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Identifying the seed nodes in networks is an important task for understanding the dynamics of information diffusion. It has many applications, such as energy usage/consumption, rumor control, viral marketing, and opinion monitoring. When compared to other nodes, seed nodes have the potential to spread information in the majority of networks. To identify seed nodes, researchers gave centrality measures based on network structures. Centrality measures based on local structure are degree, semi-local, Pagerank centralities, etc. Centrality measures based on global structure are betweenness, closeness, eigenvector, etc. Very few centrality measures exist based on the network's local and global structure. We define mixed centrality measures based on the local and global structure of the network. We propose a measure based on degree, the shortest path between vertices, and any global centrality. We generalized the definition of our mixed centrality, where we can use any measure defined on a network's global structure. By using this mixed centrality, we identify the seed nodes of various real-world networks. We also show that this mixed centrality gives good results compared with existing basic centrality measures. We also tune the different real-world parameters to study the effect of their maximum influence. [ABSTRACT FROM AUTHOR]

The identification of a central node in a network is one of the important tasks of social networks. Nowadays, the central node helps grow online businesses, spread news, advertisements, etc. Existing methods for centrality measurement capture the direct reachability of the node. In social networks, parameters such as relationships among the nodes are generally uncertain. This uncertainty can be tracked using either probability theory or fuzzy theory. In this article, the fuzzy theory, particularly the neutrosophic fuzzy theory, is used because, in this concept, more information, such as true values, falsity and indeterminacy, is incorporated. Thus, the representation of social networks using neutrosophic graphs gives more information compared to fuzzy graphs. This study introduces a new form of centrality measurement using a neutrosophic graph. This measurement considers the different merits of individuals in a network. Individual merits (self-weight) have been included in the proposed method. A small network of university faculty members has been considered to illustrate the problem and to demonstrate the potential fields of application of this new method of centrality measurement. [ABSTRACT FROM AUTHOR]

The evaluation of node importance is a critical research topic in network science, widely applied in social networks, transport systems, and computer networks. Prior works addressing this topic either consider a single metric or assign weights for multiple metrics or select features by handcraft, which exist one-sidedness and subjectivity issues. In this paper, to tackle these problems, we propose a new approach named CGNN to identify influential nodes based on deep learning methods, including Convolutional Neural Networks (CNNs) and Graph Neural Networks (GNNs). CGNN obtains the feature matrices by the contraction algorithm and gets the labels by the Susceptible-Infected-Recovered (SIR) model, which will be leveraged for learning the hidden representations of nodes without utilizing any network metrics as features. We adopt three evaluation criteria to verify CGNN concerning effectiveness and distinguishability, including Kendall's τ correlation coefficient, monotonicity index (MI), and ranking distribution function (RDF). Nine baselines are employed to compare with CGNN on thirty synthetic networks and twelve real-world networks from different domains. Simulation results demonstrate that CGNN manifests better performance than the baselines, in which the values of τ are large and significantly increase, the values of MI approach to 1, and the points in the RDF curves distribute more uniformly. These results may provide reference significance for controlling epidemic spreading and enhancing network robustness. [ABSTRACT FROM AUTHOR]

The discovery of community structures in social networks has gained significant attention since it is a fundamental problem in understanding the networks' topology and functions. However, most social network data are collected from partially observable networks with both missing nodes and edges. In this article, we address a new problem of detecting overlapping community structures in the context of such an incomplete network, where communities in the network are allowed to overlap since nodes belong to multiple communities at once. To solve this problem, we introduce KroMFac, a new framework that conducts community detection via regularized nonnegative matrix factorization (NMF) based on the Kronecker graph model. Specifically, from an inferred Kronecker generative parameter matrix, we first estimate the missing part of the network. As our major contribution to the proposed framework, to improve community detection accuracy, we then characterize and select influential nodes (which tend to have high degrees) by ranking, and add them to the existing graph. Finally, we uncover the community structures by solving the regularized NMF-aided optimization problem in terms of maximizing the likelihood of the underlying graph. Furthermore, adopting normalized mutual information (NMI), we empirically show superiority of our KroMFac approach over two baseline schemes by using both synthetic and real-world networks. [ABSTRACT FROM AUTHOR]

