LPCNN: convolutional neural network for link prediction based on network structured features

TELKOMNIKA Telecommunication Computing Electronics and Control
Vol. 20, No. 6, December 2022, pp. 1214~1224
ISSN: 1693-6930, DOI: 10.12928/TELKOMNIKA.v20i6.22990  1214
Journal homepage: http://telkomnika.uad.ac.id
LPCNN: convolutional neural network for link prediction based
on network structured features
Asia Mahdi Naser Alzubaidi1
, Elham Mohammed Thabit A. Alsaadi2
1
Department of Computer Science, Faculty of Computer Science and Information Technology, University of Kerbala, Kerbala, Iraq
2
Department of Information Technology, Faculty of Computer Science and Information Technology, University of Kerbala, Kerbala, Iraq
Article Info ABSTRACT
Article history:
Received Jan 17, 2022
Revised Aug 24, 2022
Accepted Sep 03, 2022
In a social network (SN), link prediction (LP) is the process of estimating
whether a link will exist in the future. In prior LP papers, heuristics score
techniques were used. Recent state-of-the-art studies, like Wesfeiler-Lehman
neural machine (WLNM) and learning from subgraphs, embeddings, and
attributes for link prediction (SEAL), have demonstrated that heuristics
scores may increase LP model accuracy by employing deep learning and
sub-graphing techniques. WLNM and SEAL, on the other hand, have some
limitations and perform poorly in some kinds of SNs. The goal of this
research is to present a new framework for enhancing the effectiveness of LP
models throughout various types of social networks while overcoming the
constraints of earlier techniques. We present the link prediction based
convolutional neural network (LPCNN) framework, which uses deep
learning techniques to examine common neighbors and predict relations.
Adapts the LP task into an image classification issue and classifies the links
using a convolutional neural network. On 10 various types of real-work
networks, tested the suggested LP model and compared its performance to
heuristics and state-of-the-art approaches. Results revealed that our model
outperforms the other LP benchmark approaches with an average area under
curved (AUC) above 99%.
Keywords:
Convolutional neural network
Deep learning
Heuristic scores
Social network analysis
Structural information
This is an open access article under the CC BY-SA license.
Corresponding Author:
Asia Mahdi Naser Alzubaidi
Department of Computer Science, Faculty of Computer Science and Information Technology
University of Kerbala, Kerbala, Iraq
Email: asia.m@uokerbala.edu.iq
1. INTRODUCTION
Social networks are a common way of simulating user interactions in each community. It may be
shown as a social graph, with each node representing a network member and each edge signifying the sort of
interaction between involved individuals [1]. Link prediction (LP) is a subfield of social network analysis
that determines if two nodes in a network are more likely to link soon. LP can be applied in various domains
like knowledge graph completion, information retrieval to analyze the hyperlink structure of the web and
recommendation frameworks to propose modern companions or common interests, bioinformatics within the
think about of the protein-protein interaction network, connected examination, link analysis, and mining for
recognizing hidden criminals in terrorist networks and e-commerce to facilitate purchasing the value of the
customer by recommending products to consumers via over-targeting on past basis Purchase history and
general customer data [2].
Various heuristics methods were proposed in early research to handle the link prediction problem from
different areas, which finds proximity between potential nodes and predicts link presence based on the metrics.
In contrast, heuristic techniques performed well in other social networks, such as protein-protein interaction

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TELKOMNIKA Telecommun Comput El Control, Vol. 20, No. 6, December 2022: 1214-1224
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networks, where two proteins with many common neighbors have a low chance of interacting [3]. Recent
research proposes latent approaches for improving link prediction accuracy. Those techniques, on the other
hand, may be able to advance accuracy in certain sorts of social networks, but they fared worse in others than
the simple heuristics approach [4]. Generally, the probable LP task is mainly considered from two views:
structure-based prediction and features of nodes-based and edges-based prediction. Where network structure
indicates how the network’s nodes are organized fundamentally according to the popular notion that the more
similar a node pair is, the more likely they are to connect [5].
The LP also has been considered from the view of the learning-based that referred to features of
nodes in the graph followed machine learning approaches included decision tree, support vector machine
(SVM), Naïve Bayes, deep learning, convolutional neural network (CNN), graph neural network, and random
forest [6]. Despite improvements in prediction accuracy in similarity-based methods, balancing performance
and computational complexity for attributes-based metrics is difficult. A social network is fed into the
framework, which then analyses the data and makes predictions. Each step aims to address the limits of
existing methodologies and to solve them in a novel way [7], [8].
