Abstract
Network robustness refers to a network’s resilience to stress or damage. Given that most networks are inherently dynamic, with changing topology, loads, and operational states, their robustness is also likely subject to change. However, in most analyses of network structure, it is assumed that interaction among nodes has no effect on robustness. To investigate the hypothesis that network robustness is not sensitive or elastic to the level of interaction (or flow) among network nodes, this paper explores the impacts of network disruption, namely arc deletion, over a temporal sequence of observed nodal interactions for a large Internet backbone system. In particular, a mathematical programming approach is used to identify exact bounds on robustness to arc deletion for each epoch of nodal interaction. Elasticity of the identified bounds relative to the magnitude of arc deletion is assessed. Results indicate that system robustness can be highly elastic to spatial and temporal variations in nodal interactions within complex systems. Further, the presence of this elasticity provides evidence that a failure to account for nodal interaction can confound characterizations of complex networked systems.
Highlights
The structural and operational characteristics of many types of networks, those representing physical, biological, chemical and social systems are highly dynamic and subject to constant change [1,2,3,4]
To investigate the hypothesis that network robustness is not sensitive or elastic to the level of interaction among network nodes, this paper explores the impacts of network disruption, namely arc deletion, over a temporal sequence of observed nodal interactions for a large Internet backbone system
Topology and levels of nodal interaction for this Internet system were observed at network routers
Summary
The structural and operational characteristics of many types of networks, those representing physical, biological, chemical and social systems are highly dynamic and subject to constant change [1,2,3,4]. The ability to effectively characterize the robustness of networks to the deletion of arcs and/or nodes is a tremendous analytical challenge requiring the consideration of both the structural and operative states of a network over time. Research that assesses network robustness typically addresses the problem from a structural perspective, emphasizing various measures of connectivity and performance [9,11,16,17,18]. As a result, these types of approaches primarily describe a structural state of the network, assuming that interaction or flow among all pairs of nodes is equivalent in magnitude and value to the system. Elasticity of the identified bounds relative to the magnitude of arc deletion is assessed
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