Influential Nodes In Network Research Articles

HIKS: A K‐shell‐weighted hybrid approach method for detecting influential nodes in complex networks using possible edge weights

SummaryThe influential node in the network is the node that has a higher impact on network functioning compared to the other nodes. The influential node detection in the complex network is crucial for rumor containment, virus spreading, viral marketing, and so forth. The researchers designed several influential node detection methods; still, detecting community and influential node selection with minimal computational complexity by considering the relationship between the nodes is challenging. Hence, an optimal community detection along with the hybrid K‐shell decomposition method is introduced in this research. Initially, the optimal community from the complex network is identified to reduce the computation burden. For this, the Improved Dingo (IDingo) algorithm is introduced by hybridizing the hunting behavior of Dingo and the rough encircling behavior of Harris Hawk. After detecting the optimal community, the influential node identification is devised using the proposed hybrid K‐shell decomposition methods. The potential edge weights are considered while ranking the nodes. The performance of a proposed method is analyzed using six various datasets and accomplished the maximal cluster coefficient of 0.56578, 0.25674, 0.24022, 0.5968, 0.23419, and 0.10196 for Karate, Dolphins, C‐Elegance, Facebook, Gowalla, and Power Grid Dataset.

Finding influential nodes in networks using pinning control: Centrality measures confirmed with electrochemical oscillators.

The spatiotemporal organization of networks of dynamical units can break down resulting in diseases (e.g., in the brain) or large-scale malfunctions (e.g., power grid blackouts). Re-establishment of function then requires identification of the optimal intervention site from which the network behavior is most efficiently re-stabilized. Here, we consider one such scenario with a network of units with oscillatory dynamics, which can be suppressed by sufficiently strong coupling and stabilizing a single unit, i.e., pinning control. We analyze the stability of the network with hyperbolas in the control gain vs coupling strength state space and identify the most influential node (MIN) as the node that requires the weakest coupling to stabilize the network in the limit of very strong control gain. A computationally efficient method, based on the Moore-Penrose pseudoinverse of the network Laplacian matrix, was found to be efficient in identifying the MIN. In addition, we have found that in some networks, the MIN relocates when the control gain is changed, and thus, different nodes are the most influential ones for weakly and strongly coupled networks. A control theoretic measure is proposed to identify networks with unique or relocating MINs. We have identified real-world networks with relocating MINs, such as social and power grid networks. The results were confirmed in experiments with networks of chemical reactions, where oscillations in the networks were effectively suppressed through the pinning of a single reaction site determined by the computational method.

Ranking influential nodes in networks from aggregate local information

Ranking influential nodes in networks from aggregate local information

SLGC: Identifying influential nodes in complex networks from the perspectives of self-centrality, local centrality, and global centrality

Identifying influential nodes in complex networks and ranking their importance plays an important role in many fields such as public opinion analysis, marketing, epidemic prevention and control. To solve the issue of the existing node centrality measure only considering the specific statistical feature of a single dimension, a SLGC model is proposed that combines a node’s self-influence, its local neighborhood influence, and global influence to identify influential nodes in the network. The exponential function of e is introduced to measure the node’s self-influence; in the local neighborhood, the node’s one-hop neighboring nodes and two-hop neighboring nodes are considered, while the information entropy is introduced to measure the node’s local influence; the topological position of the node in the network and the shortest path between nodes are considered to measure the node’s global influence. To demonstrate the effectiveness of the proposed model, extensive comparison experiments are conducted with eight existing node centrality measures on six real network data sets using node differentiation ability experiments, susceptible–infected–recovered (SIR) model and network efficiency as evaluation criteria. The experimental results show that the method can identify influential nodes in complex networks more accurately.

Integrating local and global information to identify influential nodes in complex networks

Centrality analysis is a crucial tool for understanding the role of nodes in a network, but it is unclear how different centrality measures provide much unique information. To improve the identification of influential nodes in a network, we propose a new method called Hybrid-GSM (H-GSM) that combines the K-shell decomposition approach and Degree Centrality. H-GSM characterizes the impact of nodes more precisely than the Global Structure Model (GSM), which cannot distinguish the importance of each node. We evaluate the performance of H-GSM using the SIR model to simulate the propagation process of six real-world networks. Our method outperforms other approaches regarding computational complexity, node discrimination, and accuracy. Our findings demonstrate the proposed H-GSM as an effective method for identifying influential nodes in complex networks.

