Link Prediction Based on Weight Assignments in Complex Networks

Link prediction algorithms in complex networks, such as social networks, biological networks, drug-drug interactions, communication networks, and so on, assign scores to predict potential links between two nodes. Link prediction (LP) enables researchers to learn unknown, new as well as future interactions among the entities being modeled in the complex networks. In addition to measures like degree distribution, clustering coefficient, centrality, etc., another metric to characterize structural properties is network assortativity which measures the tendency of nodes to connect with similar nodes. In this paper, we explore metrics that effectively predict the links based on the assortativity profiles of the complex networks. To this end, we first propose an approach that generates networks of varying assortativity levels and utilize three sets of link prediction models combining the similarity of neighborhoods and preferential attachment. We carry out experiments to study the LP accuracy (measured in terms of area under the precision-recall curve) of the link predictors individually and in combination with other baseline measures. Our analysis shows that link prediction models that explore a large neighborhood around nodes of interest, such as CH2-L2 and CH2-L3, perform consistently for assortative as well as disassortative networks. While common neighbor-based local measures are effective for assortative networks, our proposed combination of common neighbors with node degree is a good choice for the LP metric in disassortative networks. We discuss how this analysis helps achieve the best-parameterized combination of link prediction models and its significance in the context of link prediction from incomplete social and biological network data.

Link prediction is one of the most important and challenging tasks in complex network analysis, which aims to predict the existence of unknown links based on the known information in the network. As critical topological properties in the network, node’s degree and clustering coefficient are well-suited for describing the tightness of connection between nodes. The importance of node can affect the possibility of link existence to a certain extent. By analyzing the impact of different centrality on links, which concluded that the degree centrality and proximity centrality have the greatest influence on network link prediction. A link prediction algorithm combines importance of node and network topological properties, called DCCLP, is proposed in this paper, the symmetry of the adjacency matrix is considered in the DCCLP link prediction algorithm to further describe the structural similarity of network nodes. In the training phase of the DCCLP algorithm, the maximized AUC indicator in the training set as the objective, and the optimal parameters are estimated by utilizing the White Shark Optimization algorithm. Then the prediction accuracy of the DCCLP algorithm is evaluated in the test set. By experimenting on twenty-one networks with different scales, and comparing with existing algorithms, the experimental results show that the effectiveness and feasibility of DCCLP algorithm, and further illustrate the importance of the degree centrality of node pairs and proximity centrality of nodes to improve the prediction accuracy of link prediction.

Ranking influential nodes in complex network using edge weight degree based shell decomposition

Networks are mathematical structures that are universally used to describe a large variety of complex systems, such as social, biological, and technological systems. The prediction of missing links in incomplete complex networks aims to estimate the likelihood of the existence of a link between a pair of nodes. Various topological features of networks have been applied to develop link prediction methods. However, the exploration of features of links is still limited. In this paper, we demonstrate the power of node and link clustering information in predicting top -L missing links. In the existing literature, link prediction algorithms have only been tested on small-scale and middle-scale networks. The network scale factor has not attracted the same level of attention. In our experiments, we test the proposed method on three groups of networks. For small-scale networks, since the structures are not very complex, advanced methods cannot perform significantly better than classical methods. For middle-scale networks, the proposed index, combining both node and link clustering information, starts to demonstrate its advantages. In many networks, combining both node and link clustering information can improve the link prediction accuracy a great deal. Large-scale networks with more than 100 000 links have rarely been tested previously. Our experiments on three large-scale networks show that local clustering information based methods outperform other methods, and link clustering information can further improve the accuracy of node clustering information based methods, in particular for networks with a broad distribution of the link clustering coefficient.

Influential nodes refer to the ability of a node to spread information in complex networks. Identifying influential nodes is an important problem in complex networks which plays a key role in many applications such as rumor controlling, virus spreading, viral market advertising, research paper views, and citations. Basic measures like degree centrality, betweenness centrality, closeness centrality are identifying influential nodes but they are incapable of largescale networks due to time complexity issues. Chen et al. [1] proposed semi-local centrality, which is reducing computation complexity and finding influential nodes in the network. Recently Yang et al. 2020 [2] proposed a novel centrality measure based on degree and clustering coefficient for identifying the influential nodes. Sanjay et al. 2020 [3] gave voterank and neighborhood coreness-based algorithms for finding the influenced nodes in the network. Zhiwei et al. 2019 [4] considered the average shortest path to discover the influenced node in the network. These are the few recent local,global and mixed centralities. In this paper, we show a broad view of recent methods for finding influential nodes in complex networks. It also analyzes the new challenges and limitations for a better understanding of each method in detail. The experimental results based on these methods show better performance compared with existing basic centrality measures.

