Identifying influential spreaders by weight degree centrality in complex networks

The problem of identifying influential spreaders in complex networks has attracted much attention because of its great theoretical significance and wide application. In this paper, we propose a successful ranking method for identifying the influential spreaders. The proposed method measures the spreading ability of nodes based on their degree and their ability of spreading out. We also use a tuning weight parameter, which is always associated with the property of the networks such as the assortativity, to regulate the weight between the degree and the ability of spreading out. To test the effectiveness of the proposed method, we conduct the experiments on several synthetic networks and real-world networks. The results show that the proposed method outperforms the existing well-known ranking methods.     

Leverage centrality analysis of infrastructure networks

Leverage centrality is a novel centrality measure proposed to identify the critical nodes that are highly influential within the network. Leverage centrality considers the extent of connectivity of a node relative to the connectivity of its neighbors. The leverage centrality of a node in a network is determined by the extent to which its direct neighbors rely on that node for information. In this paper, leverage centralities of the nodes of infrastructure networks are computed and critical nodes within the network are identified.     

Quantifying the complexity of flow networks: How many roles are there?

Weighted flow networks are structures that arise naturally when analyzing complex systems. The countable properties of unweighted networks are not easily generalized to weighted networks. One candidate measure of complexity is the number of roles, or specialized functions in a network. It is easy to identify the number of roles in a linear or cyclic unweighted network. There is only one logically consistent way to generalize the measures of nodes, flows, connectivity, and roles into weighted networks, and these generalizations are equivalent to indices derived from information theory and used by ecologists since the late seventies. Data from ecosystem networks suggests that ecosystems inhabit a narrow window of the parameter space defined by these measures. © 2003 Wiley Periodicals, Inc.     

Design of partially survivable networks for cellular telecommunication systems

In cellular networks, cells are connected to the mobile telephone switching office (MTSO) directly or via hubs. It may also be desirable for some cells to split their traffic to two or more hubs for partial survivability in the case of equipment failures; such cells are said to have a diversity requirement greater than one. Assuming that hubs are connected to the MTSO via self-healing rings, as is common in current cellular implementations, the objective is to find the assignment of cells to hubs – including the MTSO – that meets demand as well as survivability requirements at minimum cost. With the increasing use of fiber for high capacity backbone transmission, networks have become sparser, and the consequences of link failures much more serious. Hence network survivability has taken on added urgency. Our paper models this problem in the context of cellular networks.     

Bounding blocking probabilities and throughput in queueing networks with buffer capacity constraints

We propose a new technique for upper and lower bounding of the throughput and blocking probabilities in queueing networks with buffer capacity constraints, i.e., some buffers in the network have finite capacity. By studying the evolution of multinomials of the state of the system in its assumed steady state, we obtain constraints on the possible behavior of the system. Using these constraints, we obtain linear programs whose values upper and lower bound the performance measures of interest, namely throughputs or blocking probabilities. The main advantages of this new technique are that the computational complexity does not increase with the size of the finite buffers and that the technique is applicable to systems in which some buffers have infinite capacity. The technique is demonstrated on examples taken from both manufacturing systems and communication networks. As a special case, for the M/M/s/s queue, we establish the asymptotic exactness of the bounds, i.e., that the bounds on the blocking probability asymptotically approach the exact value as the degree of the multinomials considered is increased to infinity. This revised version was published online in June 2006 with corrections to the Cover Date.     

The hub location and network design problem with fixed and variable arc costs: formulation and dual-based solution heuristic

Many air, less-than-truck load and intermodal transportation and telecommunication networks incorporate hubs in an effort to reduce total cost. These hubs function as make bulk/break bulk or consolidation/deconsolidation centres. In this paper, a new hub location and network design formulation is presented that considers the fixed costs of establishing the hubs and the arcs in the network, and the variable costs associated with the demands on the arcs. The problem is formulated as a mixed integer programming problem embedding a multi-commodity flow model. The formulation can be transformed into some previously modelled hub network design problems. We develop a dual-based heuristic that exploits the multi-commodity flow problem structure embedded in the formulation. The test results indicate that the heuristic is an effective way to solve this computationally complex problem.     

