪ E|/|E| (Liu and Terzi,
2008). The higher the rate, the better the result, as it
preserves the characteristics of the data.
5.3 Dataset
In the evaluation experiment in this study, we used
two real social network datasets.
Dolphins dataset is used as the real data (Rossi
and Ahmed, 2015). The dataset contains a social net-
work of bottlenose dolphins, consisting of 62 nodes
and 159 undirected edges, representing frequent as-
sociations among dolphins.
Facebook dataset is used as the real data
(Leskovec and Mcauley, 2012). The dataset includes
profiles, circles, and ego networks. In the evaluation
experiment, we used ego networks data composed of
4,039 nodes and 88,234 undirected edges as friend-
ships.
5.4 Experimental Results
In the Dolphins dataset, the number of nodes de-
creased to 58 for the dataset with 20% edge removal,
and to 56 for the dataset with 50% edge removal due
to the effect of removing some of the links in the ex-
periment.
As a result of link prediction, the dataset with
20% edge removal was increased to 132 edges with
4 added, and the dataset with 50% edge removal was
increased to 104 edges with 24 added.
The link match rates with the original data before
edges removed are as shown in Table 2 and 3.
Table 2: The link match rate with the original data before
edges removed (Dolphins: 20% removal).
Recall↑
k=2 k=10
(a)k-degree 0.515 0.509
(b)CCPA+k-degree 0.507 0.512
(c)CCPA+k-maximum degree 0.977 0.872
Table 3: The link match rate with the original data before
edges removed (Dolphins: 50% removal).
Recall↑
k=2 k=10
(a)k-degree 0.464 0.456
(b)CCPA+k-degree 0.364 0.347
(c)CCPA+k-maximum degree 0.840 0.720
In the Facebook dataset, the number of nodes de-
creased to 4,018 for the dataset with 20% edge re-
moval and to 3,944 for the dataset with 50% edge
removal due to the effect of removing some of the
links in the experiment. As a result of link prediction,
the dataset with 20% edge removal was increased to
71,797 edges, with 1,209 added, and the dataset with
50% edge removal was increased to 63,956 edges,
with 19,839 added.
The link match rates with the original data before
edges removed were as shown in Table 4 and 5.
Table 4: The link match rate with the original data before
edges removed (FB: 20% removal).
Recall↑
k=2 k=5 k=10
(a)k-degree NA 0.397 0.388
(b)CCPA+k-degree NA 0.390 0.379
(c)CCPA+k-maximum degree 0.995 0.979 0.939
Table 5: The link match rate with the original data before
edges removed (FB: 50% removal).
Recall↑
k=2 k=5 k=10
(a)k-degree 0.396 0.390 0.383
(b)CCPA+k-degree 0.275 0.271 0.267
(c)CCPA+k-maximum degree 0.899 0.888 0.863
The conventional method sometimes failed in
graph construction because it modifies the graph to
minimize the amount of edge modification, and the
anonymized data may not be obtained, as in the case
of k = 2 in (a) and (b) of Table 4.
The experimental results show that for (c)
CCPA+k-maximum degree, the link match rate with
ICISSP 2023 - 9th International Conference on Information Systems Security and Privacy
498

the original data before edges removal is larger than
in (a) kdegree and (b) CCPA + k-degree.
In particular, in the case of Facebook dataset, the
link match rate is larger for (c), (a), and (b), in that or-
der, and the proposed method (c) outperform the con-
ventional method of k-degree anonymization in terms
of the number of matched links.
In all results, the link match rate was worse for (b)
CCPA+k-degree than for (a) k-degree. This may be
due to an increase in the number of links in the dataset
in the link prediction, and an increase in the amount
of graph modification in anonymization, which added
links that were not in the original data.
The anonymized data generated by the proposed
anonymization method showed a higher link match
rate than the other methods, suggesting that the char-
acteristics of the data are better preserved.
There are two possible reasons for the high
accuracy of the proposed method (c) CCPA+k-
maximum degree.
First, the amount of graph modification can be re-
duced compared to anonymizing all nodes, because
the nodes that need to be anonymized are selected
based on the link prediction results.
Secondly, there is a difference in the graph modi-
fication method during anonymization. The proposed
method (c) anonymizes the graph by adding links be-
cause the amount of link modification can be sup-
pressed. On the other hand, the conventional methods
(b) anonymizes by adding and deleting links in order
to reduce the amount of link modification because the
amount of link modification is enormous.
In Tables 4 and 5, the reason why NA was ob-
tained for the results of conventional methods (a) and
(b) is that the sum of the anonymized degree sequence
is odd, and the anonymized graph cannot be con-
structed. In particular, conventional methods (a) and
(b) require anonymization of degree sequences while
minimizing the amount of modification so that all
nodes satisfy k-degree, which may result in unfeasible
degree sequences as graphs. In this respect, the pro-
posed method (C) can suppress the number of nodes
that are the main target of anonymization process and
can easily generate a feasible degree sequence.
In addition, the results of the link match rate
showed that as the value of the k value increases, the
link match rates decreased. The number of links that
match the original data before edge removal did not
change much as the value of k increases, even though
the number of edges increased. The reason why the
number of links increases as the value of the k value
increases is that the larger the k value, the higher
the anonymity required, the more nodes need to be
anonymized, and the amount of graph modification
increases.
In order to increase the utility of anonymized so-
cial network data with link prediction in the future,
it is necessary to increase the number of links that
match the original data before edge removal, such as
by preferentially selecting links that are more likely
to be present in the original data when adding links
during anonymization.
6 CONCLUSIONS
In this paper, assuming that the real data contains
missing data, we discussed an anonymity metric for
anonymization of social network data with link pre-
diction. We also applied the anonymization method
for social network data with link prediction to real
data and examined the utility.
The experimental results suggested that the pro-
posed anonymization method preserves more data
features than the application of conventional methods
in anonymized data with link prediction.
In the future, we will conduct utility studies on
other real data and safety evaluation, and investigate
better ways to anonymize SNS data through link pre-
diction.
ACKNOWLEDGEMENTS
This work was supported by JSPS KAKENHI Grant
Numbers JP21H03496, JP22K12157.
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