Link prediction is a very important field in network science with various emerging algorithms, the goal of which is to estimate the presence or absence of an edge in the network. Depending on the type of network, different link prediction algorithms can be applied, being less or more effective in the relevant scenarios. In this work, we develop a novel framework that attempts to compose the best features of link prediction algorithms when applied to a network, in order to have even more reliable predictions, especially in topologies emerging in Industrial Internet of Things (IIoT) environments. According to the proposed framework, we first apply appropriate link prediction algorithms that we have chosen for an analyzed network (basic algorithms). Each basic algorithm gives us a numerical estimate for each missing edge in the network. We store the results of each basic algorithm in appropriate structures. Then we provide them as input to a developed genetic algorithm. The genetic algorithm evaluates the results of the basic algorithms for each missing edge of the network. At each missing edge of the network and from generation to generation, it composes the estimates of the basic algorithms regarding each edge and produces a new optimized estimate. This optimization results in a vector of weights where each weight corresponds to the effectiveness of the prediction for each of the basic algorithms we have employed. With these weights, we build a new enhanced predictor tool, which can obtain new optimized estimates for each missing edge in the network. The enhanced predictor tool applies to each missing edge the basic algorithms, normalizes the basic algorithms’ estimates, and, using the weights of the estimates derived from the genetic algorithm, returns a new estimate of whether or not an edge will be added in the future. According to the results of our experiments on several types of networks with five well-known link prediction algorithms, we show that the new enhanced predictor tool yields in every case better predictions than each individual algorithm, therefore providing an accuracy-targeting alternative in the existing state of the art.

A novel potential edge weight method for identifying influential nodes in complex networks based on neighborhood and position

Interconnections among real-world entities through explicit or implicit relationships form complex networks, such as social, economic and engineering systems. Recently, the studies based on such complex networks have provided a boost to our understanding of various events and processes ranging from biology to technology. Link prediction algorithms assist in predicting, analysing and deciphering more significant details about the networks and their future structures. In this study, we propose three different link prediction algorithms based on different structural features of the network combined with the information-theoretic analyses. The first two algorithms (variants) are developed for unweighted networks, while the third approach deals with the weighted ones. The proposed methods exhibit better and robust performances in the majority of cases, and at least comparable, if not better in other cases. This work is built upon the previously published mutual information-based approaches for link prediction; however, this study considers structural features of the network to augment mutual information measures and provides insights for finding hidden links in the network.

Evaluating the importance of nodes in complex networks is an important topic in the research of network characteristics. Its relevant research has a wide range of applications, such as network supervision and rumor control. At present, many methods have been proposed to evaluate the importance of nodes in complex networks, but most of them have the deficiency of one-sided evaluation or too high time complexity. In order to break through the limitations of existing methods, in this paper a novel method of evaluating the importance of complex network nodes is proposed based on Tsallis entropy. This method takes into account both the local and global topological information of the node. It considers the structural hole characteristics and K-shell centrality of the node and fully takes into account the influence of the node itself and its neighboring nodes. To illustrate the effectiveness and applicability of this method, eight real networks are selected from different fields and five existing methods of evaluating node importance are used as comparison methods. On this basis, the monotonicity index, SIR (susceptible-infectious-recovered) model, and Kendall correlation coefficient are used to illustrate the superiority of this method and the relationship among different methods. Experimental results show that this method can effectively and accurately evaluate the importance of nodes in complex networks, distinguish the importance of different nodes significantly, and can show good accuracy of evaluating the node importance under different proportions of nodes. In addition, the time complexity of this method is <inline-formula><tex-math id="M2">\begin{document}$ O({n^2}) $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20210979_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20210979_M2.png"/></alternatives></inline-formula>, which is suitable for large-scale complex networks.

It is well known that protein-protein interaction (PPI) networks are typical evolving complex networks. Identification of important nodes has been an emerging popular topic in complex networks. Many indexes have been proposed to measure the importance of nodes in complex networks, such as degree, closeness, betweenness, k-shell, clustering coefficient, semi-local centrality, eigenvector centrality. Based on multivariate statistical analysis, through integrating the above indexes and further considering the appearances of nodes in network motifs, this paper aims at developing a new measure to characterize the structurally dominant proteins (SDP) in PPI networks. Moreover, we will further investigate the evolution of the defined dominant nodes in temporal evolving real-world and artificial PPI networks. Our results indicate that the constructed artificial networks have some similar statistical properties as those of the real-world evolving networks. In this case, the artificial PPI networks can be used to further investigate the above evolution characteristics of the real-world evolving networks. Simulation results reveal that SDP in the yeast PPI networks are evolutionary conserved, however, the undominant nodes evolve rapidly. Furthermore, PPI networks are very robust against random mutations, while fragile yet with certain robustness to targeted mutations on SDP. Our investigations shed some light on the future applications of the evolving characteristics of bio-molecular networks, such as reengineering of particular networks for technological, synthetic or pharmacological purposes.