Static and dynamic models of biological networks

We consider static and dynamic approaches to the specification of probability distributions on graphs, consistent with desired statistical properties such as degree distributions, for use in modeling biological networks. In the static approach we develop analytical approximations to the Hamiltonian and partition functions. In the dynamic approach, we use a stochastic parameterized grammar to construct an evolutionary tree in which the nodes represent elements such as genes or cells and the links represent inheritance relations between the nodes. The grammar then constructs a network based on the feature vectors of the nodes in the tree. © 2006 Wiley Periodicals, Inc. Complexity 11:57–63, 2006     

复杂网络幂律度分布和层次聚集函数标度指数的一种新的估计方法

提出一种估计复杂网络幂律度分布和层次聚集函数标度指数的新方法,并给出求解这些指数的数值算法．该方法可以克服目前网络研究中采用的图形线性拟合估计方法存在的偏差和不准确等不足之处．此外,通过对10个CNN网络进行KS检验统计量的比较,证实该方法比图形方法具有更好的拟合效果．     

基于复杂网络的中国股市房地产板块股票强相关性研究

为分析中国股市房地产板块股票的强相关特性,以101只股票为结点,以近17年股票对数回报的相关系数为加权边,建立复杂网络模型,通过对网络拓扑参数计算,发现该网络为无尺度网络,结点度分布P(s)~s-|s|δ,在不同相关系数阈值下,δ值介于0.8~1.6之间.网络平均集聚系数为0.53.文章也对网络中心性进行测量和子群划分,发现代码为000592和601588的结点在网络中具有很高的中介性,网络中大部分结点都受其影响较大.     

Contagion processes on urban bus networks in Indian cities

Bus transportation is the most convenient and cheapest way of public transportation in Indian cities. Due to cost‐effectiveness and wide reachability, buses bring people to their destinations every day. Although the bus transportation has numerous advantages over other ways of public transportation, this mode of transportation also poses a serious threat of spreading contagious diseases throughout the city. It is extremely difficult to predict the extent and spread of such an epidemic. Earlier studies have focused on the contagion processes on scale‐free network topologies; whereas, real‐world networks such as bus networks exhibit a wide‐spectrum of network topology. Therefore, we aim in this study to understand this complex dynamical process of epidemic outbreak and information diffusion on the bus networks for six different Indian cities using SI and SIR models. We identify epidemic thresholds for these networks which help us in controlling outbreaks by developing node‐based immunization techniques. © 2016 Wiley Periodicals, Inc. Complexity 21: 451–458, 2016     

复杂动态网络的有限时间同步

复杂网络无处不在,同步是自然界中广泛存在的一类非常重要的非线性现象.过去10年,人们对复杂网络的同步开展了系统而深入的研究,包括恒等同步、广义同步、簇同步以及部分同步等.上述大部分结果中对同步速度的刻画往往是渐进的,只有当时间趋于无穷的时候,网络才能实现同步,而对于网络能够在多长时间内可以实现同步却知之甚少.作者以几类典型的非线性耦合的复杂动态网络为例,深入探讨了复杂动态网络的有限时间同步的规律.具体而言,基于上述几类典型的复杂动态网络,证明了在某些合适的条件下,网络能够在有限时间内实现精确同步.此外,用一个典型的数值仿真实例验证了上述有限时间同步的准则.有限时间同步有效地避免了网络只有在无穷时刻才能实现同步的问题,对网络同步的实际工程应用具有基本的现实意义.     

Ranking hubs and authorities using matrix functions

The notions of subgraph centrality and communicability, based on the exponential of the adjacency matrix of the underlying graph, have been effectively used in the analysis of undirected networks. In this paper we propose an extension of these measures to directed networks, and we apply them to the problem of ranking hubs and authorities. The extension is achieved by bipartization, i.e., the directed network is mapped onto a bipartite undirected network with twice as many nodes in order to obtain a network with a symmetric adjacency matrix. We explicitly determine the exponential of this adjacency matrix in terms of the adjacency matrix of the original, directed network, and we give an interpretation of centrality and communicability in this new context, leading to a technique for ranking hubs and authorities. The matrix exponential method for computing hubs and authorities is compared to the well known HITS algorithm, both on small artificial examples and on more realistic real-world networks. A few other ranking algorithms are also discussed and compared with our technique. The use of Gaussian quadrature rules for calculating hub and authority scores is discussed.     

Detecting evolving patterns of self‐organizing networks by flow hierarchy measurement

Hierarchies occur widely in evolving self‐organizing ecological, biological, technological, and social networks, but detecting and comparing hierarchies is difficult. Here we present a metric and technique to quantitatively assess the extent to which self‐organizing directed networks exhibit a flow hierarchy. Flow hierarchy is a commonly observed but theoretically overlooked form of hierarchy in networks. We show that the ecological, neurobiological, economic, and information processing networks are generally more hierarchical than their comparable random networks. We further discovered that hierarchy degree has increased over the course of the evolution of Linux kernels. Taken together, our results suggest that hierarchy is a central organizing feature of real‐world evolving networks, and the measurement of hierarchy opens the way to understand the structural regimes and evolutionary patterns of self‐organizing networks. Our measurement technique makes it possible to objectively compare hierarchies of different networks and of different evolutionary stages of a single network, and compare evolving patterns of different networks. It can be applied to various complex systems, which can be represented as directed networks. © 2011 Wiley Periodicals, Inc. Complexity, 2011     

标度指数不大于2的无标度网络的若干性质

将标度指数不大于2的无标度网络称为亚标度网络.通过引入度秩函数研究了亚标度网络的最大度、平均度以及拓扑结构的非均匀性,通过与标度指数大于2的无标度网络对比,揭示了亚标度网络若干特殊性质.     