Earlier studies concentrated on utilizing topological features to generate similarity scores and predict
connections. Heuristics are the most basic and straightforward but effective techniques for the link prediction
task. It computes specific heuristic node similarity scores as the probability of influences [9]. Existing
heuristics, for example, maybe considered based on the number of neighbors that are necessary to compute
the score. First-order heuristics like common neighbors and preferred attachment only contain one-hop
neighbors of two chosen nodes. The common neighbor soundarajan hopcroft and cosine index are all first-order
heuristics. Adamic-Adar and resource allocation, on the other hand, are second-order heuristics because
they’re based on the target nodes up to two-hop proximity. In addition, high-order heuristic methods
frequently outperform low-order heuristic approaches, although they have a higher computational cost.
Because numerous heuristic techniques have been developed to handle various graphs, finding a suitable
heuristic approach becomes a difficult task [10]. Also, extended weighted common neighbors (EWCN),
extended weighted Adamic-Adar (EWAA), extended weighted Jaccard coefficient (EWJC), and extended
weighted preferential attachment (EWPA) are used in [11]. Furthermore, experiments employing well-known
classification methods such as the J48 decision tree, weighted SVM, Gboost, Naïve Bayes, random forest,
logistic regression, and extreme gradient boosting (XGBoost) showed that the expanded metrics considerably
improved the output of all supervised approaches in every validation dataset. Furthermore, the underlying
difficulty with heuristic techniques is that they do not function consistently across networks since they rely
on derived characteristics from network topology, which varies from one social network to the next.
Based on node embeddings, the similarity between pairs of nodes may also be calculated using node
embeddings. As a result, embedding algorithms that can learn node features from network topology have
been employed to resolve the LP issue; notable approaches in this line include matrix factorization and
stochastic block modeling (SBM) [12]. SBM, on the other hand, is computationally costly and only works on
specific types of social networks. Social representation of a graph’s nodes, via modeling a stream of short
random walks (DeepWalk) [13], large-scale information network embedding (LINE) [14], and node to vector
representation (node2vec) [15] have been proposed as approaches for learning node embedding utilize the
skip-gram approach that inspired from world embedding method used in natural language processing.
The variational graph auto-encoder (VGAE) is an unsupervised learning model that employed the variational
auto-encoder to analyze the pattern of graph structure data [16]. Latent techniques may learn useful features
from the graph and hence perform well in the LP challenge. However, if the graph gets exceedingly sparse,
the efficiency of the node link prediction based on embedding approaches may suffer.
Deep learning (DL), a novel way in machine learning, has been recently depicted in the literature.
DL was used for learning the distribution of associates from a graph and developed to overcome the
limitations of heuristic methods. One issue with traditional deep learning models is that the input is
distributed independently and equally, which makes it unable to represent relational data. To address this
issue, a bayesian deep learning framework that successfully learns relational data are suggested [17].
Predicting links by analyzing common neighbors (PLACN) a methodology based on convolutional neural
networks is introduced and compared their technique to the state-of-the-art method, achieving 96% area
under curve (AUC) in the benchmark [18]. Because of its accuracy, a subgraph technique known as
Weisfeiler-Lehman neural machine (WLNM) was recently designated as a state-of-the-art link prediction
method [19]. To attain significant accuracy, the WLNM utilized high-order algorithms like the Katz index
and PageRank. This, on the other hand, necessitates many hops from the enclosing subgraph to the complete
network, as well as additional calculation of time and memory. To address this issue, learning from subgraphs,
embeddings, and attributes for link prediction (SEAL) presented a way to learn general graph structure features
from local enclosing subgraphs using graph neural networks [20]. They computed first-order, second order, and
high-order heuristic scores to create a vector of the feature. The authors used the double-radius technique to

TELKOMNIKA Telecommun Comput El Control 
LPCNN: convolutional neural network for link prediction based on … (Asia Mahdi Naser Alzubaidi)
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organize nodes. Lastly, to categorize links, graph neural networks, the adjacency matrix, and the latent vector
are employed. The SEAL model yields state-of-the-art performance for the link prediction issue due to the
exceptional learning of graph neural networks. Determining an appropriate hop number for a given network,
on the other hand, is a trial-and-error process, and putting all neighbor nodes in the subgraph raises the issue
that hub nodes have many neighbors even at low hop numbers. Another issue with SEAL is that pooling
layers miss topological information, and graph convolution layers fail to learn edge embeddings.
People communicate with one another through social media apps. The graph theory concept can be
used to solve the problem of link prediction, which is a recent research approach. A social network is
represented as a graph G (V, E) at any given time, where V and E are sets of nodes and links respectively.
The goal of link prediction is to predict the missing or undetected links in the existing network, as well as
future or removed connections between nodes for a period t' in the future. A potential link prediction task can
be described by a simple social network to show the evolution of links as depicted in Figure 1, where solid
links represent previously existing connections and dotted links indicate links that have recently arisen due to
link classification algorithms.
