We study the robustness of complex networks subject to edge removal. Several network models and removing strategies are simulated. Rather than the existence of the giant component, we use total connectedness as the criterion of breakdown. The network topologies are introduced a simple traffic dynamics and the total connectedness is interpreted not only in the sense of topology but also in the sense of function. We define the topological robustness and the functional robustness, investigate their combined effect and compare their relative importance to each other. The results of our study provide an alternative view of the overall robustness and highlight efficient ways to improve the robustness of the network models.
We can construct passing networks when we regard a player as a node and a pass as a link in football games. Thus, we can analyze the networks by using tools developed in network science. Among various metrics characterizing a network, centrality metrics have often been used to identify key players in a passing network. However, a tolerance to players being marked or passes being blocked in a passing network, namely the robustness of the network, has been poorly understood so far. Because the robustness of a passing network can be connected to the increase of ball possession, it would be deeply…
The traditional approach to network robustness, is based on comparing network parameters before and after an event of nodes removal, such as the change in network diameter, the change in giant component size and the existence of giant component. Recently, a new approach to network robustness was presented, where the network functionality during its entire life span (during the node removal event) is considered. This approach considers nodes removal due to aging - a state where nodes can be degenerated and become nonfunctional, when their survival time duration - their lifetime - is passed. Acc…
The identification of modular structures is essential for characterizing real networks formed by a mesoscopic level of organization where clusters contain nodes with a high internal degree of connectivity. Many methods have been developed to unveil community structures, but only a few studies have probed their suitability in incomplete networks. Here we assess the accuracy of community detection techniques in incomplete networks generated in sampling processes. We show that the walktrap and fast greedy algorithms are highly accurate for detecting the modular structure of incomplete complex net…
The epidemic threshold of a social system is the ratio of infection and recovery rate above which a disease spreading in it becomes an epidemic. In the absence of pharmaceutical interventions (i.e. vaccines), the only way to control a given disease is to move this threshold by non-pharmaceutical interventions like social distancing, past the epidemic threshold corresponding to the disease, thereby tipping the system from epidemic into a non-epidemic regime. Modeling the disease as a spreading process on a social graph, social distancing can be modeled by removing some of the graphs links. It h…
Many critical infrastructure systems have network structure and are under stress. Despite their national importance, the complexity of large-scale transport networks means we do not fully understand their vulnerabilities to cascade failures. The research in this paper examines the interdependent rail networks in Greater London and surrounding commuter area. We focus on the morning commuter hours, where the system is under the most demand stress. There is increasing evidence that the topological shape of the network plays an important role in dynamic cascades. Here, we examine whether the diffe…
Network controllability robustness reflects how well a networked system can maintain its controllability against destructive attacks. Its measure is quantified by a sequence of values that record the remaining controllability of the network after a sequence of node-removal or edge-removal attacks. Traditionally, the controllability robustness is determined by attack simulations, which is computationally time consuming or even infeasible. In the present paper, an improved method for predicting the network controllability robustness is developed based on machine learning using a group of convolu…
Influence of the topology on the power flux of the Italian high-voltage electrical network
意大利380 kV输电网络的模型进行了分析的拓扑和功能的观点。用于评估功率通量的直流潮流模型已被解决的基础上的输入条件（注入功率提取功率，线路的电抗和每条线路的最大通量容量）从实际数据。在负载条件下的网络的脆弱性已被估计通过评估的功率通量重新分配沿线路后线的删除。当受扰网络不能维持给定的输入-输出需求时，网络可持续的最大功率已被评估以优化\texttt{Quality of Service}，定义为期望和有效调度功率之间的差。网络的不同线路的功能相关性已经根据网络必须减少的功率量进行了分类，以保持活跃，在它们被移除时。结果表明，拓扑和功能的相关性是与不同的线路，具有较强的拓扑相关性的线路可能有一个裸露的流量分布的相关性，因此，他们的删除不影响网络的功能。
In this study, we tested the robustness of three communication networks extracted from the online forums included in the intranet platforms of three large companies. For each company we analyzed the communication among employees both in terms of network structure and content (language used). Over a period of eight months, we analyzed more than 52,000 messages posted by approximately 12,000 employees. Specifically, we tested the network robustness and the stability of a set of structural and semantic metrics, while applying several different node removal strategies. We removed the forum moderat…
