Price–volume cross-correlation analysis of CSI300 index futures

We investigate the cross-correlation between price returns and trading volumes for the China Securities Index 300 (CSI300) index futures, which are the only stock index futures traded on the China Financial Futures Exchange (CFFEX). The basic statistics suggest that distributions of these two time series are not normal but exhibit fat tails. Based on the detrended cross-correlation analysis (DCCA), we obtain that returns and trading volumes are long-range cross-correlated. The existence of multifractality in the cross-correlation between returns and trading volumes has been proven with the multifractal detrended cross-correlation analysis (MFDCCA) algorithm. The multifractal analysis also confirms that returns and trading volumes have different degrees of multifractality. We further perform a cross-correlation statistic to verify whether the cross-correlation significantly exists between returns and trading volumes for CSI300 index futures. In addition, results of the test for lead-lag effect demonstrate that contemporaneous cross-correlation of return and trading volume series is stronger than cross-correlations of leaded or lagged series.     

基于区域密度曲线识别网络上的多影响力节点

复杂网络多影响力节点的识别可以帮助理解网络的结构和功能,具有重要的理论意义和应用价值.本文提出一种基于网络区域密度曲线的多影响力节点的识别方法.应用两种不同的传播模型,在不同网络上与其他中心性指标进行了比较.结果表明,基于区域密度曲线的识别方法能够更好地识别网络中的多影响力节点,选中的影响力节点之间的分布较为分散,自身也比较重要.本文所提方法是基于网络的局部信息,计算的时间复杂度较低.     

Compatibility as underlying mechanism behind the evolution of networks

In this work we propose a dynamic network model based on an evolutive rule called compatibility. The presence of common topological properties observed in two real complex networks are well reproduced by the proposed model. These results suggest that the compatibility between nodes is sufficient to generate the complexity observed in real systems even considering that the new added nodes do not have the ability to know global information of the system.     

基于多属性决策的复杂网络节点重要性综合评价方法

复杂网络中的节点重要性评价在实际应用中有着重要意义.现有的一些重要性评价指标如度、介数等存在适用范围有限,评价结果不够全面等缺点,因为节点在复杂网络中的重要性不仅仅受单一因素的影响.为此,本文提出了一种基于多属性决策的复杂网络节点重要性综合评价方法.该方法将复杂网络中的每一个节点看作一个方案,其多个重要性评价指标作为该方案的属性,通过计算每个方案到理想方案的接近程度,最终得到该节点的重要性综合评价结果.该方法不仅可以用于不同类型复杂网络的节点重要性评价,而且便于扩展,实验结果表明了该方法的有效性.     

Geographical networks: geographical effects on network properties

Complex networks describe a wide range of systems in nature and society. Since most real systems exist in certain physical space and the distance between the nodes has influence on the connections, it is helpful to study geographical complex networks and to investigate how the geographical constrains on the connections affect the network properties. In this paper, we briefly review our recent progress on geographical complex networks with respect of statistics, modelling, robustness, and synchronizability. It has been shown that the geographical constrains tend to make the network less robust and less synchronizable. Synchronization on random networks and clustered networks is also studied.      

A new information dimension of complex networks

The fractal and self-similarity properties are revealed in many complex networks. The classical information dimension is an important method to study fractal and self-similarity properties of planar networks. However, it is not practical for real complex networks. In this Letter, a new information dimension of complex networks is proposed. The nodes number in each box is considered by using the box-covering algorithm of complex networks. The proposed method is applied to calculate the fractal dimensions of some real networks. Our results show that the proposed method is efficient when dealing with the fractal dimension problem of complex networks.     

叶子节点对于网络同步能力影响的研究

系统考察了叶子节点对于网络同步能力的影响,发现随着叶子节点比例的增加,网络的同步能力下降,同时给出了数值结果以及理论解释. 关键词： 复杂网络 叶子节点 同步能力     

Clustering and community detection in directed networks: A survey

Networks (or graphs) appear as dominant structures in diverse domains, including sociology, biology, neuroscience and computer science. In most of the aforementioned cases graphs are directed — in the sense that there is directionality on the edges, making the semantics of the edges nonsymmetric as the source node transmits some property to the target one but not vice versa. An interesting feature that real networks present is the clustering or community structure property, under which the graph topology is organized into modules commonly called communities or clusters. The essence here is that nodes of the same community are highly similar while on the contrary, nodes across communities present low similarity. Revealing the underlying community structure of directed complex networks has become a crucial and interdisciplinary topic with a plethora of relevant application domains. Therefore, naturally there is a recent wealth of research production in the area of mining directed graphs — with clustering being the primary method sought and the primary tool for community detection and evaluation. The goal of this paper is to offer an in-depth comparative review of the methods presented so far for clustering directed networks along with the relevant necessary methodological background and also related applications. The survey commences by offering a concise review of the fundamental concepts and methodological base on which graph clustering algorithms capitalize on. Then we present the relevant work along two orthogonal classifications. The first one is mostly concerned with the methodological principles of the clustering algorithms, while the second one approaches the methods from the viewpoint regarding the properties of a good cluster in a directed network. Further, we present methods and metrics for evaluating graph clustering results, demonstrate interesting application domains and provide promising future research directions.     