Figure 1. An example of link prediction
Social networks are extremely dynamic objects in reality; they expand and evolve over time as a
result of the addition of new edges, which represent the emergence of new interactions in the underlying
social structure. For example, in the case of Facebook, with their “friend discoverer” merit, they can also
recommend the user you might be interested in and the relationship may lead to a real-life friendship that will
enhance both parties’ commitment to the Facebook service. In the research community, the issue of link
prediction has gained a lot of interest. However, researchers mostly focused on making predictions about
how a social network may expand by including new ties. In other words, the majority of earlier studies on
link prediction either restricted their research to the prediction of links that will be added to the network
during the period from the present time to a specific future time or implicitly devoted the link prediction to
specific domains like co-authorship. This manuscript makes the following contributions:
1) To find a novel LP approach that can learn how to optimally combine heuristic scores to improve the
performance of the LP model in any network and not only in a size and type of network.
2) Create feature adjacency matrices as layers for a specific social network to obtain evidence about
targeted nodes and common neighbors. We use a total of eight heuristic features, such as the Jaccard
index, the Adar index, resource allocation, preferential attachment, and others.
3) The LP problem may be transformed into an image classification problem by using CNN to train and
classify the positive and negative links.
The rest of the paper is organized as: section 2 specifies the link prediction framework. the experimental
data and analyses are then presented in section 3. Finally, in section 4, we offer some concluding remarks and
suggestions for further works.
2. METHOD
In network analysis, link prediction is a major study area. In recent years, new strategies based on
graph features have emerged as effective methods for determining heuristic scores. The heuristic’s score is
directly utilized to rank node pairings. They can also be used for supervised prediction by combining them
with a classifier and using some or all of them as features. We combine all heuristics with a convolution
neural network in this paper. This method of supervision has been proved to produce the best results. In this
part, we want to get a better understanding of the mechanics underlying various link prediction heuristics
metrics, therefore encouraging the notion of learning heuristics from graphs.

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2.1. Heuristic methods
Heuristic link prediction approaches are often based on topological structures, which can be
node-based, neighbor-based and path-based, or random walk-based. Neighbor-based heuristic approaches
include Jaccard coefficient, Adamic-Adar coefficient, preferential attachment, and resource allocation, while
additional topological heuristic methods, also referred to as higher-order heuristic methods, include Katz index,
PageRank, and simRank. Path-based metrics take into account more topological information than node-based
and neighbor-based metrics, which solely employ local topological information. These metrics take into
account paths between node pairs in addition to local neighbors and other significant global information.
Path-based metrics have a larger time complexity than neighbor-based ones. However, longer links aren’t
necessarily better than shorter ones. Longer paths should only be taken into account in the theoretical basis of
well-known link prediction heuristics metrics if shorter paths are insufficiently common. As a result, if networks
contain enough shorter paths, path-based metrics can improve their performances by omitting excessively long
paths. In our model, we solely examine the neighbor-based heuristic approaches as listed below.
2.1.1. Jaccard’s coefficient (JC)
We shall utilize the Jaccard coefficient to compute the similarity of node pairs in unweighted
networks in this paper. For an arbitrarily selection attribute that may be 𝑋 or 𝑌, this method calculates the
probability that both 𝑋 and 𝑌 have it. This metric solves the problem of two nodes having more different
neighbors (𝛤) simply because they have a lot of neighbors and are closely connected [21].
𝑆𝐽𝐶(𝑋, 𝑌) = |𝛤(𝑋) ∩ 𝛤(𝑌)| |𝛤(𝑋) ∪ 𝛤(𝑌)|
⁄ (1)
2.1.2. Cosine (Salton) index (CI)
The Salton similarity is strongly connected to the Jaccard index, but it generates a value that is
approximately double that of the Jaccard index. This approach would perform the vector multiplication for
each pair of nodes with common neighbors.
𝑆𝐶𝐼(𝑋, 𝑌) =
𝛤(𝑋)|𝛤(𝑌)
‖𝛤(𝑋)‖×‖𝛤(𝑌)‖
(2)
2.1.3. Adamic-Adar (AA)
Adamic Adar index used to rank features based on their logarithm and uses these features to
measure the prediction scores. This metric can be understood in a real-world social network as: if a common
neighbor of two nodes has more friends, they are less likely to expose the two nodes to each other than if they
have just a few friends [22].
𝑆𝐴𝐴(𝑋, 𝑌) = ∑
1
𝑙𝑜𝑔|𝛤(𝑍)|
𝑍∈𝛤(𝑋)∩𝛤(𝑌) (3)
Where 𝑍 represents the common neighbors between 𝑋 and 𝑌.
2.1.4. Resource allocation (RA)
This index is somewhat like Adamic-Adar, but it does not use the logarithm function, which
decreases the influence of nodes to a large degree. Since these nodes are linked to so many other nodes in the
graph, they have little insight for relation prediction[23].