SMPC-Ranking: A Privacy-Preserving Method on Identifying Influential Nodes in Multiple Private Networks

Existing methods regarding the influential nodes identification in complex networks usually assume that the structures of the networks are fully known. However, in many cases, knowing the full structure of one network is hard or impossible, and each participant can only obtain the partial structure of the networks. Therefore, each participant can be viewed as a private network (PN) of the original network, and they form multiple PNs. Then, one question arises: how to collaboratively identify influential nodes in multiple PNs while protecting the privacy of each PN. To this end, a secure multiparty computation ranking (SMPC-ranking) method is proposed to solve such an all-new problem based on the secure multiparty computation (SMPC) protocol, in which the SMPC protocol jointly computes a centrality function to measure the comprehensive importance of nodes or their ranking results by integrating each PN’s inputs without disclosing their inputs (i.e., the nodes’ importance). Experimental results in different networks demonstrate that, no matter what type of the centrality index is, the SMPC-ranking method can better identify the influential nodes in networks than that of the baseline method only using the structural information of one PN. What is more, our SMPC-ranking method does not violate the privacy of each PN. Therefore, the proposed method provides new insights on collaboratively identifying influential nodes in multiple PNs and has potential applications in many fields.

Identifying Influential Nodes in Social Networks: Exploiting Self-Voting Mechanism.

The influence maximization (IM) problem is defined as identifying a group of influential nodes in a network such that these nodes can affect as many nodes as possible. Due to its great significance in viral marketing, disease control, social recommendation, and so on, considerable efforts have been devoted to the development of methods to solve the IM problem. In the literature, VoteRank and its improved algorithms have been proposed to select influential nodes based on voting approaches. However, in the voting process of these algorithms, a node cannot vote for itself. We argue that this voting schema runs counter to many real scenarios. To address this issue, we designed the VoteRank* algorithm, in which we first introduce the self-voting mechanism into the voting process. In addition, we also take into consideration the diversities of nodes. More explicitly, we measure the voting ability of nodes and the amount of a node voting for its neighbors based on the H-index of nodes. The effectiveness of the proposed algorithm is experimentally verified on 12 benchmark networks. The results demonstrate that VoteRank* is superior to the baseline methods in most cases.

Privacy-preserving identification of the influential nodes in networks

Identifying influential nodes in social networks has drawn significant attention in the field of network science. However, most of the existing works request to know the complete structural information about networks, indeed, this information is usually sensitive, private and hard to obtain. Therefore, how to identify the influential nodes in networks without disclosing privacy is especially important. In this paper, we propose a privacy-preserving (named as HE-ranking) framework to identify influential nodes in networks based on homomorphic encryption (HE) protocol. The HE-ranking method collaboratively computes the nodes’ importance and protects the sensitive information of each private network by using the HE protocol. Extensive experimental results indicate that the method can effectively identify the influential nodes in the original networks than the baseline methods which only use each private network to identify influential nodes. More importantly, the HE-ranking method can protect the privacy of each private network in different parts.

MCD: A modified community diversity approach for detecting influential nodes in social networks

Over the last couple of decades, Social Networks have connected people on the web from across the globe and have become a crucial part of our daily life. These networks have also rapidly grown as platforms for propagating products, ideas, and opinions to target a wider audience. This calls for the need to find influential nodes in a network for a variety of reasons, including the curb of misinformation being spread across the networks, advertising products efficiently, finding prominent protein structures in biological networks, etc. In this paper, we propose Modified Community Diversity (MCD), a novel method for finding influential nodes in a network by exploiting community detection and a modified community diversity approach. We extend the concept of community diversity to a two-hop scenario. This helps us evaluate a node’s possible influence over a network more accurately and also avoids the selection of seed nodes with an overlapping scope of influence. Experimental results verify that MCD outperforms various other state-of-the-art approaches on eight datasets cumulatively across three performance metrics.

A Strategy Formulation Framework for Efficient Screening during the Early Stage of a Pandemic.

For viruses that can be transmitted by contacts of people, efficiently screening infected individuals is beneficial for controlling outbreaks rapidly and avoiding widespread diffusion, especially during the early stage of a pandemic. The process of virus transmission can be described as virus diffusion in complex networks such as trajectory networks. We propose a strategy formulation framework (SFF) for generating various screening strategies to identify influential nodes in networks. We propose two types of metrics to measure the nodes' influence and three types of screening modes. Then, we can obtain six combinations, i.e., six strategies. To verify the efficiencies of the strategies, we build a scenario model based on the multi-agent modelling. In this model, people can move according to their self-decisions, and a virtual trajectory network is generated by their contacts. We found that (1) screening people will have a better performance based on their contact paths if there is no confirmed case yet, and (2) if the first confirmed case has been discovered, it is better to screen people sequentially by their influences. The proposed SFF and strategies can provide support for decision makers, and the proposed scenario model can be applied to simulate and forecast the virus-diffusion process.