Failure in Complex Social Networks

A class of inhomogenously wired networks called “scale-free” networks have been shown to be more robust against failure than more homogenously connected exponential networks. The robustness of scale-free networks consists in their ability to remain connected even when failure occurs. The diffusion of information and disease across a network only requires a single contact between nodes, making network connectivity the crucial determinant of whether or not these “simple contagions” will spread. However, for “complex contagions,” such as social movements, collective behaviors, and cultural and social norms, multiple reinforcing ties are needed to support the spread of a behavior diffusion. I show that scale-free networks are much less robust than exponential networks for the spread of complex contagions, which highlights the value of more homogenously distributed social networks for the robust transmission of collective behavior.     

Structure Learning of \mbox{PM}_{2.5} Distribution Using Sparse Graphical Models

We consider the structure learning problem of the \mbox{PM}_{2.5} pollution data over 31 provincial capitals in China. Specifically, we make use of the graphical model tools to study the hubs and the community structures of the \mbox{PM}_{2.5} pollution networks. The results show that the hubs in the \mbox{PM}_{2.5}pollution networks are always seriously polluted cities, and the \mbox{PM}_{2.5} pollution networks have significant community structures which consist of cities which in some sense can be regarded as blocks with similar cause of pollution. In view of the results, we suggest that the government should strengthen the effort to treat the seriously polluted areas and western China areas. Moreover, the management of the \mbox{PM}_{2.5} pollution should be region-dependent.     

沪深300样本股动态网络性质研究

利用2009年1月5日到2010年12月10日所有交易日的沪深300指数样本股日数据,构建了一系列动态网络.研究发现,随网络总度数的增大,网络的幂律值按指数衰减.股指和网络总度数的波动几乎是一致的.另外,当股指出现剧烈波动时,网络平均聚集系数变大,‘特别是此时度的概率分布平均拟合误差变得非常大,进一步研究发现,它的变化和股指波动的变化是同步的,所以我们认为是市场的剧烈波动破坏了股票网络的无标度性.上述结论对收盘价网络更明显.     

����ϡ��ͼģ�͵�\mbox{PM}_{2.5}�ֲ�������ṹѧϰ

??We consider the structure learning problem of the \mbox{PM}_{2.5} pollution data over 31 provincial capitals in China. Specifically, we make use of the graphical model tools to study the hubs and the community structures of the \mbox{PM}_{2.5} pollution networks. The results show that the hubs in the \mbox{PM}_{2.5}pollution networks are always seriously polluted cities, and the \mbox{PM}_{2.5} pollution networks have significant community structures which consist of cities which in some sense can be regarded as blocks with similar cause of pollution. In view of the results, we suggest that the government should strengthen the effort to treat the seriously polluted areas and western China areas. Moreover, the management of the \mbox{PM}_{2.5} pollution should be region-dependent.     

Fourth-generation warfare: Jihadist networks and percolation

This paper studies the approach to the fourth-generation warfare (4GW) paradigm from the perspective of physical and mathematical disciplines, through the interdisciplinary bridge offered by the analysis of complex networks. The study is within an emerging multidisciplinary field, Sociophysics, which attempts to apply statistical mechanics and the science of complex systems to predict human social behavior. The fourth-generation warfare concept is reviewed, and the war of the Jihadist Islam against the West will be contextualized as 4GW. The paradigm of complex systems has in diverse branches of science changed how collective phenomena are processed. The jihadist networks phenomenon in particular is appropriate for study from the standpoint of complex networks. We present an empirical study of the 9/11 and 11M networks, implemented from public information, and we give a comparison of both networks from the standpoint of complex networks. Several authors have made use of the phenomenon of percolation in complex physical systems to analyse complex networks, particularly jihadist actions like 9/11. The relationship between jihadist networks and percolation is considered. The percolation concept is reviewed and related to 4GW, and the definition of memetic dimension is introduced.     

网络化DEMATEL方法在产业经济系统分析中的应用

决策与实验评价实验室方法(DEMATEL)是研究复杂系统各因素之间相互关系的常用方法.从复杂网络的视角重新认识这一方法,建立了网络化的DEMATEL方法模型.结合我国国民经济数据,从影响度、被影响度、中心度和原因度四个方面,分析了各产业部门在国民经济系统中的地位和作用,从而为国家制定经济政策,调整产业结构提供科学依据.