𝑆𝑅𝐴(𝑋, 𝑌) = ∑
1
|𝛤(𝑍)|
𝑍∈𝛤(𝑋)∩𝛤(𝑌) (4)
2.1.5. Preferential attachment (PA)
The PA was chosen as a prediction technique since a node with a high score is more likely to get
new connections. This index is a fundamental prediction tool that is commonly used as a baseline to assess
the efficiency of other prediction approaches. Rather than only the neighboring nodes, it computes a
similarity score for each pair of nodes in the network [24].
𝑆𝑃𝐴(𝑋, 𝑌) = 𝛤(𝑋) × 𝛤(𝑌) (5)
2.1.6. SimRank (SR)
The SR is based on the notion that two nodes are similar if their neighbors are similar as well.
SimRank of two nodes (𝑋, 𝑌) is recursively computed as:

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𝑆𝑆𝑅(𝑋, 𝑌) = 𝐶
∑ ∑ 𝑆𝑆𝑖𝑚𝑅𝑖𝑛𝑘(𝑍,𝑍′)
𝑍′𝛤(𝑌)
𝑍∈𝛤(𝑋)
𝑘𝑋.𝑘𝑌
(6)
Where 𝑍 is the set of neighbors of node 𝑋 and Z′
is the set of neighbors of node 𝑌. 𝐶 ∈ [0 … 1] is the decay
factor [25].
2.1.7. PageRank (PR)
The stationary distribution of a random walker starts at 𝑋 and iteratively moves to a random
neighbor of its current position with probability α or return to 𝑋 with probability 1 − 𝛼 calculated by the
PageRank of node 𝑋.
𝑆𝑃𝑅(𝑋) = ∑
𝑃𝑅(𝑣)
𝐿(𝑣)
𝑋∈𝐵𝑣 (7)
The PageRank value for a node 𝑣 can be calculated by dividing the PageRank of each node 𝑋 in the set 𝐵𝑣 to
the number 𝐿(𝑣) of links from node 𝑣 [26].
2.1.8. Katz index (KI)
Katz centrality calculates a node’s relative influence in a network by counting its direct neighbors
and all other nodes in the network that are connected to it through these common neighbors. Influences made
with distant neighbors are, however, penalized by an attenuation factor 𝛼. Each link between a pair of nodes
is assigned a weight value determined by α and the distance between nodes as 𝛼𝐾
.
𝑆𝐾𝑇(𝑋) = ∑ ∑ 𝛼𝐾
(𝐴𝐾
𝑌=1
𝐾=1 )𝑌𝑋 (8)
Where the element at location (𝑋, 𝑌) of the adjacency matrix 𝐴 raised to the power 𝑘 (i.e. 𝐴^{𝐾}) reflects the
total number of 𝑘 degree connections between nodes 𝑋 and 𝑌 [27].
2.2. Research method
The suggested framework termed link prediction based convolutional neural network (LPCNN)
attempts to improve the efficiency of LP models in social networks by studying the common neighbors of
targeted nodes. The LPCNN model also aims to create a methodology that can adjust to any size and sort of
social network and automate the learning of the optimal combination of heuristics scores for that networks.
LPCNN proposed a new model that combines heuristic features to generate adjacency matrices and then
classifies the positive and negative links using CNN. The LPCNN model uses the feature of CNN, which is
greatest identified for image classification, to map the link prediction task into an image classification issue.
Another reason is that earlier studies only looked at targeted nodes for LP, but our technique looks at
common neighbors between targeted nodes as well. Figure 2 depicts the LPCNN model’s architecture as well
as the link prediction process stages.
Figure 2. The Architecture of LPCNN for link prediction model

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(a) (b)
(c) (d)
(e) (f)
(g) (h)
Figure 3. The eight selected heuristic scores as adjacency matrices where (a) Adamic-Adar, (b) Jaccard’s
coefficient, (c) preferential attachment, (d) resource allocation, (e) cosine index, (f) SimRank index,
(g) Katz index, and (h) PageRank adjacency matrix

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To begin, social network visualization as a graph representation for the original, training, and testing
datasets are investigated by modeling the links between each pair of nodes. To construct the feature
adjacency matrices, the proposed LPCNN framework takes a given network as input and creates dataset of
start and goal nodes with the labels for positive link class (a link that will occur soon) and negative link class
(a link that will not appear soon). Each feature adjacency matrix of the training and testing graphs can be
represented as 𝐴𝑖,𝑗
𝐾𝑇
, 𝐴𝑖,𝑗
𝑃𝑅
, 𝐴𝑖,𝑗
𝐶𝐼
, 𝐴𝑖,𝑗
𝐴𝐴
, 𝐴𝑖,𝑗
𝐽𝐶
, 𝐴𝑖,𝑗
𝑃𝐴
, and 𝐴𝑖,𝑗
𝑆𝑅
where (𝑖, 𝑗) in range of (1: 𝐾) and ordered in the
sequence of each of the heuristic methods. Our LPCNN framework tends to improve the accurateness of link
prediction by analyzing common neighbors between targeted nodes.