Social Networks is an essential phenomenon in all aspects through various perspectives. These networks contain a large number of users better termed as nodes and the connections between the users termed as edges. For efficient information processing and retrieving, accessing the influential node is essential for improving the diffusion process. To identify the influential node inside a heterogeneous community, incorporating probability metrics with regression classifier is put forth stated by proposed method Support Vector Bayesian Machine (SVBM). Node metrics such as degree centrality, closeness centrality is measured for eliminating the nodes primarily. A standardized index based on the centrality values computed for enhancing into SVBM. After the standardized index, similarity dissimilarity index values evaluated by combining the Euclidean, Hamming, Pearson coefficient for valued relations and Jaccard for binary relations which results in a single index value considered as the power degree value(p). The value p determines the node's boundedness, which indicates the range of influence within the community. The outlier nodes in the bounded region get eliminated, and the nodes remaining taken for the final phase of SVBM, probability regression line predicts the node inhibiting the most influential nature. Experimental evaluation of the proposed system with the existing Support Vector Machine (SVM) technique resulted in 0.95 and 0.41 respectively for Area Under Curve (AUC) denoting that the true positive influential node classification process from the other existing nodes was higher than SVM. In comparison with the existing SVM, the proposed methodology SVBM attained a node detection, which influenced a higher diffusion rate within the networks. [ABSTRACT FROM AUTHOR]

In networks, dynamic phenomena such as opinions, behaviors, and information are propagated through connections between entities. Indeed, one of the main issues about a dynamic process is to find a set of individuals with a high influence on other’s decisions which is defined as the “influence maximization” problem, and aims to find a subset of nodes to maximize the total number of adopters at the end of the process. In this paper, by combining the community structure and influence maximization problem, we proposed a two-layered method for identifying influential nodes so that in the first layer an optimization-based method is applied to detect the potential communities. Then, in the second layer, a criterion is used which is a tradeoff between the low-relevant centralities and methods with high complexity. Our method is implemented on real social networks with different scales, and the performance is evaluated by using the total number of infected nodes at the end of the process. The experimental results indicate the superiority of our method in comparison to other considered approaches by considering the efficiency and scalability. [ABSTRACT FROM AUTHOR]

The growing popularity of social networks is providing a promising opportunity for different practical applications. The influence analysis is an essential technique supporting the understanding of real-life activities. Accordingly, certain reviews and surveys have been presented, focusing on models, methods, and evaluation aspects related to social influence analysis. However, the ultimate goal is that the background social influence analysis methods developed in research could be employed in real applications. In this context, social influence analysis still remains a number of challenges including the privacy of the massive networks that have been recently mentioned by researchers. Motivated from these facts, in this paper we provide a state-of-the-art survey on the influence analysis techniques in addressing these challenges. In this detailed survey, we divide the diffusion models into two categories, individual and group node-based models. Our primary focus is to investigate the research methods and techniques and compare them according to the above categories. In the sequel, we especially further provide an overview of the existing methods for influence maximization under privacy protection. The recent advanced applications of social influence are also surveyed. In the end, open issues are discussed to enable the researchers to a better understanding of the present scenario and suggest several potential future directions for research in influence maximization. • A comprehensive literature review of pertinent studies on social influence analysis. • A detailed taxonomy of individual node and group-based influence analysis models. • Parallel influence maximization approaches and their methods are illustrated. • The main contribution of the survey is to highlight the research trends for analysis of social influence under privacy protection. • Challenges/limitations in influence analysis and their perspective research direction are discussed. [ABSTRACT FROM AUTHOR]

One of the most important applications for identification of influential nodes in social networks is viral marketing. In viral marketing, there are valuable users from which companies or smaller businesses benefit most at the lowest cost. Inspired from the behavior of real ants and based on the ant colony optimization algorithm, we propose new methods named PMACO and IMOACO in this paper to find the most valuable users. First, the influence graph is derived from the analysis of users' interactions and communications in a social network. The negative influence among users is also considered in the process of generating the influence graph. For reduction of computational complexity and removal of unimportant nodes from the influence graph, the nodes the levels of influence of which on their neighbors are less than a specific threshold value are eliminated. Then, the representation of the search space as a weighted graph is constructed by the remaining nodes, where the weight of each edge is the similarity between the two nodes of which that edge is composed. Next, the ants begin their search processes with the goal of maximizing profit and minimizing the similarity among the selected nodes. Assessments have been made on real and synthetic datasets, and compared the proposed algorithm with well-known ones. The results of the experiments demonstrate the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]