Dynamic Opinion Maximization Framework With Hybrid Method in Social Networks

Dynamic Opinion Maximization (DOM) is an optimization issue, which determines some influential network nodes (i.e., seed nodes) to propagate specific opinions towards a certain object (e.g., one individual) using a dynamic opinion model, and achieve the optimal opinion propagation. In this paper, we study the DOM and construct an effective hybrid framework to address the problem. Firstly, we explicate the DOM problem and design the objective function of the DOM. Then, based on the activation status with the linear threshold model and the dynamic opinion process with the weighted Hegselmann-Krause model, we devise the activated opinion model to estimate the activation status and dynamic opinion process of activated nodes effectively. We propose an effective hybrid framework to select the seed nodes, which includes community detection, the determination of candidate seed nodes, and the seeding algorithm with discrete particle swarm optimization. In particular, to better generate the seed nodes and promote their propagation, we design the selection algorithm of candidate seed nodes and replacement strategy. Experimental results show the superiority of the proposed hybrid framework on the average opinions and the number of activated nodes than the baseline algorithms. Our method gains 17.89% more average opinions than EPN, 14.57% than RIS, 20.19% than CIDM, 2.58% than ATOM, and 7.22% than CELF on the eight social network datasets. Moreover, our method gains 28.17% more activated nodes than EPN, 25.31% than RIS, 36.34% than CIDM, 16.82% than ATOM, and 19.68% than CELF on average.

Robustness Evaluation of the Open Source Product Community Network Considering Different Influential Nodes

With the rapid development of Internet technology, the innovative value and importance of the open source product community (OSPC) is becoming increasingly significant. Ensuring high robustness is essential to the stable development of OSPC with open characteristics. In robustness analysis, degree and betweenness are traditionally used to evaluate the importance of nodes. However, these two indexes are disabled to comprehensively evaluate the influential nodes in the community network. Furthermore, influential users have many followers. The effect of irrational following behavior on network robustness is also worth investigating. To solve these problems, we built a typical OSPC network using a complex network modeling method, analyzed its structural characteristics and proposed an improved method to identify influential nodes by integrating the network topology characteristics indexes. We then proposed a model containing a variety of relevant node loss strategies to simulate the changes in robustness of the OSPC network. The results showed that the proposed method can better distinguish the influential nodes in the network. Furthermore, the network’s robustness will be greatly damaged under the node loss strategies considering the influential node loss (i.e., structural hole node loss and opinion leader node loss), and the following effect can greatly change the network robustness. The results verified the feasibility and effectiveness of the proposed robustness analysis model and indexes.

Identifying influential nodes in social networks: Centripetal centrality and seed exclusion approach

Identifying influential nodes in a network is vital for the study of social network structure and to facilitate the dissemination of requisite information. The challenge we address is that, given a complex network, which nodes are more important? How can a group of disseminators be identified and selected to maximize any given field of influence? A series of centrality measures are proposed from different perspectives based on the topology of nodes. However existing methods suffer from problems that are intrinsic to singular consideration of node topology information, and they neglect the connection relationship between nodes when filtering the spreaders, resulting in imprecise evaluation results and limited spread scale. To solve this issue, this paper proposes a new centrality, inspired by the centripetal force formula. Centripetal centrality combines global, and local, as well as semi-local topological information about the nodes resulting in a more comprehensive evaluation. For the problems related to influence maximization, we propose a heuristic algorithm called seed exclusion (SE) that filters propagators. To demonstrate the performance of the proposed measures, we conducted experiments on both real-world and synthetic networks by comparing distinct metrics, improvements in network efficiency, the propagation of nodes under the SIR model and the average shortest distance between spreaders. The experimental results show that the proposed centripetal centrality is more accurate and effective than similar measures, while comparison with baselines the SE algorithm significantly improves spread speed and infection scale.

Identify influential nodes in network of networks from the view of weighted information fusion

Identify influential nodes in network of networks from the view of weighted information fusion

A Survey on Recent Methods of Finding Influential Nodes in Complex Networks

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.

Defining Cyber Security and Cyber Security Risk within a Multidisciplinary Context using Expert Elicitation.