To evaluate nodes and their relationships with the goal node, we must compute the features of
common nodes. Heuristic scores are similarity ratings that quantify the degree to which two nodes are
similar. In the past, researchers produced different heuristic scores between just specified nodes and
attempted to estimate the links based on the results. Some heuristic scores outperformed others in certain
types of social networks. A heuristic score combination surpassed a single heuristic score. As first-order
techniques, the suggested LP model takes into account eight distinct heuristic scores such as Jaccard’s
coefficient, cosine score, and preferential attachment. While resource allocation, Adamic Adar index, and
Katz index are second-order approaches, and PageRank, SimRank index, and SimRank are high-order
methods. Heuristics scores indicated above are obtained for all nodes in training and testing graphs. Each
heuristic method used to construct feature adjacency matrix then eight feature adjacency matrices will be
stacked by using eight scores. The final feature matrix will be 𝑁 × 𝐾 × 𝐾 × 8 in size for each score, where 𝑁
is the size of training and testing datasets and 𝐾 is the size of the image. They’re also symmetric, and
diagonal values are 0 because they represent nodes that link to one other.
CNN is well-known for its ability to classify images. To tackle the LP problem, we use CNN’s
features. By generating feature matrices with different heuristic scores, our LPCNN model changes the LP
issue into an image classification task. Images have three channels, red, green, and blue (RGB) are handled
as a three-dimensional matrix while the constructed feature adjacency matrices are 𝑁 × 𝐾 × 𝐾 images with 8
channels and 𝐾 = 32. Figure 3 showed eight selected heuristic scores as image from adjacency matrices
where Figure 3(a) Adamic-Adar, Figure 3(b) Jaccard’s coefficient, Figure 3(c) preferential attachment,
Figure 3(d) resource allocation, Figure 3(e) cosine index, Figure 3(f) SimRank index, Figure 3(g) Katz index,
and Figure 3(h) PageRank.
We train CNN to distinguish between two types of links: positive and negative. Backpropagation
with loss function is used to optimize a neural network during training. The loss function is different
depending on the problem. We choose binary cross-entropy as the loss function and area AUC as the CNN
monitor because this is a binary classification task.
Figure 4. The convolution neural network configurations
To perform classification, CNN has multiple layers. The input layer is the primary layer, followed
by one or more convolutional hidden layers and pooling layers. Finally, there are one or more dense layers
and an output layer. The convolutional layer is distinct because it collects information from input matrices.
The activation mapping describes how the neurons in this layer are organized in two-dimensional arrays.
The kernel is a three-dimensional array that holds the weights. For different input sizes, the height, width,
and depth can be modified. Even for the identical input matrix, several kernels of various sizes can exist.
Kernel develops a series of activation maps by sliding through the input matrix. Figure 4 shows the CNN
layers and their parameters in detail.

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3. RESULTS AND DISCUSSION
The suggested LP model (LPCNN) aims to fit different networks while also increasing the link
prediction model’s efficiency. We utilized 80% of the data set to train the model and 20% to test it over 150
epochs. After training, we loaded the best model and reviewed the results. Running the LP model five times
and selecting the average result of AUC as the best-given prediction model.
We conduct tests using real-world networks to evaluate the proposed model, and we use the area
under curve-receiver operating characteristics (AUC-ROC) as the assessment metric. A ROC curve is a graph
that shows the probability of true positive rate and false positive rate at various threshold settings. The AUC
reflects a model’s level of distinction. The AUC value varies between 0 and 1. When the AUC reaches one,
the model can predict positive classes as positive and negative classes as negative. A larger AUC implies that
the supplied model is not making random predictions and has been trained to find a pattern to classify
the missing links.
In our LP model we not relied on calculating the time complexity of the proposed model, because
the methods that were compared with did not calculated the time complexity, and most of used networks are
not very large scale in size. By dividing links into two classes, the positive class, and the negative class, our
approach handles link prediction as a binary classification problem. The positive class indicates that the given
link will be available in the future, whereas the negative class indicates that the link will not be available
soon.
3.1. Real-world datasets
We compare the proposed missing link prediction model with state-of-the-art methodologies using
ten diverse kinds of real-world network datasets from diverse locations and sizes. All the datasets are freely
available on the internet. Table 1 lists the datasets that have been tested, with |𝑉| and |𝐸| representing the
number of nodes and edges respectively, < 𝑘 > representing the average degree, and 𝐶𝐶 representing the
clustering coefficient.
