Betweenness measures provide quantitative tools to pick out fine details from the massive amount of interaction data that is available from large complex networks. They allow us to study the extent to which a node takes part when information is passed around the network. Nodes with high betweenness may be regarded as key players that have a highly active role. At one extreme, betweenness has been defined by considering information passing only through the shortest paths between pairs of nodes. At the other extreme, an alternative type of betweenness has been defined by considering all possible walks of any length. In this work, we propose a betweenness measure that lies between these two opposing viewpoints. We allow information to pass through all possible routes, but introduce a scaling so that longer walks carry less importance. This new definition shares a similar philosophy to that of communicability for pairs of nodes in a network, which was introduced by Estrada and Hatano (Phys. Rev. E 77 (2008) 036111). Having defined this new communicability betweenness measure, we show that it can be characterized neatly in terms of the exponential of the adjacency matrix. We also show that this measure is closely related to a Frechet derivative of the matrix exponential. This allows us to conclude that it also describes network sensitivity when the edges of a given node are subject to infinitesimally small perturbations. Using illustrative synthetic and real life networks, we show that the new betweenness measure behaves differently to existing versions, and in particular we show that it recovers meaningful biological information from a protein-protein interaction network.
One of the defining representations of women from medieval times is in the role of peace-weaver, that is, a woman was expected to 'weave' peace between warring men. The underlying assumption in scholarship on this topic is that female mediation lessens male violence. This stance can however be questioned since it may be the result of gender-based peace and diplomacy models that relegate women's roles to that of conduits between men. By analyzing the concept of communicability and relevance of certain nodes in complex networks we show how our sources afford women more complex and nuanced social…
We analyze a recently proposed temporal centrality measure applied to an empirical network based on person-to-person contacts in an emergency department of a busy urban hospital. We show that temporal centrality identifies a distinct set of top-spreaders than centrality based on the time-aggregated binarized contact matrix, so that taken together, the accuracy of capturing top-spreaders improves significantly. However, with respect to predicting epidemic outcome, the temporal measure does not necessarily outperform less complex measures. Our results also show that other temporal markers such a…
Nowadays, identification and detection community structures in complex networks is an important factor in extracting useful information from networks. Label propagation algorithm with near linear-time complexity is one of the most popular methods for detecting community structures, yet its uncertainty and randomness is a defective factor. Merging LPA with other community detection metrics would improve its accuracy and reduce instability of LPA. Considering this point, in this paper we tried to use edge betweenness centrality to improve LPA performance. On the other hand, calculating edge betw…
Centrality, which quantifies the "importance" of individual nodes, is among the most essential concepts in modern network theory. As there are many ways in which a node can be important, many different centrality measures are in use. Here, we concentrate on versions of the common betweenness and it closeness centralities. The former measures the fraction of paths between pairs of nodes that go through a given node, while the latter measures an average inverse distance between a particular node and all other nodes. Both centralities only consider shortest paths (i.e., geodesics) between pairs o…
This paper provides the analysis for functional approaches of complex network systems research. In order to study the behavior of these systems the flow adjacency matrices were introduced. The concepts of strength, power, domain and diameter of influence of complex network nodes are analyzed for the purpose of determining their importance in the systems structure. The notions of measure, power, domain and diameter of betweenness of network nodes and edges are introduced to identify their significance in the operation process of network systems. These indicators quantitatively express the contr…
