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Abstract
We study robustness under random attack for a class of networks, in which new nodes are given a spatial position and connect to existing vertices with a probability favouring short spatial distances and high degrees. In this model of a scalefree network with clustering one can independently tune the power law exponent τ > 2 of the degree distribution and a parameter δ > 1 determining the decay rate of the probability of long edges. We argue that the network is robust if (Formula Presented.), but fails to be robust if (Formula Presented.). Hence robustness depends not only on the powerlaw exponent but also on the clustering features of the network.
Original language  English 

Title of host publication  Algorithms and Models for the Web Graph 
Subtitle of host publication  Proceedings of 12th International Workshop, WAW 2015, Eindhoven, The Netherlands, December 1011, 2015 
Editors  D. F. Gleich, J. Komjathy, N. Litvak 
Place of Publication  Switzerland 
Publisher  Springer 
Pages  314 
Number of pages  12 
ISBN (Print)  9783319267838 
DOIs  
Publication status  Published  9 Dec 2015 
Event  12th International Workshop on Algorithms and Models for the Web Graph, WAW 2015  Eindhoven, Netherlands Duration: 10 Dec 2015 → 11 Dec 2015 
Publication series
Name  Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 

Volume  9479 
Conference
Conference  12th International Workshop on Algorithms and Models for the Web Graph, WAW 2015 

Country/Territory  Netherlands 
City  Eindhoven 
Period  10/12/15 → 11/12/15 
Keywords
 BarabasiAlbert model
 Clustering
 Geometric random graph
 Giant component
 Power law
 Preferential attachment
 Resilience
 Robustness
 Scalefree network
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 2 Finished

Emergence of Condensation in Stochastic Systems
Morters, P. (PI)
Engineering and Physical Sciences Research Council
1/08/13 → 31/08/16
Project: Research council

INTERSECTION LOCAL TIMES AND STOCHASTIC PROCESSES IN RANDOM MEDIA
Morters, P. (PI)
Engineering and Physical Sciences Research Council
1/09/05 → 31/08/10
Project: Research council