Table 1. The Basic topological features of the networks
# Datasets Size < 𝐾 > < 𝐶𝐶 > Type
|𝑉| |𝐸|
1. NSC 1461 2742 3.7536 0.694 Co-authorship
2. Yeast 2375 11693 9.8467 0.306 Biology network
3. Power 4941 6594 2.6691 0.080 Electrical grid network
4. PB 1222 16714 27.3552 0.320 US political
5. Router 5022 6258 2.4922 0.012 Internet routing
6. E.coli 1805 14660 16.2438 0.516 Pairwise reaction
7. Facebook 4039 88234 43.6910 0.606 Friendship network
8. Wikipedia 4777 92517 38.6879 0.359 Online encyclopedia
9. PPI 3890 38739 19.9172 0.146 Protein-protein interactions
10. USAir 332 2126 12.8072 0.625 Transportation dataset
3.2. Results and analysis
We compare our LP model (LPCNN) against the state-of-the-art methods: WLNM and SEAL.
To evaluate the LPCNN model, experimental and analysis the results are conducted. Our proposed
framework provides efficient model for link prediction and delivers a best performance at variety of
networks. Table 2 depicted the results of AUC. We compared LPCCN’s performance to first-order heuristics
methods like common neighbors, Jaccard coefficient, cosine index, and preferential attachment, second-order
heuristics like Adamic Adar and resource allocation, high-order heuristics like Katz and PageRank, and
finally, state-of-the-art methods like WLNM and SEAL. Figure 5 is the chart plot of the average AUC score
of all used methods on five test runs on each dataset.
Some global indices such as SimRank and Katz index are not performing well and displaying lower
performance than most of the other heuristic approaches. Regardless of whether intra-dominant or
inter-dominant, similarity indices better as the structural gap between intra-connection and inter-connection
expands. However, in inter-dominant structures, several global indices such as Katz index perform poorly.
The number of paths between node pairs is the basis for these indices. Due to the decay factor of these
indices, connected pairs have a larger similarity than unconnected pairs. As a result, in the inter-dominant
condition, there are more node pairs of different types with higher similarity, which results in subpar
performances. However, heuristic scores such as PageRank and Adamic-Adar exhibit great performance
when compared to other heuristics that show similar results. Moreover, most of heuristics techniques perform
worse than the state-of-the-art subgraphing methods WLNM and SEAL.

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We can see that our LPCNN model outperforms all other approaches and has superior graph feature
learning ability overall heuristics and subgraphing methods. This means that discovering and concatenating
new heuristics scores for networks to catch more and more of their structural properties and utilizing them in
the learning classifier where no existing heuristics work can improve model performance dramatically.
Furthermore, due to the range of network sizes, the experimental results of similarity-based link prediction
revealed that slight variances in overall AUC values, such as those found in the USAir dataset, do not always
imply low predictability for that dataset. Because the AUC is based on the precision-recall curve, predicting a
larger number of links increases the danger of false positives, as the number of new links generated by a
network may not keep up with its growth. Furthermore, because they are built manually, existing LP
algorithms based on similarity are unable to properly represent several non-linear modes that play a critical
role in the LP network.
Table 2. Comparison of AUC with state-of-art and heuristic methods
Dataset JC CI AA RA PA SR PR KT WLMN SEAL LPCNN
NSC 94.43 95.55 94.45 94.45 68.65 94.79 94.89 94.85 98.61 98.85 99.03
Yeast 89.32 89.20 89.43 89.45 82.20 91.49 92.76 92.24 95.62 97.91 99.67
Power 58.79 60.37 58.79 58.79 44.33 76.15 66.00 65.39 84.76 87.61 99.56
PB 87.41 85.64 92.36 92.46 90.14 77.08 93.54 92.92 93.49 94.72 98.83
Router 56.40 56.4 56.43 56.43 47.58 37.40 38.76 38.62 94.41 96.38 99.31
E.coli 80.19 84.538 86.95 87.49 74.79 77.07 90.32 86.34 97.21 97.64 99.70
Facebook 98.56 98.62 98.88 8.929 83.09 96.31 96.31 98.93 99.24 99.40 99.65
Wikipedia 40.75 47.19 90.46 91.63 91.70 28.64 96.31 50.0 99.05 99.63 99.76
PPI 81.42 81.36 83.57 83.53 89.42 82.70 50.0 50.0 88.79 93.52 99.44
USAir 89.79 88.619 95.06 95.77 88.84 78.89 94.67 92.88 95.95 96.62 95.73
Average 77.706 78.749 84.638 75.893 76.074 74.052 81.356 76.217 94.713 96.23 99.068
Although the shallow neural network-based LP technique may make effective use of the network
nodes’ potential features, it cannot capture the deeply non-linear attributes such as link structural features.
Because of their excellent attribute learning capacity, CNNs can capture deeply non-linear data and learn
more valuable features, improving LP model output. As a result, we predict the missing link using a deep
CNN. In general, the research results show that our model can successfully capture the most relevant missing
LP information in many situations, implying that combining the power of eight different types of heuristic
attributes with CNN learning can result in significantly better model performance than subgraphing methods.