Complex networks are the representative graphs of interactions in many complex systems. Usually, these interactions are abstractions of the communication/diffusion channels between the units of the system. Real complex networks, e.g. traffic networks, reveal different operation phases governed by the dynamical stress of the system. Here we show how, communicability, a topological descriptor that reveals the efficiency of the network functionality in terms of these diffusive paths, could be used to reveal the transitions mentioned. By considering a vibrational model of nodes and edges in a grap…
In complex networks, especially social networks, networks could be divided into disjoint partitions that the ratio between the number of internal edges (the edges between the vertices within same partition) to the number of outer edges (edges between two vertices of different partitions) is high. Generally, these partitions are called communities. Detecting these communities helps data scientists to extract meaningful information from graphs and analyze them. In the last decades, various algorithms have been proposed to detect communities in graphs, and each one has examined this issue from a …
A complex network is a condensed representation of the relational topological framework of a complex system. A main reason for the existence of such networks is the transmission of items through the entities of these complex systems. Here, we consider a communicability function that accounts for the routes through which items flow on networks. Such a function induces a natural embedding of a network in a Euclidean high-dimensional sphere. We use one of the geometric parameters of this embedding, namely the angle between the position vectors of the nodes in the hyperspheres, to extract structur…
Robustness estimation is critical for the design and maintenance of resilient networks, one of the global challenges of the 21st century. Existing studies exploit network metrics to generate attack strategies, which simulate intentional attacks in a network, and compute a metric-induced robustness estimation. While some metrics are easy to compute, e.g. degree centrality, other, more accurate, metrics require considerable computation efforts, e.g. betweennes centrality. We propose a new algorithm for estimating the robustness of a network in sub-quadratic time, i.e., significantly faster than …
The effects of spatial constraints on the evolution of weighted complex networks
出于对航空运输系统的实证分析，我们定义了一个网络模型，其中包括地理属性以及拓扑和权重（交通）属性。地理属性的引入是通过将网络约束在真实空间中来实现的。有趣的是，几何特征的引入引起了权重、连接模式和顶点的实际空间距离之间的非平凡相关性。该模型还恢复了介度关联函数中出现的异常波动，如Guimerà和Amaral首次观察到的[Eur. J. B { \bf 38}，381（2004）]。所呈现的结果表明，权重动态和空间约束之间的相互作用是理解真实世界加权网络形成的关键因素。
In this work we introduce a new nodes attack strategy removing nodes with highest conditional weighted betweenness centrality (CondWBet). We compare its efficacy with well-known attack strategies from literature over five real-world complex weighted networks. We use the network weighted efficiency (WEFF) like a measure encompassing the weighted structure of the network in addition to the commonly used binary-topological measure, the largest connected cluster (LCC). We find that the recently proposed conditional betweenness strategy (CondBet) (Nguyen et al. 2019) is the best to fragment the LCC…
Cycle is the simplest structure that brings redundant paths in network connectivity and feedback effects in network dynamics. Focusing on cycle structure, this paper defines a new matrix, named cycle number matrix, to represent cycle information of a network, and an index, named cycle ratio, to quantify the node importance. Experiments on real networks suggest that cycle ratio contains rich information in addition to well-known benchmark indices, for example, the node rankings by cycle ratio are largely different from rankings by degree, H-index, coreness, betweenness and articulation ranking,…
Among the several topological properties of complex networks, the shortest path represents a particularly important characteristic because of its potential impact not only on other topological properties, but mainly for its influence on several dynamical processes taking place on the network. In addition, several practical situations, such as transit in cities, can benefit by modifying a network so as to reduce the respective shortest paths. In the present work, we addressed the problem of trying to reduce the average shortest path of several theoretical and real-world complex networks by addi…
Measures of complex network analysis, such as vertex centrality, have the potential to unveil existing network patterns and behaviors. They contribute to the understanding of networks and their components by analyzing their structural properties, which makes them useful in several computer science domains and applications. Unfortunately, there is a large number of distinct centrality measures and little is known about their common characteristics in practice. By means of an empirical analysis, we aim at a clear understanding of the main centrality measures available, unveiling their similariti…
Comment on "Dynamics and Directionality in Complex Networks"
