On the topologic structure of economic complex networks: Empirical evidence from large scale payment network of Estonia

This paper presents the first topological analysis of the economic structure of an entire country based on payments data obtained from Swedbank. This data set is exclusive in its kind because around 80% of Estonia's bank transactions are done through Swedbank; hence, the economic structure of the country can be reconstructed. Scale-free networks are commonly observed in a wide array of different contexts such as nature and society. In this paper, the nodes are comprised by customers of the bank (legal entities) and the links are established by payments between these nodes. We study the scaling-free and structural properties of this network. We also describe its topology, components and behaviors. We show that this network shares typical structural characteristics known in other complex networks: degree distributions follow a power law, low clustering coefficient and low average shortest path length. We identify the key nodes of the network and perform simulations of resiliency against random and targeted attacks of the nodes with two different approaches. With this, we find that by identifying and studying the links between the nodes is possible to perform vulnerability analysis of the Estonian economy with respect to economic shocks.     

Spreading of epidemics on scale-free networks with nonlinear infectivity

In this paper, we study the spreading of epidemics on scale-free networks with infectivity which is nonlinear in the connectivity of nodes. We will show that the nonlinear infectivity is more appropriate than constant or linear ones, and give the epidemic threshold of the SIS model on a scale-free network with nonlinear infectivity. In addition, we compare the effects of nonlinear infectivity on the epidemic threshold with two other cases on infinite and finite scale-free networks, and find some new results, such as: with unit recovery rate and nonlinear irrational infectivity, the epidemic threshold is always positive; and the epidemic threshold can increase with network size on finite networks, contrary to the findings in all previous work.     

Optimized network structure for full-synchronization

A network of Kuramoto oscillators with different natural frequencies is optimized for enhanced synchronizability. All node inputs are normalized by the node connectivity and some important properties of the network structure are determined in this case: (i) optimized networks present a strong anti-correlation between natural frequencies of adjacent nodes; (ii) this anti-correlation should be as high as possible since the average path length between nodes is maintained as small as in random networks; and (iii) high anti-correlation is obtained without any relation between nodes natural frequencies and the degree of connectivity. We also propose a network construction model with which it is shown that high anti-correlation and small average paths may be achieved by randomly rewiring a fraction of the links of a totally anti-correlated network, and that these networks present optimal synchronization properties.     

An evaluation of the adequacy of project network generators with systematically sampled networks

This paper evaluates and compares different network generators to generate project scheduling problem instances based on indicators measuring the topological network structure. We review six topological network indicators in order to describe the detailed structure of a project network. These indicators were originally developed by [L.V. Tavares, J.A. Ferreira and J.S. Coelho, The risk of delay of a project in terms of the morphology of its network, European Journal of Operational Research 119 (1999), 510–537] and have been modified, or sometimes completely replaced, by alternative indicators to describe the network topology. The contribution of this paper is twofold. Firstly, we generate a large amount of different networks with four project network generators. Our general conclusions are that none of the network generators are able to capture the complete feasible domain of all networks. Additionally, each network generator covers its own network-specific domain and, consequently, contributes to the generation of data sets. Secondly, we perform computational results on the well-known resource-constrained project scheduling problem to prove that our indicators are reliable and have significant, predictive power to serve as complexity indicators.     

Emergence of epidemics in rapidly varying networks

We describe a simple model mimicking disease spreading on a network with dynamically varying connections, and investigate the dynamical consequences of switching links in the network. Our central observation is that the disease cycles get more synchronized, indicating the onset of epidemics, as the underlying network changes more rapidly. This behavior is found for periodically switched links, as well as links that switch randomly in time. We find that the influence of changing links is more pronounced in networks where the nodes have lower degree, and the disease cycle has a longer infective stage. Further, when the switching of links is periodic we observe finer dynamical features, such as beating patterns in the emergent oscillations and resonant enhancement of synchronization, arising from the interplay between the time-scales of the connectivity changes and that of the epidemic outbreaks.     

Survey on path and cycle embedding in some networks

To find a cycle (resp. path) of a given length in a graph is the cycle (resp. path) embedding problem. To find cycles of all lengths from its girth to its order in a graph is the pancyclic problem. A stronger concept than the pancylicity is the panconnectivity. A graph of order n is said to be panconnected if for any pair of different vertices x and y with distance d there exist xy-paths of every length from d to n. The pancyclicity or the panconnectivity is an important property to determine if the topology of a network is suitable for some applications where mapping cycles or paths of any length into the topology of the network is required. The pancyclicity and the panconnectivity of interconnection networks have attracted much research interest in recent years. A large amount of related work appeared in the literature, with some repetitions. The purpose of this paper is to give a survey of the results related to these topics for the hypercube and some hypercube-like networks.      

