Central nodes are critical in establishing structural connectivity in a complex network. Attacking such nodes can create real havoc in a complex system. We propose attack strategies based on four types of centers, namely betweenness center, degree center, median, and center. We study the vulnerability of synthetic as well as real-world networks in these center-based attacks. These attacks are node-removal attacks which involve identifying the central node set and removing them from the network. We observed that the attacks based on recalculated network information are more efficient than ones based on initial network information. This work shows that the median-based attack, which is a novel strategy proposed in this work, is highly destructive in real as well as synthetic networks.
We suggest an approach to study hierarchy, especially hidden one, of complex networks based on the analysis of their vulnerability. Two quantities are proposed as a measure of network hierarchy. The first one is the system vulnerability V. We show that being quite suitable for regular networks this characteristic does not allow one to estimate the hierarchy of large random networks. The second quantity is a relative variance h of the system vulnerability that allows us to characterize a "natural" hierarchy level of random networks. We find that hierarchical properties of random networks depend crucially on a ratio between the number of nodes and the number of edges. We note that any graph with a transitive isometry group action (i.e. an absolutely symmetric graph) is not hierarchical. Breaking such a symmetry leads to appearance of hierarchy. The study of networks pervades all of science, from neurobiology to statistical physics. The most basic issues are structural: how does one characterize the wiring diagram of a food web or the Internet or the metabolic network of the bacterium Escherichia coli? Are there any unifying principles underlying their topology? From the perspective of nonlinear dynamics, we would also like to understand how an enormous network of interacting dynamical systems — be they neurons, power stations or lasers — will behave collectively, given their individual dynamics and coupling architecture. Researchers are only now beginning to unravel the structure and dynamics of complex networks. We present a novel approach to quantify the vulnerability of a complex network, i.e., the capacity of a graph to maintain its functional performance under random damages or malicious attacks. The proposed measure represents a multiscale evaluation of vulnerability, and makes use of combined powers of the links’ betweenness. We show that the proposed approach is able to properly describe some cases for which earlier measures of vulnerability fail. The relevant applications of our method for technological network design are outlined.