作者：Phys. Rev. Lett. 103，228702（2009）声称“残差度梯度（RDG）方法可以通过简单地改变链接的方向来增强网络的可扩展性”。在本文中，我们认为，在某些情况下，RDG方法将导致失败的同步（$R=λ^{r}_{2}/λ^{r}_{N}=0$）。此外，我们还提出了一个所谓的残差介数梯度（RBG）方法来解决这个问题。
Vulnerabilities of complex networks have became a trend topic in complex systems recently due to its real world applications. Most real networks tend to be very fragile to high betweenness adaptive attacks. However, recent contributions have shown the importance of interconnected nodes in the integrity of networks and module-based attacks have appeared promising when compared to traditional malicious non-adaptive attacks. In the present work we deeply explore the trade-off associated with attack procedures, introducing a generalized robustness measure and presenting an attack performance index…
Efficiency of attack strategies on complex model and real-world networks
针对多个复杂模型和真实网络，研究了网络节点攻击策略的有效性。我们测试了5种攻击策略，其中3种是首次在本文中引入的，用于攻击3个模型（Erdos和Renyi，Barabasi和Albert优先连接网络和无标度网络配置模型）和3个真实网络（Gnutella对等网络，Rovira i Ravili大学的电子邮件网络和免疫球蛋白相互作用网络）。根据攻击策略定义的节点重要性标准依次删除节点。我们使用最大连通分量（LCC）的大小作为网络损坏的度量。我们发现，攻击策略的效率（对于给定的LCC大小的减少要删除的节点的分数）取决于网络的拓扑结构，虽然基于节点的连接数和介数中心性的攻击通常是最有效的策略。以介数中心度递减顺序依次删除节点是针对真实网络的最有效的攻击策略。特别是对于幂律度分布的网络，我们观察到最有效的策略在顺序删除节点的过程中发生了变化。
When dealing with the dissemination of epidemics, one important question that can be asked is the location where the contamination began. In this paper, we analyze three spreading schemes and propose and validate an effective methodology for the identification of the source nodes. The method is based on the calculation of the centrality of the nodes on the sampled network, expressed here by degree, betweenness, closeness and eigenvector centrality. We show that the source node tends to have the highest measurement values. The potential of the methodology is illustrated with respect to three th…
In complex network analysis, centralities based on shortest paths, such as betweenness and closeness, are widely used. More recently, many complex systems are being represented by time-varying, multilayer, and time-varying multilayer networks, i.e. multidimensional (or high order) networks. Nevertheless, it is well-known that the aggregation process may create spurious paths on the aggregated view of such multidimensional (high order) networks. Consequently, these spurious paths may then cause shortest-path based centrality metrics to produce incorrect results, thus undermining the network cen…
We present a systematic and detailed study of the robustness of directed networks under random and targeted removal of links. We work with a set of network models of random and scale free type, generated with specific features of clustering and assortativity. Various strategies like random deletion of links, or deletions based on betweenness centrality and degrees of source and target nodes, are used to breakdown the networks. The robustness of the networks to the sustained loss of links is studied in terms of the sizes of the connected components and the inverse path lengths. The effects of c…
Complex networks usually exhibit a rich architecture organized over multiple intertwined scales. Information pathways are expected to pervade these scales reflecting structural insights that are not manifest from analyses of the network topology. Moreover, small-world effects correlate with the different network hierarchies complicating the identification of coexisting mesoscopic structures and functional cores. We present a communicability analysis of effective information pathways throughout complex networks based on information diffusion to shed further light on these issues. We employ a va…
Comment on ``Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality"
本文研究了Newman [M. E. J. Newman，Phys. Rev. E { \bf 64}，016132（2001）]来计算所有顶点的介数中心性。指出了Newman算法的不准确性，并给出了一个时间复杂度为O（$MN$）的修正算法.此外，针对酵母蛋白质相互作用网络，比较了两种算法的计算结果。
Graph theory constitutes a widely used and established field providing powerful tools for the characterization of complex networks. The intricate topology of networks can also be investigated by means of the collective dynamics observed in the interactions of self-sustained oscillations (synchronization patterns) or propagation-like processes such as random walks. However, networks are often inferred from real data forming dynamic systems, which are different from those employed to reveal their topological characteristics. This stresses the necessity for a theoretical framework dedicated to th…
Indian Railway Network has been analyzed on the basis of number of trains directly linking two railway zones. The network has been displayed as a weighted graph where the weights denote the number of trains between the zones. It may be pointed out that each zone is a complex network in itself and may depict different characteristic features. The zonal network therefore can be considered as a network of complex networks. In this paper, self links, in-degree and out-degree of each zone have been computed which provides information about the inter and intra zonal connectivity. Degree passenger co…
