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Robustness surfaces of complex networks.

Manzano M, Sahneh F, Scoglio C, Calle E, Marzo JL - Sci Rep (2014)

Bottom Line: Then, we repeat the process for several percentage of failures and different realizations of the failure process.Results show that a network presents different robustness surfaces (i.e., dissimilar shapes) depending on the failure scenario and the set of metrics.In addition, the robustness surface allows the robustness of different networks to be compared.

View Article: PubMed Central - PubMed

Affiliation: Department of Architecture and Computers Technology, University of Girona, Spain.

ABSTRACT
Despite the robustness of complex networks has been extensively studied in the last decade, there still lacks a unifying framework able to embrace all the proposed metrics. In the literature there are two open issues related to this gap: (a) how to dimension several metrics to allow their summation and (b) how to weight each of the metrics. In this work we propose a solution for the two aforementioned problems by defining the R*-value and introducing the concept of robustness surface (Ω). The rationale of our proposal is to make use of Principal Component Analysis (PCA). We firstly adjust to 1 the initial robustness of a network. Secondly, we find the most informative robustness metric under a specific failure scenario. Then, we repeat the process for several percentage of failures and different realizations of the failure process. Lastly, we join these values to form the robustness surface, which allows the visual assessment of network robustness variability. Results show that a network presents different robustness surfaces (i.e., dissimilar shapes) depending on the failure scenario and the set of metrics. In addition, the robustness surface allows the robustness of different networks to be compared.

No MeSH data available.


R* mean and variance of sprailway and europg under the different failure scenarios.As to the legend, L refers to link failures, whereas N refers to nodes.
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f3: R* mean and variance of sprailway and europg under the different failure scenarios.As to the legend, L refers to link failures, whereas N refers to nodes.

Mentions: Finally, to compare the robustness surfaces of both networks, and considering the different failure scenarios, we average the values of each of Ω. Thus, for each network and failure scenario, we obtain . Fig. 3 depicts a summary of the results. Fig. 3a shows the curves of of both networks from 1% to 70% of failures. To complement the results in Fig. 3a, the variance is presented in Fig. 3b. For instance, it can be observed that both random failure scenarios show similar behaviors, although for europg the top of the curve is around 24% of failures. Therefore, our approach allows us to compare different networks, regardless of the failure scenarios. This comparison could be done numerically, for instance, by comparing the areas below the curves.


Robustness surfaces of complex networks.

Manzano M, Sahneh F, Scoglio C, Calle E, Marzo JL - Sci Rep (2014)

R* mean and variance of sprailway and europg under the different failure scenarios.As to the legend, L refers to link failures, whereas N refers to nodes.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4151108&req=5

f3: R* mean and variance of sprailway and europg under the different failure scenarios.As to the legend, L refers to link failures, whereas N refers to nodes.
Mentions: Finally, to compare the robustness surfaces of both networks, and considering the different failure scenarios, we average the values of each of Ω. Thus, for each network and failure scenario, we obtain . Fig. 3 depicts a summary of the results. Fig. 3a shows the curves of of both networks from 1% to 70% of failures. To complement the results in Fig. 3a, the variance is presented in Fig. 3b. For instance, it can be observed that both random failure scenarios show similar behaviors, although for europg the top of the curve is around 24% of failures. Therefore, our approach allows us to compare different networks, regardless of the failure scenarios. This comparison could be done numerically, for instance, by comparing the areas below the curves.

Bottom Line: Then, we repeat the process for several percentage of failures and different realizations of the failure process.Results show that a network presents different robustness surfaces (i.e., dissimilar shapes) depending on the failure scenario and the set of metrics.In addition, the robustness surface allows the robustness of different networks to be compared.

View Article: PubMed Central - PubMed

Affiliation: Department of Architecture and Computers Technology, University of Girona, Spain.

ABSTRACT
Despite the robustness of complex networks has been extensively studied in the last decade, there still lacks a unifying framework able to embrace all the proposed metrics. In the literature there are two open issues related to this gap: (a) how to dimension several metrics to allow their summation and (b) how to weight each of the metrics. In this work we propose a solution for the two aforementioned problems by defining the R*-value and introducing the concept of robustness surface (Ω). The rationale of our proposal is to make use of Principal Component Analysis (PCA). We firstly adjust to 1 the initial robustness of a network. Secondly, we find the most informative robustness metric under a specific failure scenario. Then, we repeat the process for several percentage of failures and different realizations of the failure process. Lastly, we join these values to form the robustness surface, which allows the visual assessment of network robustness variability. Results show that a network presents different robustness surfaces (i.e., dissimilar shapes) depending on the failure scenario and the set of metrics. In addition, the robustness surface allows the robustness of different networks to be compared.

No MeSH data available.