节点中心性对复杂网络传播模式的影响分析

在众多的重要节点评估方法研究中,具有较高中心性的节点一直是关注的焦点,许多传播行为的研究也主要围绕高中心性节点展开,因此在一定程度上忽略了低中心性节点对传播行为的影响.本文从传播异构性角度,通过初始感染最大中心性节点和最小中心性节点揭示网络结构异构性对信息传播的影响.实验结果表明,传播过程中存在"链型"和"扇型"两种传播模式,在初始感染比例不断提升的情况下,两种传播模式的相互转换引发传播速率的变化,进一步促使非线性传播规模交叉现象的产生.这一现象说明,在宏观的信息传播过程中,最小中心性节点的影响力不容忽视,尤其在初始感染比例升高时,最小中心性节点比最大中心性节点更具传播优势.     

复杂网络牵制控制优化选点算法及节点组重要性排序

本文研究复杂网络动力学模型的无向网络牵制控制的优化选点及节点组重要性排序问题.根据牵制控制的同步准则,网络的牵制控制同步取决于网络的Laplacian删后矩阵的最小特征值.因此,通过合理选择受控节点集得到一个较大的Laplacian删后矩阵最小特征值,是牵制控制优化选点问题的核心所在.基于Laplacian删后矩阵最小特征值的图谱性质,本文提出了多个受控节点选取的递归迭代算法,该算法适用于任意类型的网络.通过BA无标度网络、NW小世界网络及一些实际网络中的仿真实验表明:该算法在控制节点数较少时,能有效找到最优受控节点集.最后讨论了在复杂网络牵制控制背景下节点组重要性排序问题,提出节点组的重要性排序与受控节点的数目有关.     

Ranking important nodes in complex networks by simulated annealing

In this paper, based on simulated annealing a new method to rank important nodes in complex networks is presented.First, the concept of an importance sequence(IS) to describe the relative importance of nodes in complex networks is defined. Then, a measure used to evaluate the reasonability of an IS is designed. By comparing an IS and the measure of its reasonability to a state of complex networks and the energy of the state, respectively, the method finds the ground state of complex networks by simulated annealing. In other words, the method can construct a most reasonable IS. The results of experiments on real and artificial networks show that this ranking method not only is effective but also can be applied to different kinds of complex networks.     

Identifying missing and spurious connections via the bi-directional diffusion on bipartite networks

Link prediction and spurious link detection in complex networks have attracted increasing attention from both physical and computer science communities, due to their wide applications in many real systems. Related previous works mainly focus on monopartite networks while these problems in bipartite networks are not yet systematically addressed. Containing two different kinds of nodes, bipartite networks are essentially different from monopartite networks, especially in node similarity calculation: the similarity between nodes of different kinds (called inter-similarity) is not well defined. In this letter, we employ the local diffusion processes to measure the inter-similarity in bipartite networks. We find that the inter-similarity is asymmetric if the diffusion is applied in different directions. Accordingly, we propose a bi-directional hybrid diffusion method which is shown to achieve higher accuracy than the existing diffusion methods in identifying missing and spurious links in bipartite networks.     

An Efficient Partition-Based Approach to Identify and Scatter Multiple Relevant Spreaders in Complex Networks

One of the main problems in graph analysis is the correct identification of relevant nodes for spreading processes. Spreaders are crucial for accelerating/hindering information diffusion, increasing product exposure, controlling diseases, rumors, and more. Correct identification of spreaders in graph analysis is a relevant task to optimally use the network structure and ensure a more efficient flow of information. Additionally, network topology has proven to play a relevant role in the spreading processes. In this sense, more of the existing methods based on local, global, or hybrid centrality measures only select relevant nodes based on their ranking values, but they do not intentionally focus on their distribution on the graph. In this paper, we propose a simple yet effective method that takes advantage of the underlying graph topology to guarantee that the selected nodes are not only relevant but also well-scattered. Our proposal also suggests how to define the number of spreaders to select. The approach is composed of two phases: first, graph partitioning; and second, identification and distribution of relevant nodes. We have tested our approach by applying the SIR spreading model over nine real complex networks. The experimental results showed more influential and scattered values for the set of relevant nodes identified by our approach than several reference algorithms, including degree, closeness, Betweenness, VoteRank, HybridRank, and IKS. The results further showed an improvement in the propagation influence value when combining our distribution strategy with classical metrics, such as degree, outperforming computationally more complex strategies. Moreover, our proposal shows a good computational complexity and can be applied to large-scale networks.     

相依网络的条件依赖群逾渗

相依网络鲁棒性研究多集中于满足无反馈条件的一对一依赖,但现实网络节点往往依赖于多节点构成的依赖群,即使群内部分节点失效也不会导致依赖节点失效.针对此现象提出了一种相依网络的条件依赖群逾渗模型,该模型允许依赖群内节点失效比例不超过容忍度γ时,依赖节点仍可正常工作.通过理论分析给出了基于生成函数方法的模型巨分量方程,仿真结果表明方程理论解与相依网络模拟逾渗值相吻合,增大γ值和依赖群规模可提高相依网络鲁棒性.本文模型有助于更好地理解现实网络逾渗现象,对如何增强相依网络鲁棒性有一定指导作用.     