Figure 5. The average AUC score of all methods
4. CONCLUSION
The goal of link prediction is to discover missing links in a network and predicate the future links.
Link prediction attracted the interest from a variety of scientific disciplines as a key research issue in
complex network analysis. Heuristics-based methods have gained the majority among diverse approaches
due to their minimal complexity and excellent interpretability.

 ISSN: 1693-6930
10
In this paper, we implemented extended feature extraction and generated eight different heuristics
feature matrices. These features provide our framework autonomy in learning and adopting the topological
patterns of diverse networks. LPCNN transforms the link prediction problem into an image classification
problem, which CNN then classifies. Our model outperforms both state-of-the-art and the heuristic baseline
approaches, according to AUC metric. However, we should agree that assessing associates using heuristics
scores as features in the learning model is a reliable way to differentiate between the test and non-existent
node edges. The goal of future research will be to improve node association predictions. By extracting and
adding additional node features to the model instead of graph structure attributes may assist in improve the
performance because it adds more information. Our methodology also opens new avenues for study into
recommendation systems and knowledge graph completion.
REFERENCES
[1] M. A. Hasan and M. J. Zaki, “A Survey of Link Prediction in Social Network,” Social Network Data Analytics, pp. 243–275,
2011, doi: 10.1007/978-1-4419-8462-3_9.
[2] N. Barbieri, F. Bonchi, and G. Manco, “Who to follow and why: link prediction with explanations,” in Proc. of the 20th ACM
SIGKDD International Conference on Knowledge Discovery and Data Mining, 2014, pp. 1266–1275,
doi: 10.1145/2623330.2623733.
[3] L. Cai, J. Li, J. Wang, and S. Ji, “Line Graph Neural Networks for Link Prediction,” IEEE Transactions on Pattern Analysis and
Machine Intelligence, vol. 44, no. 9, pp. 5103-5113, 2022 doi: 10.1109/TPAMI.2021.3080635.
[4] P. M. Chuan, C. N. Giap, L. H. Son, C. Bhatt, and T. D. Khang, “Enhance link prediction in online social networks using
similarity metrics, sampling, and classification,” Information Systems Design and Intelligent Applications, vol. 672, pp. 823-833,
2018, doi: 10.1007/978-981-10-7512-4_81.
[5] S. Fu, W. Liu, K. Zhang, Y. Zhou, and D. Tao, “Semi-supervised classification by graph p-Laplacian convolutional networks,”
Information Sciences, vol. 560, pp. 92–106, 2021, doi: 10.1016/j.ins.2021.01.075.
[6] F. Gao, K. Musial, C. Cooper, and S. Tsoka, “Link prediction methods and their accuracy for different social networks and
network metrics,” Scientific Programming, vol. 2015, 2015, doi: 10.1155/2015/172879.
[7] S. Gaucher, O. Klopp, and G. Robin, “Outlier detection in networks with missing links,” Computational Statistics and Data
Analysis, vol. 164, 2021, doi: 10.1016/j.csda.2021.107308.
[8] A. Gupta and Y. Raghav, “Deep Learning Roles based Approach to Link Prediction in Networks,” Computer Science and
Information Technology (CS & IT), pp. 203–222, 2020, doi: 10.5121/csit.2020.101416.
[9] D. L. -Nowell and J. Kleinberg, “The link-prediction problem for social networks,” Journal of the American Society for
Information Science and Technology, vol. 58, no. 7, pp. 1019–1031, 2007, doi: 10.1002/asi.20591.
[10] L. Lu and T. Zhou, “Link prediction in complex networks: A survey,” Physica A: Statistical Mechanics and its Applications,
vol. 390, no. 6, pp. 1150–1170, 2011, doi: 10.1016/j.physa.2010.11.027.
[11] X. Li, N. Du, H. Li, K. Li, J. Gao, and A. Zhang, “A deep learning approach to link prediction in dynamic networks,” in Proc. of
the 2014 SIAM International Conference on Data Mining (SDM), 2014, pp. 289–297, doi: 10.1137/1.9781611973440.33.
[12] J. Qiu, Y. Dong, H. Ma, J. Li, K. Wang, and J. Tang, “Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE,
PTE, and node2vec,” in Proc. of the Eleventh ACM International Conference on Web Search and Data Mining, 2018,
pp. 459–467, 2018, doi:10.1145/3159652.3159706.
[13] B. Perozzi, R. Al-Rfou, and S. Skiena, “DeepWalk: Online learning of social representations,” in Proc. of the 20th ACM SIGKDD
international conference on Knowledge discovery and data mining, pp. 701–710, Aug. 2014, doi: 10.1145/2623330.2623732.
[14] J. Tang, M. Qu, M. Wang, M. Zhang, J. Yan, and Q. Mei, “LINE: Large-scale Information Network Embedding,” in Proc. of the
24th International Conference on World Wide Web, 2015, pp. 1067–1077, doi: 10.1145/2736277.2741093.