In this paper we investigate how the modularity of model and real-world social networks affect their robustness and the efficacy of node attack (removal) strategies based on node degree (ID) and node betweenness (IB). We build Barabasi-Albert model networks with different modularity by a new ad hoc algorithm that rewire links forming networks with community structure. We traced the network robustness using the largest connected component (LCC). We find that higher level of modularity decreases the model network robustness under both attack strategies, i.e. model network with higher community s…
Due to the increasingly complex and interconnected nature of global supply chain networks (SCNs), a recent strand of research has applied network science methods to model SCN growth and subsequently analyse various topological features, such as robustness. This paper provides: (1) a comprehensive review of the methodologies adopted in literature for modelling the topology and robustness of SCNs; (2) a summary of topological features of the real world SCNs, as reported in various data driven studies; and (3) a discussion on the limitations of existing network growth models to realistically repr…
The capability of a network to cope with threats and survive attacks is referred to as its robustness. This paper discusses one kind of robustness, commonly denoted structural robustness, which increases when the spectral radius of the adjacency matrix associated with the network decreases. We discuss computational techniques for identifying edges, whose removal may significantly reduce the spectral radius. Nonsymmetric adjacency matrices are studied with the aid of their pseudospectra. In particular, we consider nonsymmetric adjacency matrices that arise when people seek to avoid being infect…
We present exact analysis of the physical properties of bimodal networks specified by the two peak degree distribution fully incorporating the degree-degree correlation between node connection. The structure of the correlated bimodal network is uniquely determined by the Pearson coefficient of the degree correlation, keeping its degree distribution fixed. The percolation threshold and the giant component fraction of the correlated bimodal network are analytically calculated in the whole range of the Pearson coefficient from $-1$ to $1$ against two major types of node removal, which are the ran…
While link prediction in networks has been a hot topic over the years, its robustness has not been well discussed in literature. In this paper, we study the robustness of some mainstream link prediction methods under various kinds of network attack strategies, including the random attack (RDA), centrality based attacks (CA), similarity based attacks (SA), and simulated annealing based attack (SAA). Through the variation of precision, a typical evaluation index of link prediction, we find that for the SA and SAA, a small fraction of link removals can significantly reduce the performance of link…
During the last decade, road network vulnerability assessment has received an increasing attention. On one hand, it is due to the significant advances in Network Science and the potentialities that its tools offer. On the other hand, it is due to its utility for urban planning and emergency response. Despite these facts and the increasingly available data, related work is still sparse in Latin America, even more so in Ecuador. Due to its geographical, historical, and social characteristics, the city of Quito is considered as a case study. At first, the spatial distributions of several topologi…
It is often claimed that the entropy of a network's degree distribution is a proxy for its robustness. Here, we clarify the link between degree distribution entropy and giant component robustness to node removal by showing that the former merely sets a lower bound to the latter for randomly configured networks when no other network characteristics are specified. Furthermore, we show that, for networks of fixed expected degree that follow degree distributions of the same form, the degree distribution entropy is not indicative of robustness. By contrast, we show that the remaining degree entropy…
Bypass rewiring improves connectivity and robustness of networks against removal of nodes including failures and attacks. A concept of bypass rewiring on directed networks is proposed, and random bypass rewiring on infinite directed random networks is analytically and numerically investigated with simulations. As a result, random bypass rewiring makes infinite directed (undirected) random networks extremely robust for arbitrary occupation probabilities if and only if in-degree of every node except a fixed number of nodes is equal to the out-degree (every node except a finite number of nodes ha…
ETH Zürich（苏黎世联邦理工学院）；Rudjer Bošković Institute（鲁杰尔·博什科维奇研究所）
The robustness of complex networks under targeted attacks is deeply connected to the resilience of complex systems, i.e., the ability to make appropriate responses to the attacks. In this article, we investigated the state-of-the-art targeted node attack algorithms and demonstrate that they become very inefficient when the cost of the attack is taken into consideration. In this paper, we made explicit assumption that the cost of removing a node is proportional to the number of adjacent links that are removed, i.e., higher degree nodes have higher cost. Finally, for the case when it is possible…
