A Notion of Robustness in Complex Networks

Zhang, Haotian; Fata, Elaheh; Sundaram, Shreyas

doi:10.1109/tcns.2015.2413551

Cited by 131 publications

(98 citation statements)

References 29 publications

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“…The plethora of the relevant studies can be divided into two groups: (a) A vast number of studies only consider topological characteristics of networks, such as accessibility, connectivity, shortest path [25][26][27][28][29][30]. What is missing in such approaches is the dynamic of the flow on the network.…”

Section: Literature Reviewmentioning

confidence: 99%

Identifying Achilles-heel roads in real-sized networks

et al. 2017

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Ensuring a minimum operational level of road networks in the presence of unexpected incidents is becoming a hot subject in academic circles as well as industry. To this end, it is important to understand the degree to which each single element of the network contributes to the operation and performance of a network. In other words, a road can become an ''Achilles-heel'' for the entire network if it is closed due to a simple incident. Such insight of the detrimental loss of the closure of the roads would help us to be more vigilant and prepared. In this study, we develop an index dubbed as Achilles-heel index to quantify detrimental loss of the closure of the respective roads. More precisely, the Achilles-heel index indicates how many drivers are affected by the closure of the respective roads (the number of affected drivers is also called travel demand coverage). To this end, roads with maximum travel demand coverage are sorted as the most critical ones, for which a method-known as ''link analysis''-is adopted. In an iterative process, first, a road with highest traffic volume is first labeled as ''target link,'' and second, a portion of travel demand which is captured by the target link is excluded from travel demand. For the next iteration, the trimmed travel demand is then assigned to the network where all links including the target links run on the initial travel times. The process carries on until all links are labeled. The proposed methodology is applied to a largesized network of Winnipeg, Canada. The results shed light on also bottleneck points of the network which may warrant provision of additional capacity or parallel roads.

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Section: Literature Reviewmentioning

confidence: 99%

Identifying Achilles-heel roads in real-sized networks

et al. 2017

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“…Recent work has shown that these properties also share thresholds in Erdos-Renyi random graphs [Zhang et al (2015)] and random intersection graphs [Zhao et al (2014)], and our work in this paper adds random k-partite graphs to this list. We identify a bound p r for the probability of inter-layer edge formation p such that for p > p r , random interdependent networks with arbitrary intra-layer topologies are guaranteed to be r-robust asymptotically almost surely.…”

Section: Introductionmentioning

confidence: 97%

“…Due to the prevalence of such networks, their robustness to intentional disruption or natural malfunctions has started to attract attention by a variety of researchers [Schneider et al (2013); Yagan et al (2012); Parandehgheibi and Modiano (2013)]. As we will describe further in the next section, r-robustness has strong connotations for the ability of networks to withstand structural and dynamical disruptions: it guarantees that the network will remain connected even if up to r − 1 nodes are removed from the neighborhood of every node in the network, and facilitates certain consensus dynamics that are resilient to adversarial nodes [LeBlanc et al (2013); Zhao et al (2014); Dibaji and Ishii (2015); Zhang et al (2015); Vaidya et al (2012)]. As we will describe further in the next section, r-robustness has strong connotations for the ability of networks to withstand structural and dynamical disruptions: it guarantees that the network will remain connected even if up to r − 1 nodes are removed from the neighborhood of every node in the network, and facilitates certain consensus dynamics that are resilient to adversarial nodes [LeBlanc et al (2013); Zhao et al (2014); Dibaji and Ishii (2015); Zhang et al (2015); Vaidya et al (2012)].…”

Section: Introductionmentioning

confidence: 99%

Robustness and Algebraic Connectivity of Random Interdependent Networks

2015

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We investigate certain structural properties of random interdependent networks. We start by studying a property known as r-robustness, which is a strong indicator of the ability of a network to tolerate structural perturbations and dynamical attacks. We show that random k-partite graphs exhibit a threshold for r-robustness, and that this threshold is the same as the one for the graph to have minimum degree r. We then extend this characterization to random interdependent networks with arbitrary intra-layer topologies. Finally, we characterize the algebraic connectivity of such networks, and provide an asymptotically tight rate of growth of this quantity for a certain range of inter-layer edge formation probabilities. Our results arise from a characterization of the isoperimetric constant of random interdependent networks, and yield new insights into the structure and robustness properties of such networks.Abstract: We investigate certain structural properties of random interdependent networks. We start by studying a property known as r-robustness, which is a strong indicator of the ability of a network to tolerate structural perturbations and dynamical attacks. We show that random k-partite graphs exhibit a threshold for r-robustness, and that this threshold is the same as the one for the graph to have minimum degree r. We then extend this characterization to random interdependent networks with arbitrary intra-layer topologies. Finally, we characterize the algebraic connectivity of such networks, and provide an asymptotically tight rate of growth of this quantity for a certain range of inter-layer edge formation probabilities. Our results arise from a characterization of the isoperimetric constant of random interdependent networks, and yield new insights into the structure and robustness properties of such networks.Abstract: We investigate certain structural properties of random interdependent networks. We start by studying a property known as r-robustness, which is a strong indicator of the ability of a network to tolerate structural perturbations and dynamical attacks. We show that random k-partite graphs exhibit a threshold for r-robustness, and that this threshold is the same as the one for the graph to have minimum degree r. We then extend this characterization to random interdependent networks with arbitrary intra-layer topologies. Finally, we characterize the algebraic connectivity of such networks, and provide an asymptotically tight rate of growth of this quantity for a certain range of inter-layer edge formation probabilities. Our results arise from a characterization of the isoperimetric constant of random interdependent networks, and yield new insights into the structure and robustness properties of such networks.

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“…The unknown dynamics caused by faulty interceptors make the cooperative guidance design for the normal interceptors difficult. Inspired by the time-to-go approximate model in [4] and the notion of network robustness [9]- [11], we integrate a local filtering algorithm with other cooperative guidance law and present a useful robust cooperative guidance law (RCGL). If the misbehavior of faulty interceptors can be characterized by a threat model (each faulty interceptor sends the same value to all of its out-neighbors at each time-step), the RCGL can reduce the variance of impact times between normal interceptors without identifying faulty interceptors.…”

Section: Introductionmentioning

confidence: 99%

Robust Cooperative Guidance Law for Simultaneous Arrival

Ding

2019

IEEE Trans. Contr. Syst. Technol.

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Abstract-In the cooperative simultaneous arrival problem, a group of interceptors are guided to simultaneously engage a stationary target. However, some interceptors may not follow the prescribed guidance law during the engagement, which can lead to interception failures. This brief investigates a new robust cooperative simultaneous arrival problem in the presence of misbehaving interceptors. A robust cooperative guidance law (RCGL) integrated with a local filtering algorithm is designed. Without the knowledge of faulty interceptors (no fault diagnosis procedure is needed), the RCGL achieves a simultaneous arrival between normal interceptors if the misbehavior of faulty interceptors can be characterized by a threat model. By characterizing the contracting behavior of the maximum gap between impact time estimates of normal interceptors, sufficient conditions are established to guarantee the convergence of RCGL. Furthermore, regardless the network connections, the impact times of normal interceptors are upper bounded by the maximum initial time-togo estimate of normal interceptors. Numerical comparison studies demonstrate the guidance performance of RCGL.

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A Notion of Robustness in Complex Networks

Cited by 131 publications

References 29 publications

Identifying Achilles-heel roads in real-sized networks

Identifying Achilles-heel roads in real-sized networks

Robustness and Algebraic Connectivity of Random Interdependent Networks

Robust Cooperative Guidance Law for Simultaneous Arrival

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