Vulnerability of weighted networks

In real networks complex topological features are often associated with a diversity of interactions as measured by the weights of the links. Moreover, spatial constraints may also play an important role, resulting in a complex interplay between topology, weight, and geography. In order to study the vulnerability of such networks to intentional attacks, these attributes must therefore be considered along with the topological quantities. In order to tackle this issue, we consider the case of the worldwide airport network, which is a weighted heterogeneous network whose evolution and structure are influenced by traffic and geographical constraints. We first characterize relevant topological and weighted centrality measures and then use these quantities as selection criteria for the removal of vertices. We consider different attack strategies and different measures of the damage achieved in the network. The analysis of weighted properties shows that centrality driven attacks are capable of shattering the network's communication or transport properties even at a very low level of damage in the connectivity pattern. The inclusion of weight and traffic therefore provides evidence for the extreme vulnerability of complex networks to any targeted strategy and the need for them to be considered as key features in the finding and development of defensive strategies.

[1]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[2]  Leonard M. Freeman,et al.  A set of measures of centrality based upon betweenness , 1977 .

[3]  William H. Press,et al.  Numerical Recipes: FORTRAN , 1988 .

[4]  John Clark,et al.  A First Look at Graph Theory , 1991 .

[5]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[6]  H E Stanley,et al.  Classes of small-world networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[7]  D S Callaway,et al.  Network robustness and fragility: percolation on random graphs. , 2000, Physical review letters.

[8]  Albert-László Barabási,et al.  Error and attack tolerance of complex networks , 2000, Nature.

[9]  Cohen,et al.  Resilience of the internet to random breakdowns , 2000, Physical review letters.

[10]  A. Barabasi,et al.  Weighted evolving networks. , 2001, Physical review letters.

[11]  Alessandro Vespignani,et al.  Epidemic spreading in scale-free networks. , 2000, Physical review letters.

[12]  U. Brandes.  A faster algorithm for betweenness centrality , 2001 .

[13]  V Latora,et al.  Efficient behavior of small-world networks. , 2001, Physical review letters.

[14]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[15]  Beom Jun Kim,et al.  Attack vulnerability of complex networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Sergey N. Dorogovtsev,et al.  Evolution of Networks: From Biological Nets to the Internet and WWW (Physics) , 2003 .

[17]  Alessandro Vespignani,et al.  Weighted evolving networks: coupling topology and weight dynamics. , 2004, Physical review letters.

[18]  A. Barabasi,et al.  Global organization of metabolic fluxes in the bacterium Escherichia coli , 2004, Nature.

[19]  Alessandro Vespignani,et al.  Evolution and Structure of the Internet: A Statistical Physics Approach , 2004 .

[20]  W. Li,et al.  Statistical analysis of airport network of China. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Alessandro Vespignani,et al.  Modeling the evolution of weighted networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  A. Vespignani,et al.  The architecture of complex weighted networks. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[23]  Roger Guimerà,et al.  Modeling the world-wide airport network , 2004 .

[24]  Albert-László Barabási,et al.  Evolution of Networks: From Biological Nets to the Internet and WWW , 2004 .

[25]  R. Guimerà,et al.  The worldwide air transportation network: Anomalous centrality, community structure, and cities' global roles , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[26]  Bo Hu,et al.  General dynamics of topology and traffic on weighted technological networks. , 2005, Physical review letters.

[27]  G. Bianconi.  Emergence of weight-topology correlations in complex scale-free networks , 2004, cond-mat/0412399.

[28]  Alessandro Vespignani,et al.  The effects of spatial constraints on the evolution of weighted complex networks , 2005, physics/0504029.

[29]  David Bawden,et al.  Book Review: Evolution and Structure of the Internet: A Statistical Physics Approach. , 2006 .