ELASTICITY: Topological Characterization of Robustness in Complex Networks

Abstract

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 a network's survivability 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 "test-drive" the performance of elasticity on Internet topologies and online social networks, and articulate results. *

Robustness Comparison of 15 Real Telecommunication Networks: Structural and Centrality Measurements

“…The set of networks with high robustness to random node failures has low values of average shortest path length ðhliÞ and diameter (D), and they are the most disassortative networks (r \ 0). Furthermore, it can be observed that networks with high average nodal degree ðhkiÞ show robustness to random attacks, which is in accordance with the results found in [30].…”

On the Characterization of the Structural Robustness of Data Center Networks

“…Elasticity (E): relates to the total throughput in response to the node removal [8]. The fundamental idea is to successively remove a certain fixed number of nodes r (in the original definition, r ¼ 1%) and measure the consequent throughput degradation.…”

“…Sydney et al [8] defined robustness as the "ability of a network to maintain its total throughput under node and link removal". Ali et al [3] consider a system robust, when the system is able to operate as expected in presence of uncertainties and perturbations.…”

“…Ali et al [3] consider a system robust, when the system is able to operate as expected in presence of uncertainties and perturbations. System robustness, and network robustness in particular, has been widely discussed in the literature [7], [8], [9], [10], [11], [12], [13], [14], [15]. Network robustness metrics generally consider the graph theory-based topological features of the network [7].…”

Evaluating robustness of cloud-based systems

“…Although this more of a theoretical framework, the method remains similar: removing elements and measuring the evolution of some key properties. Endurance [24] and elasticity [25] are other attempt to understand robustness in terms of failures and how the propagate through a graph. By contrast with these work, our approach permits to finely tuned the propagation of failure for each component.…”