Social networks are absolutely a useful and important place for connecting people within the world. A basic issue in a social network is to identify the key persons within it. This is why different centrality measures have been found over the years. In this survey paper, we present past and present research works on measures of centrality in social network. For this plan, we discuss mathematical definitions and different developed centrality measures. We also present some applications of centrality measures in biology, research, security, traffic, transportation, drug, class room. At last, our future research work on centrality measure is given.

Study on centrality measures in social networks: a survey

Identifying key players in collective dynamics remains a challenge in several research fields, from the efficient dissemination of ideas to drug target discovery in biomedical problems. The difficulty lies at several levels: how to single out the role of individual elements in such intermingled systems, or which is the best way to quantify their importance. Centrality measures describe a node's importance by its position in a network. The key issue obviated is that the contribution of a node to the collective behavior is not uniquely determined by the structure of the system but it is a result of the interplay between dynamics and network structure. We show that dynamical influence measures explicitly how strongly a node's dynamical state affects collective behavior. For critical spreading, dynamical influence targets nodes according to their spreading capabilities. For diffusive processes it quantifies how efficiently real systems may be controlled by manipulating a single node.

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A measure of individual role in collective dynamics

To maximize the spreading influence of multiple spreaders in complex networks, one important fact cannot be ignored: the multiple spreaders should be dispersively distributed in networks, which can effectively reduce the redundance of information spreading. For this purpose, we define a generalized closeness centrality (GCC) index by generalizing the closeness centrality index to a set of nodes. The problem converts to how to identify multiple spreaders such that an objective function has the minimal value. By comparing with the K-means clustering algorithm, we find that the optimization problem is very similar to the problem of minimizing the objective function in the K-means method. Therefore, how to find multiple nodes with the highest GCC value can be approximately solved by the K-means method. Two typical transmission dynamics—epidemic spreading process and rumor spreading process are implemented in real networks to verify the good performance of our proposed method.

Identifying multiple influential spreaders based on generalized closeness centrality

Influential spreaders are the key players in maximizing or controlling the spreading in a complex network. Identifying the influential spreaders using kshell decomposition method has become very popular in the recent time. In the literature, the core nodes i.e. with the largest kshell index of a network are considered as the most influential spreaders. We have studied the kshell method and spreading dynamics of nodes using Susceptible–Infected–Recovered (SIR) epidemic model to understand the behavior of influential spreaders in terms of its topological location in the network. From the study, we have found that every node in the core area is not the most influential spreader. Even a strategically placed lower shell node can also be a most influential spreader. Moreover, the core area can also be situated at the periphery of the network. The existing indexing methods are only designed to identify the most influential spreaders from core nodes and not from lower shells. In this work, we propose a kshell hybrid method to identify highly influential spreaders not only from the core but also from lower shells. The proposed method comprises the parameters such as kshell power, node’s degree, contact distance, and many levels of neighbors’ influence potential. The proposed method is evaluated using nine real world network datasets. In terms of the spreading dynamics, the experimental results show the superiority of the proposed method over the other existing indexing methods such as the kshell method, the neighborhood coreness centrality, the mixed degree decomposition, etc. Furthermore, the proposed method can also be applied to large-scale networks by considering the three levels of neighbors’ influence potential.

Identifying influential spreaders in complex networks based on kshell hybrid method

Identifying influential spreaders in complex networks is a fundamental network project. It has drawn great attention in recent years because of its great theoretical significance and practical value in some fields. K-shell is an efficient method for identifying influential spreaders. However, k-shell neglects information about the topological position of the nodes. In this paper, we propose an improved algorithm based on the k-shell and node information entropy named IKS to identify influential spreaders from the higher shell as well as the lower shell. The proposed method employs the susceptible–infected–recovered (SIR) epidemic model, Kendall’s coefficient τ , the monotonicity M, and the average shortest path length L s to evaluate the performance and compare with other benchmark methods. The results of the experiment on eight real-world networks show that the proposed method can rank the influential spreaders more accurately. Moreover, IKS has superior computational complexity and can be extended to large-scale networks.

Identifying influential spreaders in complex networks based on improved k-shell method

Identifying the most influential spreaders in complex networks is crucial for optimally using the network structure and designing efficient strategies to accelerate information dissemination or prevent epidemic outbreaks. In this paper, by taking into account the centrality of a node and its neighbors’ centrality which depends on the diffusion importance of links, we propose a novel influence measure, the weight neighborhood centrality, to quantify the spreading ability of nodes in complex networks. To evaluate the performance of our method, we use the Susceptible–Infected–Recovered (SIR) model to simulate the epidemic spreading process on six real-world networks and four artificial networks. By measuring the rank imprecision and the rank correlation between the rank lists generated by simulation results via SIR and the ones generated by centrality measures, it shows that in general the weight neighborhood centrality can rank the spreading ability of nodes more accurately than its benchmark centrality, especially when using the degree k or coreness k s as the benchmark centrality. Further, we compare the monotonicity and the computational complexity of different ranking methods, which show that our method not only can be better at distinguishing the spreading ability of nodes but also can be used in large-scale networks due to the high computation efficiency.

Junyi Wang

Papers

A novel weight neighborhood centrality algorithm for identifying influential spreaders in complex networks