Betweenness centrality is one of the most significant and commonly used centralities, where centrality is a notion of measuring the importance of nodes in networks. In 2001, Brandes proposed an algorithm for computing betweenness centrality efficiently, and it can compute those values for all nodes in O(nm) time for unweighted networks, where n and m denote the number of nodes and links in networks, respectively. However, even Brandes' algorithm is not fast enough for recent large-scale real-world networks, and therefore, much faster algorithms are expected. The objective of this research is to theoretically improve the efficiency of Brandes' algorithm by introducing graph decompositions, and to verify the practical effectiveness of our approaches by implementing them as computer programs and by applying them to various kinds of real-world networks. A series of computational experiments shows that our proposed algorithms run several times faster than the original Brandes' algorithm, which are guaranteed by theoretical analyses.

Recently, the controllability of complex networks has become a hot topic in the field of network science, where the driver nodes play a key and central role. Therefore, studying their structural characteristics is of great significance to understand the underlying mechanism of network controllability. In this paper, we systematically investigate the nodal centrality of driver nodes in controlling complex networks, we find that the driver nodes tend to be low in-degree but high out-degree nodes, and most of driver nodes tend to have low betweenness centrality but relatively high closeness centrality. We also find that the tendencies of driver nodes towards eigenvector centrality and Katz centrality show very similar behaviors, both high eigenvector centrality and high Katz centrality are avoided by driver nodes. Finally, we find that the driver nodes towards PageRank centrality demonstrate a polarized distribution, i.e., the vast majority of driver nodes tend to be low PageRank nodes whereas only few driver nodes tend to be high PageRank nodes.

The proliferation of Massive Open Online Courses has made it a challenge for the user to select a proper course. We assume a situation in which the user has targeted on the knowledge defined by some knowledge categories. Then, knowing how much of the knowledge in the category is covered by the courses will be helpful in the course selection. In this study, we define a concept of knowledge category coverage and aim to estimate it in a semi-automatic manner. We first model the knowledge category and the course as a set of concepts, and then utilize a taxonomy and the idea of centrality to differentiate the importance of concepts. Finally, we obtain the coverage value by calculating how much of the concepts required in a knowledge category is also taught in a course. Compared with treating the concepts uniformly important, we found that our proposed method can effectively generate closer coverage values to the ground truth assigned by domain experts.

In wireless networks, efficient topology improves the performance of network protocols. The previous research mainly focuses on how to construct a cost-efficient network structure from a static and connected topology. Due to lack of continuous connectivity in the underlying topology, most traditional topology control methods are not applicable to the delay or disruption tolerant networks (DTNs). In this paper, we consider the topology control problem in a predictable DTN where the dynamic topology is known a priori or can be predicted over time. First, this dynamic topology is modeled by a directed space-time graph that includes spatial and temporal information. Second, the topology control problem of the predictable DTN is formulated as building a sparse structure. For any pair devices, there is an efficient path connecting them to improve the efficiency of the generated structure. Then, a topology control strategy is proposed for this optimization problem by using a kth shortest paths algorithm. Finally, simulations are conducted on random networks and a real-world DTN tracing date. The results demonstrate that the proposed method can significantly improve the efficiency of the generated structure and reduce the total cost.

In recent years, with the rapid development of the Internet and cloud computing, an enormous amount of information is exchanged on various social networking services. In order to handle and maintain such a mountain of information properly by limited resources in the network, it is very important to comprehend the dynamics for propagation of information or activity on the social network. One of many indices used by social network analysis which investigates the network structure is “node centrality”. A common characteristic of conventional node centralities is that it depends on the topological structure of network and the value of node centrality does not change unless the topology changes. The network dynamics is generated by interaction between users whose strength is asymmetric in general. Network structure reflecting the asymmetric interaction between users is modeled by a directed graph, and it is described by an asymmetric matrix in matrix-based network model. In this paper, we showed an oscillation model for describing dynamics on networks generated from a certain kind of asymmetric interaction between nodes by using a symmetric matrix. Moreover, we propose a new extended index of well-known two node centralities based on the oscillation model. In addition, we show that the proposed index can describe various aspect of node centrality that considers not only the topological structure of the network, but also asymmetry of links, the distribution of source node of activity, and temporal evolution of activity propagation by properly assigning the weight of each link. The proposed model is regarded as the fundamental framework for different node centralities.

This paper proposes an oscillation model for analyzing the dynamics of activity propagation across social media networks. In order to analyze such dynamics, we generally need to model asymmetric interactions between nodes. In matrix-based network models, asymmetric interaction is frequently modeled by a directed graph expressed as an asymmetric matrix. Unfortunately, the dynamics of an asymmetric matrix-based model is difficult to analyze. This paper, first of all, discusses a symmetric matrix-based model that can describe some types of link asymmetry, and then proposes an oscillation model on networks. Next, the proposed oscillation model is generalized to arbitrary link asymmetry. We describe the outlines of four important research topics derived from the proposed oscillation model. First, we show that the oscillation energy of each node gives a generalized notion of node centrality. Second, we introduce a framework that uses resonance to estimate the natural frequency of networks. Natural frequency is important information for recognizing network structure. Third, by generalizing the oscillation model on directed networks, we create a dynamical model that can describe flaming on social media networks. Finally, we show the fundamental equation of oscillation on networks, which provides an important breakthrough for generalizing the spectral graph theory applicable to directed graphs.

