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Register a new userEffect of edge removal on topological and functional robustness of complex networks
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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.
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In this paper, we explore the relationship between the topological characteristics of a complex network and its robustness to sustained targeted attacks. Using synthesised scale-free, small-world and random networks, we look at a number of network measures, including assortativity, modularity, average path length, clustering coefficient, rich club profiles and scale-free exponent (where applicable) of a network, and how each of these influence the robustness of a network under targeted attacks. We use an established robustness coefficient to measure topological robustness, and consider sustained targeted attacks by order of node degree. With respect to scale-free networks, we show that assortativity, modularity and average path length have a positive correlation with network robustness, whereas clustering coefficient has a negative correlation. We did not find any correlation between scale-free exponent and robustness, or rich-club profiles and robustness. The robustness of small-world networks on the other hand, show substantial positive correlations with assortativity, modularity, clustering coefficient and average path length. In comparison, the robustness of Erdos-Renyi random networks did not have any significant correlation with any of the network properties considered. A significant observation is that high clustering decreases topological robustness in scale-free networks, yet it increases topological robustness in small-world networks. Our results highlight the importance of topological characteristics in influencing network robustness, and illustrate design strategies network designers can use to increase the robustness of scale-free and small-world networks under sustained targeted attacks.
Controlling a complex network is of great importance in many applications. The network can be controlled by inputting external control signals through some selected nodes, which are called input nodes. Previous works found that the majority of the nodes in dense networks are either the input nodes or not, which leads to the bimodality in controlling the complex networks. Due to the physical or economic constraints of many real control scenarios, altering the control mode of a network may be critical to many applications. Here we develop a graph-based algorithm to alter the control mode of a network. The main idea is to change the control connectivity of nodes by removing carefully selected edges. We rigorously prove the correctness of our algorithm and evaluate its performance on both synthetic and real networks. The experimental results show that the control mode of a network can be easily changed by removing few selected edges. Our methods provide the ability to design the desired control mode for different control scenarios, which may be useful in many applications.
Just as a herd of animals relies on its robust social structure to survive in the wild, similarly robustness is a crucial characteristic for the survival of a complex network under attack. The capacity to measure robustness in complex networks defines the resolve of a network to maintain functionality in the advent of classical component failures and at the onset of cryptic malicious attacks. To date, robustness metrics are deficient and unfortunately the following dilemmas exist: accurate models necessitate complex analysis while conversely, simple models lack applicability to our definition of robustness. In this paper, we define robustness and present a novel metric, elasticity- a bridge between accuracy and complexity-a link in the chain of network robustness. Additionally, we explore the performance of elasticity on Internet topologies and online social networks, and articulate results.
Spatially embedded networks have attracted increasing attention in the last decade. In this context, new types of network characteristics have been introduced which explicitly take spatial information into account. Among others, edge directionality properties have recently gained particular interest. In this work, we investigate the applicability of mean edge direction, anisotropy and local mean angle as geometric characteristics in complex spherical networks. By studying these measures, both analytically and numerically, we demonstrate the existence of a systematic bias in spatial networks where individual nodes represent different shares on a spherical surface, and describe a strategy for correcting for this effect. Moreover, we illustrate the application of the mentioned edge directionality properties to different examples of real-world spatial networks in spherical geometry (with or without the geometric correction depending on each specific case), including functional climate networks, transportation and trade networks. In climate networks, our approach highlights relevant patterns like large-scale circulation cells, the El Ni~{n}o--Southern Oscillation and the Atlantic Ni~{n}o. In an air transportation network, we are able to characterize distinct air transportation zones, while we confirm the important role of the European Union for the global economy by identifying convergent edge directionality patterns in the world trade network.
The generalized $H(n)$ Hirsch index of order $n$ has been recently introduced and shown to interpolate between the degree and the $K$-core centrality in networks. We provide a detailed analytical characterization of the properties of sets of nodes having the same $H(n)$, within the annealed network approximation. The connection between the Hirsch indices and the degree is highlighted. Numerical tests in synthetic uncorrelated networks and real-world correlated ones validate the findings. We also test the use of the Hirsch index for the identification of influential spreaders in networks, finding that it is in general outperformed by the recently introduced Non-Backtracking centrality.
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