Influential nodes in ray cluster hypergraph 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.

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.

Controlling COVID-19 transmission with isolation of influential nodes

Pandemics like COVID-19 have a huge impact on human society and the global economy. Vaccines are effective in the fight against these pandemics but often in limited supplies, particularly in the early stages. Thus, it is imperative to distribute such crucial public goods efficiently. Identifying and vaccinating key spreaders (i.e., influential nodes) is an effective approach to break down the virus transmission network, thereby inhibiting the spread of the virus. Previous methods for identifying influential nodes in networks lack consistency in terms of effectiveness and precision. Their applicability also depends on the unique characteristics of each network. Furthermore, most of them rank nodes by their individual influence in the network without considering mutual effects among them. However, in many practical settings like vaccine distribution, the challenge is how to select a group of influential nodes. This task is more complex due to the interactions and collective influence of these nodes together. This paper introduces a new framework integrating Graph Neural Network (GNN) and Deep Reinforcement Learning (DRL) for vaccination distribution. This approach combines network structural learning with strategic decision-making. It aims to efficiently disrupt the network structure and stop disease spread through targeting and removing influential nodes. This method is particularly effective in complex environments, where traditional strategies might not be efficient or scalable. Its effectiveness is tested across various network types including both synthetic and real-world datasets, demonstrting a potential for real-world applications in fields like epidemiology and cybersecurity. This interdisciplinary approach shows the capabilities of deep learning in understanding and manipulating complex network systems.

A most influential node group discovery method for influence maximization in social networks: A trust-based perspective

Abstract. Connecting points of interest through a well-planned, inter-connected network provides manifold benefits to commuters and service providers. In the South African context, traffic congestion has become of great concern. Given how the South Africa community is slowly developing towards the use of multi-modes of mobility, the Gautrain network can be used to promote the use of multi-modes of mobility, as the Gautrain has been identified as the backbone of mobility within the Gauteng province. Currently commuters have the option to board the Gaubus (a form of Bus Rapid Transit) at their origin points which will take them to the Gautrain station to board the Gautrain. The problem to be solved arises when a commuter wishes to traverse from any bus stop to the Gautrain station, currently he/she only has one option and if the bus network has a shutdown at any point in the network the commuter’s journey will not be possible. In solving this problem, we consider the problem of graph robustness (that is creating new alternative routes to increase node/bus stop connectivity). We initial use Strava data, to identify locations were cyclist prefer to cycle and at what time of day. In graph theory, the nodes with most spreading ability are called influential nodes. Identification of most influential nodes and ranking them based on their spreading ability is of vital importance. Closeness centrality and betweenness are one of the most commonly used methods to identify influential nodes in complex networks. Using the Gaubus network we identify the influential nodes/ bus stops, using the betweenness centrality measure. The results reveal the influential nodes with the highest connectivity as these have cross-connections in the network. Identification of the influential nodes presents an important implication for future planning, accessibility, and, more generally, quality of life.

Identifying influential nodes is one of the basic issues in managing large social networks. Identifying influence nodes in social networks and other networks, including transportation, can be effective in applications such as identifying the sources of spreading rumors, making advertisements more effective, predicting traffic, predicting diseases, etc. Therefore, it will be important to identify these people and nodes in social networks from different aspects. In this article, a new method is presented to identify influential nodes in the social network. The proposed method utilizes the combination of users’ social characteristics and their reaction information to identify influential users. Since the identification of these users in the large social network is a complex process and requires high processing power and time, clustering and identifying communities have been used in the proposed method to reduce the complexity of the problem. In the proposed method, the structure of the social network is divided into its constituent communities and thus the problem of identifying influential nodes (in the entire network) turns into several problems of identifying an influential node (in each community). The suggested method for predicting the nodes first predicts the links that may be created in the future and then identifies the influential nodes based on an iterative strategy. The proposed algorithm uses the criteria of centrality and influence domain to identify this category of users and performs the identification process both at the community and network levels. The efficiency of the method has been evaluated using real databases and the results have been compared with previous works. The results demonstrate that the proposed method provides a more suitable performance in detecting the influential nodes and is superior in terms of accuracy, recall and processing time.

A social network is a set of relationships and interactions among social entities such as individuals, organizations, and groups. The social network analysis is one of the major topics in the ongoing research field. The major problem regarding the social network is finding the most influential objects or persons. Identification of most influential nodes in a social network is a tedious task as large numbers of new users join the network every day. The most commonly used method is to consider the social network as a graph and find the most influential nodes by analyzing it. The degree centrality method is node based and has the advantage of easy identification of most influential nodes. In this paper a method called "Enhanced Degree Centrality Measure" is proposed which integrates clustering co-efficient value along with node based degree centrality. The enhanced degree centrality measure is applied to three different datasets which are obtained from the Facebook to analyze the performance. The response obtained is compared with existing methods such as degree centrality method and SPIN algorithm. By comparison, it is found that highest number of active nodes identified by the proposed method is 64 when compared with SPIN algorithm which identifies only 55.