Generalized function projective (lag, anticipated and complete) synchronization between two different complex networks with nonidentical nodes

Generalized function projective (lag, anticipated and complete) synchronization between two different complex networks with nonidentical nodes is investigated in this paper. Based on Barbalat’s lemma, some sufficient synchronization criteria are derived by applying the nonlinear feedback control. Although previous work studied function projective synchronization on complex dynamical networks, the dynamics of the nodes are coupled partially linear chaotic systems. In our work, the dynamics of the nodes of the complex networks are any chaotic systems without the limitation of the partial linearity. In addition, each network can be undirected or directed, connected or disconnected, and nodes in either network may have identical or different dynamics. The proposed strategy is applicable to almost all kinds of complex networks. Numerical simulations further verify the effectiveness and feasibility of the proposed synchronization method. Numeric evidence shows that the synchronization rate is sensitively influenced by the feedback strength, the time delay, the network size and the network topological structure.     

Framework for link reliability in inter-working multi-hop wireless networks

With the increase in deployment of multi-hop wireless networks and the desire for seamless internet access through ubiquitous connectivity, the inter-working of heterogeneous multi-hop wireless networks will become prominent in the near future. To complement the quest for ubiquitous service access, multi-mode mobile terminals are now in existence. Inter-working heterogeneous multi-hop wireless networks can provide seamless connectivity for such multi-mode nodes but introduces a number of challenges due to its dynamic network topology. One of the challenges in ensuring seamless access to service through these terminals in an inter-working environment is the selection of reliable wireless point-to-point links by the multi-hop nodes. A wireless link is said to be reliable if its radio attribute satisfies the minimum requirements for successful communication. Successful communication is specified by metrics such as signal to interference and noise ratio (SINR), probability of bit error etc. However, the multi-hop wireless networks being inter-worked may operate with different link layer protocols. Therefore, how can the reliability of a wireless link be estimated irrespective of the link level technologies implemented in the networks being inter-worked so that optimal paths can be used for multi-hopping between nodes? In this paper, a generic framework which can estimate the reliability of a link in inter-working multi-hop wireless network is presented. The framework uses the relationship between inter-node interference, SINR and the probability of bit error to determine the reliability of a wireless link between two nodes. There is a threshold for the probability of bit error on a link for the link to be termed reliable. Using parameters such as the SINR threshold, nodes’ transmission power, link distance and interfering node density, the framework can evaluate the reliability of a link in an inter-working multi-hop network.     

Circular/wrap-around self-organizing map networks: an empirical study in clustering and classification

Kohonen's self-organizing map (SOM) network is one of the most important network architectures developed during the 1980s. The main function of SOM networks is to map the input data from an n-dimensional space to a lower-dimensional (usually one or two dimensional) plot while maintaining the original topological relations. A well known limitation of the Kohonen network is the ‘boundary effect’ of nodes on or near the edge of the network. The boundary effect is responsible for the undue influence of the initial random weights assigned to the nodes of the network, which can lead to incorrect topological representations. To overcome this limitation, we use a modified, ‘circular’, weight adjustment algorithm. Our procedure is most effective with the class of problems where the actual coordinates of the output map do not need to correspond to the original input topology. This class of problems includes applications requiring clustering or classification of input data. We tested our method with a well known example problem from the domain of Group Technology, which is typical of this class of problems. Test results show that the circular weight adjustment procedure has better convergence properties, and that the clusters formed using the circular approach are at least as good as, and in many cases superior to, the basic SOM method for these types of problems.     