Graph regularization weighted nonnegative matrix factorization for link prediction in weighted complex network

Link prediction is the problem of predicting the location of either unknown or fake links from uncertain structural information of a network. Link prediction algorithms are useful in gaining insight into different network structures from partial observations of exemplars. However, existing link prediction algorithms only focus on regular complex networks and are overly dependent on either the closed triangular structure of networks or the so-called preferential attachment phenomenon. The performance of these algorithms on highly sparse or treelike networks is poor. In this letter, we proposed a method that is based on the network heterogeneity. We test our algorithms for three real large sparse networks: a metropolitan water distribution network, a Twitter network, and a sexual contact network. We find that our method is effective and performs better than traditional algorithms, especially for the Twitter network. We further argue that heterogeneity is the most obvious defining pattern for complex networks, while other statistical properties failed to be predicted. Moreover, preferential attachment based link prediction performed poorly and hence we infer that preferential attachment is not a plausible model for the genesis of many networks. We also suggest that heterogeneity is an important mechanism for online information propagation.

Efficiently identifying multiple influential nodes is crucial for maximizing information diffusion and minimizing rumor spread in complex networks. Selecting multiple influential seed nodes requires consideration of both their individual influence potential and their spatial dispersion within the network topology to avoid overlapping propagation ranges ("rich-club effect"). Traditional VoteRank method suffer from two key limitations: (1) they assume uniform voting contributions from a node to all its neighbors, neglecting the impact of topological similarity (structural homophily) on voting preferences observed in real-world scenarios, and (2) they employ a homogeneous voting attenuation strategy which inadequately suppresses the propagation range overlap among selected seed nodes. To address these shortcomings, this paper proposes IMVoteRank, an improved VoteRank algorithm featuring dual innovations. First, we introduce a Structural Similarity-Driven Voting Contribution Mechanism. Recognizing that voters (nodes) are more likely to support candidates (neighbors) with whom they share stronger topological ties, we decompose a neighbor's voting contribution into two components: a Direct Connection Contribution and a Structural Similarity Contribution (quantified using common neighbors). A dynamic weight parameter θ, adjusted based on the candidate node's degree, balances these components, significantly refining vote allocation accuracy. Second, we devise a Dynamic Group Isolation Strategy. During each iteration, after selecting the highest-scoring seed node <i>v<sub>max</sub></i>, we identify and isolate a tightly-knit group (OG) centered around it. This involves: (i) forming an initial group based on shared neighbor density with <i>v<sub>max</sub></i>, (ii) expanding it by incorporating nodes with more connections inside the group than outside, and (iii) isolating this group by setting the voting capacity (Va) of all its members to zero and virtually removing their connections from the adjacency matrix. Neighbors of <i>v<sub>max</sub></i> not in OG have their <i>Va</i> halved. This strategy proactively enforces spatial dispersion among seeds. Extensive simulations using the Susceptible-Infected-Recovered (SIR) propagation model on nine diverse real-world networks (ECON-WM3, Facebook-SZ, USAir, Celegans, ASOIAF, Dnc-corecipient, ERIS1176, DNC-emails, Facebook-combined) demonstrate the superior performance of IMVoteRank. Compared to seven benchmark methods (Degree, K-shell, VoteRank, NCVoteRank, VoteRank++, AIGCrank, EWV), IMVoteRank consistently achieves significantly larger final propagation coverage (infected scale) for a given number of seed nodes and transmission probability (<i>β</i>=0.1). Furthermore, seeds selected by IMVoteRank exhibit a consistently larger average shortest path length (<i>Ls</i>) among themselves across most networks, confirming their effective topological dispersion. This combination of high individual influence potential (optimized voting) and low redundancy (group isolation) directly translates to more efficient global information spread, as evidenced by the SIR results. Tests on LFR benchmark networks further validate these advantages, particularly at transmission rates above the epidemic threshold. IMVoteRank effectively overcomes the limitations of traditional voting models by integrating structural similarity into the voting process and employing dynamic group isolation to ensure seed dispersion. It provides a highly effective and physically well-grounded approach for identifying multiple influential nodes in complex networks, optimizing the trade-off between influence strength and spatial coverage. Future work will focus on enhancing computational efficiency for large-scale networks and exploring the impact of meso-scale community structures.

A novel method of evaluating key nodes in complex networks

Robust link prediction in criminal networks: A case study of the Sicilian Mafia