The application of complex network theory to power grid analysis has been a hot topic in recent years, which mainly manifests itself in four aspects. The first aspect is to model power system networks. The second aspect is to reveal the topology of the grid itself. The third aspect is to reveal the inherent vulnerability and weakness of the power network itself and put forward the pertinent improvement measures to provide guidance for the construction of power grid. The last aspect is to analyze the mechanism of cascading failure and establish the cascading fault model of large power failure. In the past ten years, by using the complex network theory, many researchers have investigated the structural vulnerability of power grids from the point of view of topology. This letter studies the structural vulnerability of power grids according to the effect of selective node removal. We apply several kinds of node centralities including recently-presented second-order centrality (SOC) to guide the node removal attack. We test the effectiveness of all these centralities in guiding the node removal based on several IEEE power grids. Simulation results show that, compared with other node centralities, the SOC is relatively effective in guiding the node removal and can destroy the power grid with negative degree-degree correlation in less steps.

We propose a heuristic approximation algorithm for the 1-median problem. The 1-median problem is the problem of finding a vertex with the highest closeness centrality. Starting from a randomly selected vertex, our algorithm repeats to find a vertex with higher closeness centrality by approximately calculating closeness centrality of each vertex using simpler spanning subgraphs, which are called k-neighbor dense shortest path graphs with shortcuts. According to our experimental results using real networks with more than 10,000 vertices, our algorithm is more than 100 times faster than the exhaustive search and more than 20 times faster than the state-of-the-art approximation algorithm using annotated information to the vertices while the solutions output by our algorithm have higher approximation ratio.

The power grid defines one of the most important technological networks of our times and has been widely studied as a kind of complex network. It has been developed for more than one century and becomes an extremely huge and seemingly robust system. But it becomes extremely fragile as well because some unexpected minimal failures may lead to sudden and massive blackouts. Many works have been carried out to investigate the structural vulnerability of power grids from the topological point of view based on the complex network theory. This Letter focuses on the structural vulnerability of the power grid under the effect of selective node removal. We propose a new kind of node centrality called overall information centrality (OIC) to guide the node removal attack. We test the effectiveness of our centrality in guiding the node removal based on several IEEE power grids. Simulation results show that, compared with other node centralities such as degree centrality (DC), betweenness centrality (BC) and closeness centrality (CC), our OIC is more effective to guide the node removal and can destroy the power grid in less steps.

Routing is a challenging issue in mobile social networks (MSNs) because of time-varying links and intermittent connectivity. In order to enable nodes to make right decisions while forwarding messages, exploiting social relationship has become an important method for designing efficient routing protocols in MSNs. In this paper, we first use the temporal evolution graph model to accurately capture the dynamic topology of the MSN. Based on the model, we introduce the social relationship metric for detecting the quality of human social relationship from contact history records. Utilizing this metric, we propose social relationship based betweenness centrality metric to identify influential nodes to ensure messages forwarded by the nodes with stronger social relationship and higher likelihood of contacting other nodes. Then, we present SRBet, a novel social-based forwarding algorithm, which utilizes the aforementioned metric to enhance routing performance. Simulations have been conducted on two real world data sets and results demonstrate that the proposed forwarding algorithm achieves better performances than the existing algorithms.

In complex network analysis, there are various measures to characterize the centrality of each node within a graph, which determines the relative importance of each node. The more centrality a node has in a network, the more significance it has in the spread of infection. As one of the important extensions to shortest-path based betweenness centrality, the flow betweenness centrality is defined as the degree to which each node contributes to the sum of maximum flows between all pairs of nodes. One of the drawbacks of the flow betweenness centrality is that its time complexity is somewhat high. This Letter proposes an approximate method to calculate the flow betweenness centrality and provides experimental results as evidence.

Congestion inherently occurs on the Internet due to traffic concentration on certain nodes or links of networks. The traffic concentration is caused by inefficient use of topological information of networks in existing routing protocols, which reduces to inefficient mapping between traffic demands and network resources. Actually, the route with minimum cost, i.e., number of hops, selected as a transmission route by existing routing protocols would pass through specific nodes with common topological characteristics that could contribute to a large improvement in minimizing the cost. However, this would result in traffic concentration on such specific nodes. Therefore, we propose a measure of the distance between two nodes that is suitable for reducing traffic concentration on specific nodes. To consider the topological characteristics of the congestion points of networks, we define node-to-node distance by using a generalized norm, p-norm, of a vector of which elements are degrees of intermediate nodes of the route. Simulation results show that both the maximum Stress Centrality (SC) and the coefficient of variation of the SC are minimized in some network topologies by selecting transmission routes based on the proposed measure of node-to-node distance.