The heterogeneous nature of a complex network determines the roles of each node in the network that are quite different. Mechanisms of complex networks such as spreading dynamics, cascading reactions, and network synchronization are highly affected by a tiny fraction of so-called important nodes. Node importance ranking is thus of great theoretical and practical significance. Network entropy is usually utilized to characterize the amount of information encoded in the network structure and to measure the structural complexity at the graph level. We find that entropy can also serve as a local level metric to quantify node importance. We propose an entropic metric, Entropy Variation, defining the node importance as the variation of network entropy before and after its removal, according to the assumption that the removal of a more important node is likely to cause more structural variation. Like other state-of-the-art methods for ranking node importance, the proposed entropic metric is also used to utilize structural information, but at the systematical level, not the local level. Empirical investigations on real life networks, the Snake Idioms Network, and several other well-known networks, demonstrate the superiority of the proposed entropic metric, notably outperforming other centrality metrics in identifying the top-k most important nodes.Entropy 2017, 19, 303 2 of 17 ranking important nodes make use of the structural information [6]. For more details about the above mentioned centralities, we refer to [6,29].Structural complexity is perhaps the most important property of a complex network [1]. Network entropy is usually utilized to characterize the amount of information encoded in the network structure and to measure the structural complexity [30]. Recently, considerable effort has focused on quantifying network complexity using entropy measures [31], and several entropic metrics have been proposed; to name a few, network connectivity entropy [32], cyclic entropy [33], mapping entropy [34], hotspot entropy [35], Riemannian-geometric entropy [36], and q-entropy [37]. These measures have been shown to be extremely successful in quantifying the level of organization encoded in structural features of networks.As was mentioned before, we often resort to network structural information for ranking node importance, while entropy can serve as a fundamental tool to capture the structural information of complex networks. However, to the best of our knowledge, there are seldom entropic metrics developed to measure node importance. Two recent exceptions are the Relative Entropy [38] and Expected Force [39]. Relative entropy [38] is proposed as an integrated evaluation approach for node importance, which generates an optimal solution from different individual centrality indices by linear programming. Thus relative entropy serves not as a direct metric for node importance ranking, but a hybrid approach for synthesizing the existing ones. Expected Force [39] is a node property derived from local network topology to depict the ...

Topological measures are crucial to describe, classify and understand complex networks. Lots of measures are proposed to characterize specific features of specific networks, but the relationships among these measures remain unclear. Taking into account that pulling networks from different domains together for statistical analysis might provide incorrect conclusions, we conduct our investigation with data observed from the same network in the form of simultaneously measured time series. We synthesize a transfer entropy-based framework to quantify the relationships among topological measures, and then to provide a holistic scenario of these measures by inferring a drive-response network. Techniques from Symbolic Transfer Entropy, Effective Transfer Entropy, and Partial Transfer Entropy are synthesized to deal with challenges such as time series being nonstationary, finite sample effects and indirect effects. We resort to kernel density estimation to assess significance of the results based on surrogate data. The framework is applied to study 20 measures across 2779 records in the Technology Exchange Network, and the results are consistent with some existing knowledge. With the drive-response network, we evaluate the influence of each measure by calculating its strength, and cluster them into three classes, i.e., driving measures, responding measures and standalone measures, according to the network communities.

Electricity theft detection issue has drawn lots of attention during last decades. Timely identification of the electricity theft in the power system is crucial for the safety and availability of the system. Although sustainable efforts have been made, the detection task remains challenging and falls short of accuracy and efficiency, especially with the increase of the data size. Recently, convolutional neural network-based methods have achieved better performance in comparison with traditional methods, which employ handcrafted features and shallow-architecture classifiers. In this paper, we present a novel approach for automatic detection by using a multi-scale dense connected convolution neural network (multi-scale DenseNet) in order to capture the long-term and short-term periodic features within the sequential data. We compare the proposed approaches with the classical algorithms, and the experimental results demonstrate that the multiscale DenseNet approach can significantly improve the accuracy of the detection. Moreover, our method is scalable, enabling larger data processing while no handcrafted feature engineering is needed.

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The task of partial copy detection in videos aims at determine if one or more segments of the query video are already present in the data-set, while giving the information of similar portion time period. At present, most effective algorithms of partial copy detection in videos are designed as three steps: feature extraction, feature matching and time alignment. The separation of feature matching and time alignment module ignores the spatio-temporal information of partial copy to some extent. Therefore, satisfactory performance is not obtained. In order to reduce this loss, this article does not decompose it into two separate tasks, but using a single convolution neural network to solve these two aspects. First, we sample video frames and extract CNN features, calculate the spatio-temporal relationship matrix of the source video and the query video, and then graphically map the matrix and train the convolution neural network based on the object detection task of the RefineDet model. Finally, in the query phase, the time period of the partial copy is deduced based on the detection result. In this paper, we evaluate the performance of the algorithm on the real complex video copy detection data-set VCDB which is significantly improved compared with the state-of-the-art partial copy detection framework.