[15] K. Prajapati, H. Shah, and R. Mehta, “A survey of link prediction in social network using deep learning approach” International
Journal of Scientific and Technology Research, vol. 9, no. 4, pp. 2540–2543, 2020. [Online]. Available: http://www.ijstr.org/final-
print/apr2020/A-Survey-Of-Link-Prediction-In-Social-Network-Using-Deep-Learning-Approach.pdf
[16] K. Narang, K. Lerman, and P. Kumaraguru, “Network flows and the link prediction problem,” in Proc. of the 7th Workshop on
Social Network Mining and Analysis, 2013, no. 3, pp. 1-8, doi: 10.1145/2501025.2501031.
[17] H. Wang, X. Shi, and D. -Y. Yeung, “Relational deep learning: A deep latent variable model for link prediction,” in Proc. of the
Thirty-First AAAI Conference on Artificial Intelligence (AAAI-17), 2017, vol. 31, no. 1, pp. 2688–2694,
doi: 10.1609/aaai.v31i1.10805.
[18] K. Ragunathan, K. Selvarajah, and Z. Kobti, “Link prediction by analyzing common neighbors based subgraphs using
convolutional neural network,” Frontiers in Artificial Intelligence and Applications, vol. 325, pp. 1906–1913, 2020,
doi: 10.3233/FAIA200308.
[19] M. Zhang and Y. Chen, “Weisfeiler-lehman neural machine for link prediction,” in Proc. of the ACM SIGKDD International
Conference on Knowledge Discovery and Data Mining, 2017, pp. 575–583. [Online]. Available:
https://muhanzhang.github.io/papers/KDD_2017.pdf
[20] M. Zhang and Y. Chen, “Link prediction based on graph neural networks,” in 32nd Conference on Neural Information Processing
Systems (NeurIPS 2018), 2018, pp. 5165–5175. [Online]. Available: https://proceedings.neurips.cc/paper/2018/file/
53f0d7c537d99b3824f0f99d62ea2428-Paper.pdf
[21] P. Srilatha and R. Manjula, “Similarity index based link prediction algorithms in social networks: A survey,” Journal of
Telecommunications and Information Technology, pp. 87–94, 2016. [Online]. Available:
https://core.ac.uk/download/pdf/235205592.pdf
[22] S. A. Fadaee and M. A. Haeri, “Classification using link prediction,” Neurocomputing, vol. 359, pp. 395–407, 2019,
doi: 10.1016/j.neucom.2019.06.026.
[23] Y. Xiao, R. Li, X. Lu, and Y. Liu, “Link prediction based on feature representation and fusion,” Information Sciences, vol. 548,
pp. 1–17, 2021, doi: 10.1016/j.ins.2020.09.039.
[24] P. Wang, B. Xu, Y. Wu, and X. Zhou, “Link Prediction in Social Networks: the State-of-the-art,” Science China Information
Sciences, vol. 58, pp. 1–38, 2015, doi: 10.1007/s11432-014-5237-y.

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[25] R. Guns, “Link Prediction,” in Measuring scholarly impact, Springer, 2018, pp. 35-55, doi: 10.1007/978-3-319-10377-8_2.
[26] L. Yao, L. Wang, L. Pan, and K. Yao, “Link Prediction Based on Common-Neighbors for Dynamic Social Network,” Procedia
Computer Science, vol. 83, pp. 82–89, 2016, doi: 10.1016/j.procs.2016.04.102.
[27] I. Ahmad, M. U. Akhtar, S. Noor, and A. Shahnaz, “Missing Link Prediction using Common Neighbor and Centrality based
Parameterized Algorithm,” Scientific Reports, vol. 10, no. 364, 2020, doi: 10.1038/s41598-019-57304-y.
BIOGRAPHIES OF AUTHORS
Asia Mahdi Naser Alzubaidi received the BSc degree in computer science from
the University of Babylon, Hilla, Iraq, and the master’s degree in computer science/ Artificial
Intelligence. The Ph.D from College of Information Technology at Babylon University-Iraq.
She is currently an Assist Professor in Department of computer science, College of Computer
Science & Information Technology, University of Kerbala. Her current research interests
include Data Mining, Computer Vision, Natural Language Processing, and Custermer Churn
Prediction. She can be contacted at email: asia.m@uokerbala.edu.iq.
Elham Mohammed Thabit A. Alsaadi received the BSc. in Computer Scince
from Al-Mustansiriya University -Iraq, MSc. in Real Time Systems from UK. PhD. from
College of Information Technology at Babylon University-Iraq. She is a lecturer in College of
Computer Science & Information Technology, Karbala University. Her research interests
include: Artificial Intelligence, Computer Vision, Image Processing, Database, System
Analysis, and E- business. She can be contacted at email: elham.thabit@uokerbala.edu.iq.

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