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

Identifying a set of influential nodes is an important topic in complex networks which plays a crucial role in many applications, such as market advertising, rumor controlling, and predicting valuable scientific publications. In regard to this, researchers have developed algorithms from simple degree methods to all kinds of sophisticated approaches. However, a more robust and practical algorithm is required for the task. In this paper, we propose the EnRenew algorithm aimed to identify a set of influential nodes via information entropy. Firstly, the information entropy of each node is calculated as initial spreading ability. Then, select the node with the largest information entropy and renovate its l-length reachable nodes' spreading ability by an attenuation factor, repeat this process until specific number of influential nodes are selected. Compared with the best state-of-the-art benchmark methods, the performance of proposed algorithm improved by 21.1%, 7.0%, 30.0%, 5.0%, 2.5%, and 9.0% in final affected scale on CEnew, Email, Hamster, Router, Condmat, and Amazon network, respectively, under the Susceptible-Infected-Recovered (SIR) simulation model. The proposed algorithm measures the importance of nodes based on information entropy and selects a group of important nodes through dynamic update strategy. The impressive results on the SIR simulation model shed light on new method of node mining in complex networks for information spreading and epidemic prevention.

Influential Nodes Identification in Complex Networks via Information Entropy

A challenging issue in viral marketing is to effectively identify a set of influential users. By sending the advertising messages to this set, one can reach out the largest area of the network. In this paper, we formulate the influence maximization problem as an optimization problem with cost functions as the influentiality of the nodes and the distance between them. Maximizing the distance between the seed nodes guarantees reaching to different parts of the network. We use gray wolf optimization algorithm to solve the problem. Our experimental results on three real-world networks show that proposed method outperforms state-of-the-art influence maximization algorithms. Furthermore, it has lower computational time than other meta-heuristic methods.

Identification of influential users in social network using gray wolf optimization algorithm

Identifying influential spreaders in complex networks is a crucial problem which relates to wide applications. Many methods based on the global information such as $k$-shell and PageRank have been applied to rank spreaders. However, most of related previous works overwhelmingly focus on the number of paths for propagation, while whether the paths are diverse enough is usually overlooked. Generally, the spreading ability of a node might not be strong if its propagation depends on one or two paths while the other paths are dead ends. In this Letter, we introduced the concept of path diversity and find that it can largely improve the ranking accuracy. We further propose a local method combining the information of path number and path diversity to identify influential nodes in complex networks. This method is shown to outperform many well-known methods in both undirected and directed networks. Moreover, the efficiency of our method makes it possible to be applied to very large systems.

Path diversity improves the identification of influential spreaders

Community detection plays an important role in social networks, since it can help to naturally divide the network into smaller parts so as to simplify network analysis. However, on the other hand, it arises the concern that individual information may be overmined, and the concept community deception has been proposed to protect individual privacy on social networks. Here, we introduce and formalize the problem of community detection attack and develop efficient strategies to attack community detection algorithms by rewiring a small number of connections, leading to privacy protection. In particular, we first give two heuristic attack strategies, i.e., Community Detection Attack (CDA) and Degree Based Attack (DBA), as baselines, utilizing the information of detected community structure and node degree, respectively. Then, we propose an attack strategy called “genetic algorithm (GA)-based Q-Attack,” where the modularity $Q$ is used to design the fitness function. We launch community detection attack based on the above three strategies against six community detection algorithms on several social networks. By comparison, our Q-Attack method achieves much better attack effects than CDA and DBA, in terms of the larger reduction of both modularity $Q$ and normalized mutual information (NMI). In addition, we further take transferability tests and find that adversarial networks obtained by Q-Attack on a specific community detection algorithm also show considerable attack effects while generalized to other algorithms.

GA-Based Q-Attack on Community Detection

Identifying multiple influential spreaders by a heuristic clustering algorithm

The problem of identifying influential nodes in complex networks has attracted much attention owing to its wide applications, including how to maximize the information diffusion, boost product promotion in a viral marketing campaign, prevent a large scale epidemic and so on. From spreading viewpoint, the probability of one node propagating its information to one other node is closely related to the shortest distance between them, the number of shortest paths and the transmission rate. However, it is difficult to obtain the values of transmission rates for different cases, to overcome such a difficulty, we use the reciprocal of average degree to approximate the transmission rate. Then a semi-local centrality index is proposed to incorporate the shortest distance, the number of shortest paths and the reciprocal of average degree simultaneously. By implementing simulations in real networks as well as synthetic networks, we verify that our proposed centrality can outperform well-known centralities, such as degree centrality, betweenness centrality, closeness centrality, k-shell centrality, and nonbacktracking centrality. In particular, our findings indicate that the performance of our method is the most significant when the transmission rate nears to the epidemic threshold, which is the most meaningful region for the identification of influential nodes.

Identification of influential nodes in complex networks: Method from spreading probability viewpoint

Complex networks hosting binary-state dynamics can represent many phenomena in real world systems. Therefore, some approaches were proposed to reconstruct the structures of networks with binary-state dynamics. However, they often hold two assumptions: 1) require a priori knowledge about which state is the active state, or one state is imposed as the active state; and 2) only one side of transition probability is utilized for network reconstruction. Many binary-state dynamics, such as cooperative/defective state in evolutionary game, agree/disagree of two competing opinions, it is hard to define which state is the active state, what’s more, both sides of the transition probability depend on the states of neighbors. For this situation, if we only consider one side of transition probability, the reconstruction accuracy is greatly discounted because many data are not effectively used. By abandoning the two assumptions, we here develop a generalized statistical inference approach by exploiting the expectation-maximization algorithm to reconstruct networks. Our approach requires less information regarding the dynamics, indicating more potential applications. More importantly, our approach sufficiently mines the given data, the results on empirical and synthetic networks demonstrate the high-reconstruction accuracy. In addition, the method is parameter free and robust to the stochastic fluctuations.

Reconstructing of Networks With Binary-State Dynamics via Generalized Statistical Inference

The core-periphery structure and the community structure are two typical meso-scale structures in complex networks. Although community detection has been extensively investigated from different perspectives, the definition and the detection of the core-periphery structure have not received much attention. Furthermore, the detection problems of the core-periphery and community structure were separately investigated. In this paper, we develop a unified framework to simultaneously detect the core-periphery structure and community structure in complex networks. Moreover, there are several extra advantages of our algorithm: our method can detect not only single but also multiple pairs of core-periphery structures; the overlapping nodes belonging to different communities can be identified; different scales of core-periphery structures can be detected by adjusting the size of the core. The good performance of the method has been validated on synthetic and real complex networks. So, we provide a basic framework to detect the two typical meso-scale structures: the core-periphery structure and the community structure.

Zhong-Kui Bao

Papers

Identifying multiple influential spreaders by a heuristic clustering algorithm

Identification of influential nodes in complex networks: Method from spreading probability viewpoint

Reconstructing of Networks With Binary-State Dynamics via Generalized Statistical Inference

A unified method of detecting core-periphery structure and community structure in networks

Improving link prediction in complex networks by adaptively exploiting multiple structural features of networks