Hierarchical routing over dynamic wireless networks

The topology of a mobile wireless network changes over time. Maintaining routes between all nodes requires the continuous transmission of control information, which consumes precious power and bandwidth resources. Many routing protocols have been developed, trading off control overhead and route quality. In this paper, we ask whether there exist low‐overhead schemes that produce low‐stretch routes, even in large networks where all the nodes are mobile. We present a scheme that maintains a hierarchical structure within which constant‐stretch routes can be efficiently computed between every pair of nodes. The scheme rebuilds each level of the hierarchy periodically, at a rate that decreases exponentially with the level of the hierarchy. We prove that this scheme achieves constant stretch under a mild smoothness condition on the nodal mobility processes. Furthermore, we prove tight bounds for the network‐wide control overhead under the additional assumption of the connectivity graph forming a doubling metric space. Specifically, we show that for a connectivity model combining the random geometric graph with obstacles, constant‐stretch routes can be maintained with a total overhead of bits of control information per time unit. © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 47, 669–709, 2015     

Integrity of Total Graphs via Certain Parameters

Communication networks have been characterized by high levels of service reliability. Links cuts, node interruptions, software errors or hardware failures, and transmission failures at various points can interrupt service for long periods of time. In communication networks, greater degrees of stability or less vulnerability is required. The vulnerability of communication network measures the resistance of the network to the disruption of operation after the failure of certain stations or communication links. If we think of a graph G as modeling a network, many graph-theoretic parameters can be used to describe the stability of communication networks, including connectivity, integrity, and tenacity. We consider two graphs with the same connectivity, but with unequal orders of theirs largest components. Then these two graphs must be different in respect to stability. How can we measure that property? The idea behind the answer is the concept of integrity, which is different from connectivity. Total graphs constitute a large class of graphs. In this paper, we study the integrity of total graphs via some graph parameters.

     

Effective measurement of network vulnerability under random and intentional attacks

The study of the security and stability of complex networks plays a central role in reducing the risk and consequences of attacks or disfunctions of any type. The concept of vulnerability helps to measure the response of complex networks subjected to attacks on vertices and edges and it allows to spot the critical component of a network in order to improve its security. We introduce an accurate and computable definition of network vulnerability which is directly connected with its topology and we analyze its basic properties. We discuss the relationship of the vulnerability with other parameters of the network and we illustrate this with some examples.     

Viral conductance: Quantifying the robustness of networks with respect to spread of epidemics

In this paper, we propose a novel measure, viral conductance (VC), to assess the robustness of complex networks with respect to the spread of SIS epidemics. In contrast to classical measures that assess the robustness of networks based on the epidemic threshold above which an epidemic takes place, the new measure incorporates the fraction of infected nodes at steady state for all possible effective infection strengths. Through examples, we show that VC provides more insight about the robustness of networks than does the epidemic threshold. We also address the paradoxical robustness of Barabási–Albert preferential attachment networks. Even though this class of networks is characterized by a vanishing epidemic threshold, the epidemic requires high effective infection strength to cause a major outbreak. On the contrary, in homogeneous networks the effective infection strength does not need to be very much beyond the epidemic threshold to cause a major outbreak. To overcome computational complexities, we propose a heuristic to compute the VC for large networks with high accuracy. Simulations show that the heuristic gives an accurate approximation of the exact value of the VC. Moreover, we derive upper and lower bounds of the new measure. We also apply the new measure to assess the robustness of different types of network structures, i.e. Watts–Strogatz small world, Barabási–Albert, correlated preferential attachment, Internet AS-level, and social networks. The extensive simulations show that in Watts–Strogatz small world networks, the increase in probability of rewiring decreases the robustness of networks. Additionally, VC confirms that the irregularity in node degrees decreases the robustness of the network. Furthermore, the new measure reveals insights about design and mitigation strategies of infrastructure and social networks.     

CONNECTIVITY OF CARTESIAN PRODUCT DIGRAPHS AND FAULT-TOLERANT ROUTINGS OF GENERALIZED HYPERCUBE

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随机交通网络渐近连通可靠性分析

应用原有拓扑法获得城市交通网络的拓扑结构图,利用对偶拓扑法得到交通网络的对偶图,建立交通网络的随机网络模型。定义交通网络的渐近连通可靠性,得到路段连通可靠性、路网规模及整个路网连通可靠性之间的定量关系,结合随机图论、大数定律、渐近方法等证明所得结论;通过实例说明结论的应用价值。     

Two-Connected Augmentation Problems in Planar Graphs

Given a weighted undirected graph G and a subgraph S of G, we consider the problem of adding a minimum-weight set of edges of G to S so that the resulting subgraph satisfies specified (edge or vertex) connectivity requirements between pairs of nodes of S. This has important applications in upgrading telecommunication networks to be invulnerable to link or node failures. We give a polynomial algorithm for this problem when S is connected, nodes are required to be at most 2-connected, and G is planar. Applications to network design and multicommodity cut problems are also discussed.     

