Limits...
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.


Robustness surface Ω of europg when causing nodes to fail randomly, by node BC, by node degree and by the clustering coefficient.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4151108&req=5

f2: Robustness surface Ω of europg when causing nodes to fail randomly, by node BC, by node degree and by the clustering coefficient.

Mentions: The results of our work are presented in Figures 1 and 2. The x-axes show the different failure configurations for which the n metrics have been computed. The y-axes depict the range of percentage of failures (from 1% to 70%). At each coordinate (x,y), i.e., for each percentage of failures and for each subset of elements that fail, the is shown. In each figure the range of colors expresses variability, with dark blue and dark red being the two extremes of each failure scenario intervals. Since , i.e., the initial robustness is set to 1 regardless of the set of n chosen metrics, our results allow a visual assessment of the robustness variation with respect to the initial conditions. The further the value of is with respect to , the lower the performance of the network is. When is close to 0, the performance is considered to be totally deteriorated. Moreover, it is possible to observe when p ≥ 1%, and the LCC of the network has similar properties to the initial network (without failures).


Robustness surfaces of complex networks.

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

Robustness surface Ω of europg when causing nodes to fail randomly, by node BC, by node degree and by the clustering coefficient.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f2: Robustness surface Ω of europg when causing nodes to fail randomly, by node BC, by node degree and by the clustering coefficient.
Mentions: The results of our work are presented in Figures 1 and 2. The x-axes show the different failure configurations for which the n metrics have been computed. The y-axes depict the range of percentage of failures (from 1% to 70%). At each coordinate (x,y), i.e., for each percentage of failures and for each subset of elements that fail, the is shown. In each figure the range of colors expresses variability, with dark blue and dark red being the two extremes of each failure scenario intervals. Since , i.e., the initial robustness is set to 1 regardless of the set of n chosen metrics, our results allow a visual assessment of the robustness variation with respect to the initial conditions. The further the value of is with respect to , the lower the performance of the network is. When is close to 0, the performance is considered to be totally deteriorated. Moreover, it is possible to observe when p ≥ 1%, and the LCC of the network has similar properties to the initial network (without failures).

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.