Influential Node Identification in Command and Control Networks Based on Integral k-Shell

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.

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.

Identification of influential nodes has emerged as one of the major challenges, especially after their use in the rapid propagation of information, epidemics, and so on in social media. Most of the previous works in this field deal with the homogeneous interactions that are not pertinent in the determination of the accurate context of the nodes due to their noisy and sparse nature. Hence, heterogeneous interactions need to be explored for the identification of influential nodes in the network. To consider heterogeneous interactions available within the network, a multilayer network (ML) has been designed in this work. Each layer of the network represents a particular type of interaction, e.g., upload, comment, retweet, reply, and mention. A heterogeneous degree ranking (HDR)-based influential nodes’ detection and ranking are proposed for the designed ML. Furthermore, multiple-criteria decision-making (MCDM) methods, such as the analytic hierarchy process (AHP), the technique for order of preference by similarity to ideal solution (TOPSIS), fuzzy AHP, fuzzy TOPSIS, and the analytic network process (ANP), are explored for the proposed ML for identification and ranking of the influential nodes. The susceptible–infected–recovered (SIR) model is used to evaluate the proposed work. In addition to this, statistical analysis is performed using the Pearson correlation, Kendall’s correlation, Spearman’s correlation, and the Friedman test on the ranks generated by different methods, which shows that the results generated by different proposed methods are consistent. Furthermore, the performance of the proposed method is compared with state-of-the-art approaches.

Influential nodes identification in complex networks is vital for understanding and controlling the propagation process in complex networks. Some existing centrality measures ignore the impacts of neighbor node. It is well-known that degree is a famous centrality measure for influential nodes identification, and the contributions of neighbors also should be taken into consideration. Furthermore, topological connections among neighbors will affect nodes' spreading ability, that is, the denser the connections among neighbors, the greater the chance of infection. In this paper, we propose a novel centrality, called DCC, to identify influential nodes by comprehensively considering degree and clustering coefficient as well as neighbors. The weights of degree and clustering coefficient are calculated by entropy technology. To verify the feasibility and effectiveness of DCC, the comparisons between DCC and other centrality measures in four aspects are conducted based on four real networks. The experimental results demonstrate that DCC is more effective in identifying influential nodes.

Identifying influential nodes in complex networks is essential for network robust and stability, such as viral marketing and information control. Various methods have been proposed to define the influence of nodes. In this paper, we comprehensively consider the global position and local structure to identify influential nodes. The number of iterations in the process of k-shell decomposition is taken into consideration, and the improved k-shell decomposition is then put forward. The improved k-shell decomposition and degree of target node are taken as the benchmark centrality, in addition, as is well known, the effect between node pairs is inversely proportional to the shortest path length between two nodes, and then we also consider the effect of neighbors on target node. To evaluate the performance of the proposed method, susceptible-infected (SI) model is adopted to simulate the spreading process in four real networks, and the experimental results show that the proposed method has obvious advantages over classical centrality measures in identifying influential nodes.

Controlling COVID-19 transmission with isolation of influential nodes

Influence maximization refers to selecting a small number of influential nodes in a given network to maximize the influence affected by the subset. In social network analysis and viral marketing, influence maximization is greatly significant. The greedy-based algorithm is time-consuming in estimating the expected influence diffusion of a given node set, which is unsuitable for large-scale network. The traditional heuristics often have the problem of low accuracy. In this study, in order to solve the influence maximization problem more effectively, a meta-heuristic discrete crow search algorithm (DCSA) using the intelligence of crow population is proposed. In DCSA, a new coding mechanism and discrete evolution rules are constructed. The degree-based initialization method and the random walk strategy are adopted to enhance the search ability. Moreover, according to the network topology, influential nodes Candidates are generated to avoid blindness in the process of crow search. Extensive experiments are conducted on six real-world social networks under independent cascade (IC) model, the results show that DCSA outperforms other state-of-the-art algorithms and obtains comparable influence diffusion results to CELF but with lower time complexity.

The identification of influential nodes in complex networks is a hot topic among scholars. Classical methods commonly analyze single node information or static structures but seldom emphasize dynamic properties and the interactive influence of nodes. Here, we proposed an improved Dynamic-Sensitive centrality (IDS) method by considering the interactive influence of both the self and neighbor nodes. Based on six real aviation networks and the Susceptible Infected Recovered (SIR) spreading disease model, we simulated the actual spreading process within these networks. Relevant experiments were conducted through Kendall’s correlation coefficient, the imprecision function, and the complementary cumulative distribution function. The experimental results demonstrated that the IDS can more accurately identify the influential node and effectively differentiate the node influence in the network compared with other benchmark methods. Especially in the EU air-2 network, the IDS results in Kendall’s correlation coefficient are improved by 105% compared to the DS centrality.

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

CAGM: A communicability-based adaptive gravity model for influential nodes identification in complex networks

Accurate identification of influential nodes facilitates the control of rumor propagation and interrupts the spread of computer viruses. Many classical approaches have been proposed by researchers regarding different aspects. To explore the impact of location information in depth, this paper proposes an improved global structure model to characterize the influence of nodes. The method considers both the node’s self-information and the role of the location information of neighboring nodes. First, degree centrality of each node is calculated, and then degree value of each node is used to represent self-influence, and degree values of the neighbor layer nodes are divided by the power of the path length, which is path attenuation used to represent global influence. Finally, an extended improved global structure model that considers the nearest neighbor information after combining self-influence and global influence is proposed to identify influential nodes. In this paper, the propagation process of a real network is obtained by simulation with the SIR model, and the effectiveness of the proposed method is verified from two aspects of discrimination and accuracy. The experimental results show that the proposed method is more accurate in identifying influential nodes than other comparative methods with multiple 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.

Ranking nodes in complex networks based on local structure and improving closeness centrality

The identification of influential nodes in complex networks is one of the most exciting topics in network science. The latest work successfully compares each node using local connectivity and weak tie theory from a new perspective. We study the structural properties of networks in depth and extend this successful node evaluation from single-scale to multi-scale. In particular, one novel position parameter based on node transmission efficiency is proposed, which mainly depends on the shortest distances from target nodes to high-degree nodes. In this regard, the novel multi-scale information importance (MSII) method is proposed to better identify the crucial nodes by combining the network’s local connectivity and global position information. In simulation comparisons, five state-of-the-art algorithms, i.e. the neighbor nodes degree algorithm (NND), betweenness centrality, closeness centrality, Katz centrality and the k-shell decomposition method, are selected to compare with our MSII. The results demonstrate that our method obtains superior performance in terms of robustness and spreading propagation for both real-world and artificial networks.

The aftermath of including new technologies in a modern electric system in conjunction with the incessant rise in power demand could pose a risk to the optimal operation of the system. Therefore, it becomes imperative to identify the most influential and critical nodes of such a system to avert future problems in network operation. In this paper, to identify most significant nodes of the system, the authors propose two measures of centrality in accordance with the network structural properties of a power system, namely, degree centrality (DC) and eigenvector centrality (EC). These are expressed considering the admittance matrix that exists among the interconnection of load to load nodes in an electrical power network. A critical node closeness centrality (CNCC) method is also proposed to identify critical nodes of the system. This is done by modifying the conventional closeness centrality (CC) to include the influence of interconnection that exists between network load to load nodes as captured by the admittance matrix between them. A comparative analysis of the proposed techniques with other conventional methods is also carried out. The result of the simulation shows that the proposed methods could serve as alternative tools in the identification of influential and weak nodes in a power system.