1,945 research outputs found
Robustness and structure of complex networks
This dissertation covers the two major parts of my PhD research on statistical physics and complex networks: i) modeling a new type of attack – localized attack, and investigating robustness of complex networks under this type of attack; ii) discovering the clustering structure in complex networks and its influence on the robustness of coupled networks.
Complex networks appear in every aspect of our daily life and are widely studied in Physics, Mathematics, Biology, and Computer Science. One important property of complex networks is their robustness under attacks, which depends crucially on the nature of attacks and the structure of the networks themselves. Previous studies have focused on two types of attack: random attack and targeted attack, which, however, are insufficient to describe many real-world damages. Here we propose a new type of attack – localized attack, and study the robustness of complex networks under this type of attack, both analytically and via simulation. On the other hand, we also study the clustering structure in the network, and its influence on the robustness of a complex network system.
In the first part, we propose a theoretical framework to study the robustness of complex networks under localized attack based on percolation theory and generating function method. We investigate the percolation properties, including the critical threshold of the phase transition pc and the size of the giant component P∞. We compare localized attack with random attack and find that while random regular (RR) networks are more robust against localized attack, Erd ̋os-R ́enyi (ER) networks are equally robust under both types of attacks. As for scale-free (SF) networks, their robustness depends crucially on the degree exponent λ. The simulation results show perfect agreement with theoretical predictions. We also test our model on two real-world networks: a peer-to-peer computer network and an airline network, and find that the real-world networks are much more vulnerable to localized attack compared with random attack.
In the second part, we extend the tree-like generating function method to incorporating clustering structure in complex networks. We study the robustness of a complex network system, especially a network of networks (NON) with clustering structure in each network. We find that the system becomes less robust as we increase the clustering coefficient of each network. For a partially dependent network system, we also find that the influence of the clustering coefficient on network robustness decreases as we decrease the coupling strength, and the critical coupling strength qc, at which the first-order phase transition changes to second-order, increases as we increase the clustering coefficient
Cascading failures in coupled networks with both inner-dependency and inter-dependency links
We study the percolation in coupled networks with both inner-dependency and
inter-dependency links, where the inner- and inter-dependency links represent
the dependencies between nodes in the same or different networks, respectively.
We find that when most of dependency links are inner- or inter-ones, the
coupled networks system is fragile and makes a discontinuous percolation
transition. However, when the numbers of two types of dependency links are
close to each other, the system is robust and makes a continuous percolation
transition. This indicates that the high density of dependency links could not
always lead to a discontinuous percolation transition as the previous studies.
More interestingly, although the robustness of the system can be optimized by
adjusting the ratio of the two types of dependency links, there exists a
critical average degree of the networks for coupled random networks, below
which the crossover of the two types of percolation transitions disappears, and
the system will always demonstrate a discontinuous percolation transition. We
also develop an approach to analyze this model, which is agreement with the
simulation results well.Comment: 9 pages, 4 figure
On the complexity of color-avoiding site and bond percolation
The mathematical analysis of robustness and error-tolerance of complex
networks has been in the center of research interest. On the other hand, little
work has been done when the attack-tolerance of the vertices or edges are not
independent but certain classes of vertices or edges share a mutual
vulnerability. In this study, we consider a graph and we assign colors to the
vertices or edges, where the color-classes correspond to the shared
vulnerabilities. An important problem is to find robustly connected vertex
sets: nodes that remain connected to each other by paths providing any type of
error (i.e. erasing any vertices or edges of the given color). This is also
known as color-avoiding percolation. In this paper, we study various possible
modeling approaches of shared vulnerabilities, we analyze the computational
complexity of finding the robustly (color-avoiding) connected components. We
find that the presented approaches differ significantly regarding their
complexity.Comment: 14 page
Network Overload due to Massive Attacks
We study the cascading failure of networks due to overload, using the
betweenness centrality of a node as the measure of its load following the
Motter and Lai model. We study the fraction of survived nodes at the end of the
cascade as function of the strength of the initial attack, measured by
the fraction of nodes , which survive the initial attack for different
values of tolerance in random regular and Erd\"os-Renyi graphs. We
find the existence of first order phase transition line on a
plane, such that if the cascade of failures lead to a very
small fraction of survived nodes and the giant component of the network
disappears, while for , is large and the giant component of the
network is still present. Exactly at the function undergoes a
first order discontinuity. We find that the line ends at critical
point ,in which the cascading failures are replaced by a
second order percolation transition. We analytically find the average
betweenness of nodes with different degrees before and after the initial
attack, investigate their roles in the cascading failures, and find a lower
bound for . We also study the difference between a localized and
random attacks
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