CBIM: Community-based influence maximization in multilayer networks

The issue of mining influential nodes in complex networks is a topic of immense interest. Recently, many methods have been proposed, but they suffer from certain limitations. In this article, a novel centrality measure based on local fuzzy information centrality (LFIC) is proposed. LFIC puts forward the concept that the inner structure of a node’s box contains information about the node’s importance. LFIC uses the amount of information contained in the node’s box as a measure of its importance. In LFIC, the uncertainty of information contained in nodes’ boxes is measured by the improved Shannon entropy. Most importantly, fuzzy logic is applied to deal with the uncertainty of neighbor nodes’ contributions to the center node’s importance, which is neglected by most existing methods. To verify the effectiveness of our proposed method, six existing methods are used for comparison and five experiments are conducted using six real-world complex networks. The experimental results indicate that the influential nodes identified by LFIC can cause a wider scope of infection in networks and have a larger effect on the network connectivity, thereby proving the effectiveness and accuracy of LFIC. The correlation between nodes’ LFIC values and their real infection ability is highly positive according to Kendall’s tau coefficient, proving LFIC’s credibility and superiority. The extension of LFIC, namely the bi-directional local fuzzy information centrality, is also proposed to explore its feasibility in weighted directed complex networks.

In a complex network, the identification of node influence and the localization of key nodes play a crucial role in analyzing network structure and determining the positioning of nodes for information transmission control, resource redistribution, and network regulation. In this study, we propose a method for identifying influential nodes called "Multi-order Neighbors and Exclusive Neighborhood" (MNEN) after analyzing and investigating existing methods in the field. The MNEN method calculates a node's influence based on two factors: the node itself, its neighboring nodes, and its exclusive neighborhood. The influence of the node itself is determined by its degree value and K-shell (Ks) value, while the influence contribution of the neighbor node is calculated based on its degree value, Ks value, and the contribution from its exclusive neighbor node. To evaluate the algorithm's performance, we employ the SIR model as the benchmark and conduct simulation experiments to validate the MNEN method, comparing the results with other influential node identification methods. Our analysis demonstrates that the algorithm accurately identifies influential nodes in networks of different scales, yielding a positive overall impact and demonstrating a certain level of universality.

The research concerns the meta-network (multimodal) approach to an IT sector organisation where employees, knowledge, resources (intangible assets), tasks, and value creation play a key role and are dependent on each other. At the centre of considerations is the look at value creation from intangible assets understood, inter alia, as legally protected software. A meta-network approach was used to identify and measure influential network nodes using out-degree and in-degree centralities and visualisation of two-mode networks. Each network is two-mode, which illustrates the multimodal approach to human behaviour in an organisation understood as interaction with resources, tasks performed, or value creation. Influential nodes were identified and the network was correlated using the quadratic assignment procedure (QAP). Value creation in the network perspective is a consequence of interactions and interdependencies occurring between the knowledge network, the resource network, and the task network. The concept of this research is a valuable and innovative approach for managers who, in the network approach to the analysis of value creation and intangible assets, will see a comprehensive vein to employee behaviour in organisational conditions based on relationships and interactions.

Identifying influential nodes in complex networks is crucial for applications like information diffusion, rumor propagation, and epidemic spreading. Existing methods often assume uniform importance among neighbor nodes or fail to account for the structural and semantic diversity of relationships in heterogeneous networks. This leads to suboptimal identification of influential nodes, particularly in complex, attribute-rich networks. To address these shortcomings, a meta-path embedding-based graph attention network model is proposed, namely MEGA. MEGA is utilized to identify influential nodes in heterogeneous networks. This paper attempts to identify the influential set of author nodes in academic networks, defined as the set of nodes whose influence maximizes the spread of information. MEGA is described as follows. Firstly, the required meta-paths are defined, and node embeddings are obtained using a meta-path embedding method. Then, the subgraph networks corresponding to each meta-path network are generated based on random walks. Further, the graph attention network is employed to assign different weight values to neighbor nodes within the subgraph networks, indicating the varying influence of nodes on their neighbor nodes. Finally, the influence of nodes in the subgraph network is calculated using entropy, and the influence values from all subgraphs are aggregated to obtain the final influence value of each node. The effectiveness of MEGA is validated using analysis metrics from the independent cascade model. Experimental results demonstrate MEGA exceeds six baseline methods in terms of the influence spread across three datasets.