Pinning control of weighted general complex dynamical networks with time delay

Time delays commonly exist in the real world. In the present work we consider weighted general complex dynamical networks with time delay, which are undirected and connected. Control of such networks, by applying local feedback injections to a fraction of network nodes, is investigated for both continuous-time and discrete-time cases. Both delay-independent and delay-dependent asymptotical stability criteria for network stabilization are derived. It is also shown that the whole network can be stabilized by controlling only one node. The efficiency of the derived results was illustrated by numerical examples.     

Planar unclustered scale-free graphs as models for technological and biological networks

Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases — usually associated with topological restrictions — their clustering is low and they are almost planar. In this paper we introduce a family of graphs which share all these properties and are defined by two parameters. As their construction is deterministic, we obtain exact analytic expressions for relevant properties of the graphs including the degree distribution, degree correlation, diameter, and average distance, as a function of the two defining parameters. Thus, the graphs are useful to model some complex networks, in particular several families of technological and biological networks, and in the design of new practical communication algorithms in relation to their dynamical processes. They can also help understanding the underlying mechanisms that have produced their particular structure.     

Identifying influential nodes in complex networks

Identifying influential nodes that lead to faster and wider spreading in complex networks is of theoretical and practical significance. The degree centrality method is very simple but of little relevance. Global metrics such as betweenness centrality and closeness centrality can better identify influential nodes, but are incapable to be applied in large-scale networks due to the computational complexity. In order to design an effective ranking method, we proposed a semi-local centrality measure as a tradeoff between the low-relevant degree centrality and other time-consuming measures. We use the Susceptible-Infected-Recovered (SIR) model to evaluate the performance by using the spreading rate and the number of infected nodes. Simulations on four real networks show that our method can well identify influential nodes.     

Social power and opinion formation in complex networks

In this paper we investigate the effects of social power on the evolution of opinions in model networks as well as in a number of real social networks. A continuous opinion formation model is considered and the analysis is performed through numerical simulation. Social power is given to a proportion of agents selected either randomly or based on their degrees. As artificial network structures, we consider scale-free networks constructed through preferential attachment and Watts–Strogatz networks. Numerical simulations show that scale-free networks with degree-based social power on the hub nodes have an optimal case where the largest number of the nodes reaches a consensus. However, given power to a random selection of nodes could not improve consensus properties. Introducing social power in Watts–Strogatz networks could not significantly change the consensus profile.     

一种基于文本互信息的金融复杂网络模型

复杂网络能够解决许多金融问题,能够发现金融市场的拓扑结构特征,反映不同金融主体之间的相互依赖关系.相关性度量在金融复杂网络构建中至关重要.通过将多元金融时间序列符号化,借鉴文本特征提取以及信息论的方法,定义了一种基于文本互信息的相关系数.为检验方法的有效性,分别构建了基于不同相关系数(Pearson和文本互信息)和不同网络缩减方法(阈值和最小生成树)的4个金融复杂网络模型.在阈值网络中提出了使用分位数来确定阈值的方法,将相关系数6等分,取第4部分的中点作为阈值,此时基于Pearson和文本互信息的阈值模型将会有相近的边数,有利于这两种模型的对比.数据使用了沪深两地证券市场地区指数收盘价,时间从2006年1月4日至2016年12月30日,共计2673个交易日.从网络节点相关性看,基于文本互信息的方法能够体现出大约20%的非线性相关关系;在网络整体拓扑指标上,本文计算了4种指标,结果显示能够使所保留的节点联系更为紧密,有效提高保留节点的重要性以及挖掘出更好的社区结构;最后,计算了阈值网络的动态指标,将数据按年分别构建网络,缩减方法只用了阈值方法,结果显示本文提出的方法在小世界动态和网络度中心性等指标上能够成功捕捉到样本区间内存在的两次异常波动.此外,本文构建的地区金融网络具有服从幂律分布、动态稳定性、一些经济欠发达地区在金融地区网络中占据重要地位等特性.     

Efficient overlapping community detection in huge real-world networks

The detection of overlapping community structure in networks can give insight into the structures and functions of many complex systems. In this paper, we propose a simple but efficient overlapping community detection method for very large real-world networks. Taking a high-quality, non-overlapping partition generated by existing, efficient, non-overlapping community detection methods as input, our method identifies overlapping nodes between each pair of connected non-overlapping communities in turn. Through our analysis on modularity, we deduce that, to become an overlapping node without demolishing modularity, nodes should satisfy a specific condition presented in this paper. The proposed algorithm outputs high quality overlapping communities by efficiently identifying overlapping nodes that satisfy the above condition. Experiments on synthetic and real-world networks show that in most cases our method is better than other algorithms either in the quality of results or the computational performance. In some cases, our method is the only one that can produce overlapping communities in the very large real-world networks used in the experiments.