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Almost all real-world objects can be represented by a graph. Due to this reason, graph-based techniques are broadly utilized in numerous recommendation system applications such as network analysis, machine learning, and bioinformatics. Graphs show valuable connection information among the things. Graph data growth resulted (Valverde-Rebaza & de Andrade Lopes, 2013), (Zhang et al., 2020) a huge assortment of explicit issues which influences the Machine Learning community to make an effort to provide valuable information (Cai et al., 2021), which consist of node-based clustering (Zhang et al., 2007), graph generation (Malliaros & Vazirgiannis, 2013), influence maximization (Simonovsky & Komodakis, 2018) and link prediction. To address the link prediction problem, different methods such as path-based (Aziz, Gul, Uddin et al, 2020), random walk (Ayoub et al., 2020), higher-order (Curado, 2020), deep generative (Atarashi et al., 2020), and hyperbolic geometry (Wang et al., 2020) based methods are commonly used. In recent years, social networks have gain importance in daily life which gave rise to the challenge for researchers to analyze and mine social network data. Some sort of limitations exists in analyzing social network data. The primary issue is, incomplete information is presented in social networks which only covers some behavioral aspects. The secondary issue is the dynamic data i.e. information changes very rapidly. Therefore, to predict the future uncover and missing links is a great challenge in social networks. Both issues are notable as link prediction problems. Link prediction compromises new connections or unobserved collaborations [edges] between sets of nodes in view of detectable links and their properties (Kitsak et al., 2020). Link prediction has been effectively applied to predict new relationships in many domains like biological networks (Liben-Nowell & Kleinberg, 2007), social networks, etc. In social communities, link prediction is used for certain types of suggestions like friends, groups, products, etc. (Ahmed et al., 2018)(Gul et al., 2021). A complex network is the representation of a network in which we study the characteristics of a real-world network. Interaction among people is a basic element of the social complex networks. Networks can be expressed by a graph in which links show interaction and nodes represent by people or some others kinds of connection between people (Zhang et al., 2020) like common interests or friendship. These networks are the tone internet application of Linked In, Facebook, Twitter, and Amazon. In complex networks, too much attention is given to link prediction nowadays. The link prediction problem aims to evaluate the possibility of link occurrence between node pairs in a complex network, this evaluation is performed based on the reviewed links (Berg et al., 2017). Link prediction has been truly tended via graph mining heuristics, utilizing the development similitude indices among nodes, catching the probability of their association in the complex network. Alongside, expanding efforts in extending Deep Learning methodologies in graphs (Lü & Zhou, 2011), these methodologies have been surpassed by the node embedding model (Bruna et al., 2013). Concisely, the methodology is to arrange graph neural networks to speak to vertices as vectors in a low-dimensional vector space, particularly the embedding space. In such spaces, nodes with an auxiliary closeness in the complex network ought to be close to one another. In this manner, one can turn to surround estimates such as inner items among vector portrayals to hope for new unobserved edges in the primary graph. Link prediction can also predict the undetected non-network edges currently in the network. Similarly, the link prediction problem is employed to estimate which of the present network edge have been falsely predicted. The idea of the link prediction problem is very significant in various applications. Companies like Twitter, Facebook in order to understand the present state and to evaluate or anticipate the subsequent structure and shape of the societal networks, properly categorize the data using link prediction (Grover & Leskovec, 2016). In the biomedical field, the biologist evaluated that biochemical responses are affected by groups of enzymes or not. The obstruction in identifying either link exists truly, is that trying, discovering, and analyzing collaboration in the complex network need important observational work on the testing ground (Barzel & Barabási, 2013). Similarly analyzing experimentally where and when a new edge will be formed may likewise be unfeasible and particularly when the absolute methods for the edge creation are unobserved. Due to these multiple motives, this is very prominent to estimate design for the problem of edge prediction. Presently, there are various proposed methods for link mining in real-world complex networks (Clauset et al., 2008). Some researchers introduced link prediction techniques used to predict the formation of links more accurately compared to others. Networks give a significant abstraction for real-world complex systems by expressing the underlying set of pairwise interactions, but the abundance of the structure within these systems involved interactions that take place among more than a couple of nodes at once. While these higher-order interactions are omnipresent, an evaluation of the fundamental characteristics and structural principles in such systems is lacking. Here we study some data-sets from biology, medicine, social networks, and the web.