Topology design for on-demand dual-path routing in wireless networks

One way to achieve reliability with low-latency is through multi-path routing and transport protocols that build redundant delivery channels (or data paths) to reduce end-to-end packet losses and retransmissions. However, the applicability and effectiveness of such protocols are limited by the topological constraints of the underlying communication infrastructure. Multiple data delivery paths can only be constructed over networks that are capable of supporting multiple paths. In mission-critical wireless networks, the underlying network topology is directly affected by the terrain, location and environmental interferences, however the settings of the wireless radios at each node can be properly configured to compensate for these effects for multi-path support. In this work we investigate optimization models for topology designs that enable end-to-end dual-path support on a distributed wireless sensor network. We consider the case of a fixed sensor network with isotropic antennas, where the control variable for topology management is the transmission power on network nodes. For optimization modeling, the network metrics of relevance are coverage, robustness and power utilization. The optimization models proposed in this work eliminate some of the typical assumptions made in the pertinent network design literature that are too strong in this application context.     

国内外黄金现货价格联动波动复杂网络拓扑性质

为了研究国内外黄金现货价格联动性波动特征,选取2003年1月1日至2013年9月6日上海黄金交易所Au9999黄金现货收盘价与伦敦标准黄金现货的下午定盘价分别作为国内与国外黄金现货价格的样本数据.依据粗粒化方法,将Au9999与伦敦标准金价格的联动波动转化为由5个{P,O,M}三个字符构成的字符串,每一个字符串代表每5天的黄金现货价格联动波动模态,共产生106个模态.将模态作为节点,模态之间的转化为边,构建国内外黄金现货价格联动性波动复杂网络.对联动性复杂网络的点强度与强度分布、聚集系数、平均路径长度、中介中心性及凝集子群特征进行研究分析.结果表明:点强度值较大的前32个节点累积强度分布达到了92.05%,点强度与度分布、点强度与其等级均呈幂律分布;加权集聚系数与点强度之间并没有表现出良好的相关性,网络中存在14个小群簇;网络平均最短路径长度为7.668;节点中介性差异不太明显,前40个节点对整个网络的中介中心性贡献率为62.29%;8个节点的凝集子群有2个,8个节点以上的子群不存在.从网络结构拓扑性质角度验证了国内外黄金现货价格变化的复杂特征,这些对于掌握国内外黄金价格波动的内在规律和了解价格变化信息有一定指导意义,能够为我国黄金价格制定、风险投资和规避经济风险提供决策参考.     

尾部风险网络视角下的金融机构系统性风险贡献研究

金融机构的尾部风险关联模式及结构在金融系统性风险的形成演化中发挥重要作用。利用CoVaR指标及分位数回归方法,衡量金融机构之间的尾部风险传染强度,进而建立金融机构尾部风险动态网络。分析全连接网络及阈值法下过滤网络的全局和局部拓扑结构特征及其动态演化规律。建立面板数据回归模型,研究网络拓扑结构特征对金融机构系统性风险贡献的影响。实证研究发现,全连接网络的节点强度,能有效地衡量金融机构尾部风险传染强度及承受强度,并揭示其动态变化规律;各机构的尾部风险传染强度及承受强度排序匹配性存在差异;随着时间推进,各金融机构间的平均尾部风险传染路径缩短、系统性风险更易迅速累积和爆发;滞后一期的节点出度、节点入度及聚集系数越大,相应金融机构的系统性风险贡献越小;滞后一期的节点介数和节点接近中心度越大,相应金融机构的系统性风险贡献越大。研究结果对于金融机构的宏观审慎监管及系统性风险管理,提供了一个全新的基于金融机构尾部风险网络的视角。     

A cross entropy approach to design of reliable networks

One of the most important parameters determining the performance of communication networks is network reliability. The network reliability strongly depends on not only topological layout of the communication networks but also reliability and availability of the communication facilities. The selection of optimal network topology is an NP-hard problem so that computation time of enumeration-based methods grows exponentially with network size. This paper presents a new solution approach based on cross-entropy method, called NCE, to design of communication networks. The design problem is to find a network topology with minimum cost such that all-terminal reliability is not less than a given level of reliability. To investigate the effectiveness of the proposed NCE, comparisons with other heuristic approaches given in the literature for the design problem are carried out in a three-stage experimental study. Computational results show that NCE is an effective heuristic approach to design of reliable networks.