It is important to have and use standardized terminology and develop a comprehensive common understanding of what is meant by cyber security and cyber security risk given the multidisciplinary nature of cyber security and the pervasiveness of cyber security concerns throughout society. Using expert elicitation methods, collaborating cyber researchers from multiple disciplines and two sectors (academia, government–military) were individually interviewed and asked to define cyber security and cyber security risk. Data‐driven thematic analysis was used to identify the most salient themes within each definition, sector, and cyber expert group as a whole with results compared to current standards definitions. Network analysis was employed to visualize the interconnection of salient themes within and across sectors and disciplines. When examined as a whole group, “context‐driven,” “resilient system functionality,” and “maintenance of CIA (confidentiality, integrity, availability)” were the most salient themes and influential network nodes for the definition of cyber security, while “impacts of CIA vulnerabilities,” “probabilities of outcomes,” and “context‐driven” were the most salient themes for cyber security risk. We used this expert elicitation process to develop comprehensive definitions of cyber security (cybersecurity) and cyber security risk that encompass the contextual frameworks of all the disciplines represented in the collaboration and explicitly incorporates human factors as significant cyber security risk factors.

Recognizing Influential Nodes in Social Networks With Controllability and Observability

The analysis for social networks, such as the sensor-networks in socially networked industries, has shown a deep influence of intelligent information processing technology on industrial systems. The large amounts of data on these networks raise the urgent demands of analyzing the topological content effectively and efficiently in Industrial Internet of Things. One of the ways to locate important information amongst such large troves of data is to recognize influential nodes. In this article, we examine an intelligent way to recognize the influence of such nodes automatically. Motivated by the concepts of system controllability and observability from control theory, we introduce a novel method to evaluate nodes from two different aspects, namely, the ability of “observe” information on the network (i.e., observability), and the ability to propagate information to other nodes (i.e., controllability). We propose a unified data mining framework that incorporates content analysis with nodes behavioral tendencies, and show that it is able to outperform competitive baselines in recognizing influential nodes in networks. We also show that it is important to detect the presence of spammer nodes within networks, which might otherwise be wrongly recognized as influential nodes. The experimental results demonstrate the superiority of the proposed approach in comparison with baseline methods.

Identifying Influential Nodes of Complex Networks Based on Trust-Value

The real world contains many kinds of complex network. Using influence nodes in complex networks can promote or inhibit the spread of information. Identifying influential nodes has become a hot topic around the world. Most of the existing algorithms used for influential node identification are based on the structure of the network such as the degree of the nodes. However, the attribute information of nodes also affects the ranking of nodes’ influence. In this paper, we consider both the attribute information between nodes and the structure of networks. Therefore, the similarity ratio, based on attribute information, and the degree ratio, based on structure derived from trust-value, are proposed. The trust–PageRank (TPR) algorithm is proposed to identify influential nodes in complex networks. Finally, several real networks from different fields are selected for experiments. Compared with some existing algorithms, the results suggest that TPR more rationally and effectively identifies the influential nodes in networks.

Integrated Value of Influence: An Integrative Method for the Identification of the Most Influential Nodes within Networks

SummaryBiological systems are composed of highly complex networks, and decoding the functional significance of individual network components is critical for understanding healthy and diseased states. Several algorithms have been designed to identify the most influential regulatory points within a network. However, current methods do not address all the topological dimensions of a network or correct for inherent positional biases, which limits their applicability. To overcome this computational deficit, we undertook a statistical assessment of 200 real-world and simulated networks to decipher associations between centrality measures and developed an algorithm termed Integrated Value of Influence (IVI), which integrates the most important and commonly used network centrality measures in an unbiased way. When compared against 12 other contemporary influential node identification methods on ten different networks, the IVI algorithm outperformed all other assessed methods. Using this versatile method, network researchers can now identify the most influential network nodes.

Ranking Influential Nodes in Complex Networks with Information Entropy Method

The ranking of influential nodes in networks is of great significance. Influential nodes play an enormous role during the evolution process of information dissemination, viral marketing, and public opinion control. The sorting method of multiple attributes is an effective way to identify the influential nodes. However, these methods offer a limited improvement in algorithm performance because diversity between different attributes is not properly considered. On the basis of the k-shell method, we propose an improved multiattribute k-shell method by using the iterative information in the decomposition process. Our work combines sigmod function and iteration information to obtain the position index. The position attribute is obtained by combining the shell value and the location index. The local information of the node is adopted to obtain the neighbor property. Finally, the position attribute and neighbor attribute are weighted by the method of information entropy weighting. The experimental simulations in six real networks combined with the SIR model and other evaluation measure fully verify the correctness and effectiveness of the proposed method.