Identification of influential vertices plays a very prominent task in a complex network. So, the fundamental task in complex networks is to determine the influential nodes whose expulsion crucially cutoff network harmony. The analysis of the network’s topological characteristics, such as susceptibility and resilience, can be aided by identifying influential nodes. This work uses the notion of Maximize the Number of Connected Components Problem, which helps in determining influential nodes, and whose removal yields optimum number of connected components. This work includes application of topology-based centrality measures on real-world networks. However, conventional methods fail to detect most influential nodes that cause the network to split into the optimum number of components. To address this, our work introduces new centrality called global isolating centrality with half of the diameter hops, that focus on network connectedness. The results reveal that the new centrality is better than the existing centralities for certain probability values.

In recent years, social networks have become an integral part of people's lives and play a significant role in the real world.The primary aim of influence maximization problem is finding a set of nodes in the network which can maximize the influence if the diffusion process starts from them.Therefore, the problem's goal is to find influential people in large scale real social networks.The penetration phenomenon is carried out according to an influence model in the network.Two independent cascade and linear threshold influence models, the most common of which is the independent cascade model, are utilized for broadcasting in the network.Theoreticaly, optimizing the selection influential nodes problem is NP-hard in both models.The problem will start by considering the social network's graph, a specific influence model and a given number k.The problem's goal is to select k nodes (users) from the graph (network) as influential nodes, so that the number of active nodes is maximized at the end of the diffusion process.Due to the influence 4 62 30 maximization problem and finding influential people is an NP-hard optimization problem in the social network, meta-heuristic algorithms can be used to solve the problem.With regard to the privous researches, there is just one objective function as the problem's goal and it is maximizing the number of effective nodes of the diffusion model.While other objective functions such as maximizing the number of effective nodes in the diffusion model and minimizing the budget value k (the number of initial nodes as seed) are not considered, minimizing the time required for effective diffusion can be achieved by having k initial nodes.Although various models for the problem and various optimization algorithms have been presented to discover influential nodes in social networks, paying attention to the multi-objective nature of the problem and improving the performance of the proposed optimization algorithms are a serious research challenge in this field.In this paper.A fuzzy version of the NSGA-II as a multi-objective genetic algorithm, whose mutation and crossover rates are adjusted by Fuzzy Inference System, is utilized to simultaneously optimize the three objectives of maximizing the number of effective nodes, minimizing the number of initial nodes and minimizing the required diffusion time.In the proposed method, the Expected Diffusion Value (EDV) of the diffusion model is replaced instead the simulation of the independent cascade diffusion model with heavy calculations to calculate the diffusion spread (the number of effective nodes of the diffusion model).Therefore, the EDV function is satisfied as the thied objective (minimizing the required diffusion time).The second objective function can also be converted into a maximization function by considering N-k nodes, where k is the number of selected initial nodesand N is the total graph nodes.The decimal numerical coding with fixed length is used in the proposed method.Based on the coding, each chromosome has k genes in the search space.The integer part of each gene is the selected node number.The decimal part is also used to determine whether that initial node exists or not.In the maximizing influence process using the fuzzy NSGA-II algorithm, the solution space (chromosomes) consists of k number of initial nodes, which should be encoded into the fuzzy NSGA-II comprehensible space.Also, a Fuzzy Inference System is proposed to adjust the mutation and recombination rates for filling up a serious challenge of genetic algorithms.In the fuzzy system, NF and FitBest are considered as two input variables, and Pm (mutation rate) and Pc (crossover rate) are returned as outputs NF is the number of chromosomes in the first frontier (F1) of the multi-objective genetic algorithm and FitBest is the average of the normalized objective functions for the chromosomes in F1.To analysis the efficiency of the proposed method, the obtained exprimental results have been compared with conventional maximizing influence methods, i.e., degree centrality, distance centrality, closeness centerality, betweenness, eigenvector and page rank methods, non-fuzzy version of NSGA-II, the latest methods presented for maximizing penetration based on multi-objective meta-heuristic algorithms, i.e. GP multi-objective evolutionary algorithm, multi-objective crow search algorithm (MOCSA), greedy randomized adaptive search process algorithm (GRASP) and the Multi-Transformation Evolutionary Framework (MTEF) on five benchmark graph datasets Arenasjazz, Canetscience, EgoFacebook, Higgs-Reply and Slashdot.This comparison is based on four criteria: EDV, cost (the number of nodes selected as seed), the influence expansion criterion (s), i.e. the number of active nodes with the independent cascade (IC) propagation model, and the execution time of the method in seconds.The obtained results show the superiority of the proposed method over the other methods.