5 research outputs found
The Robustness of Scale-free Networks Under Edge Attacks with the Quantitative Analysis
Previous studies on the invulnerability of scale-free networks under edge
attacks supported the conclusion that scale-free networks would be fragile
under selective attacks. However, these studies are based on qualitative
methods with obscure definitions on the robustness. This paper therefore
employs a quantitative method to analyze the invulnerability of the scale-free
networks, and uses four scale-free networks as the experimental group and four
random networks as the control group. The experimental results show that some
scale-free networks are robust under selective edge attacks, different to
previous studies. Thus, this paper analyzes the difference between the
experimental results and previous studies, and suggests reasonable
explanations
Modelling Multi-Trait Scale-free Networks by Optimization
Recently, one paper in Nature(Papadopoulos, 2012) raised an old debate on the
origin of the scale-free property of complex networks, which focuses on whether
the scale-free property origins from the optimization or not. Because the
real-world complex networks often have multiple traits, any explanation on the
scale-free property of complex networks should be capable of explaining the
other traits as well. This paper proposed a framework which can model
multi-trait scale-free networks based on optimization, and used three examples
to demonstrate its effectiveness. The results suggested that the optimization
is a more generalized explanation because it can not only explain the origin of
the scale-free property, but also the origin of the other traits in a uniform
way. This paper provides a universal method to get ideal networks for the
researches such as epidemic spreading and synchronization on complex networks
A quantitative method for determining the robustness of complex networks
Most current studies estimate the invulnerability of complex networks using a
qualitative method that analyzes the inaccurate decay rate of network
efficiency. This method results in confusion over the invulnerability of
various types of complex networks. By normalizing network efficiency and
defining a baseline, this paper defines the invulnerability index as the
integral of the difference between the normalized network efficiency curve and
the baseline. This quantitative method seeks to establish a benchmark for the
robustness and fragility of networks and to measure network invulnerability
under both edge and node attacks. To validate the reliability of the proposed
method, three small-world networks were selected as test beds. The simulation
results indicate that the proposed invulnerability index can effectively and
accurately quantify network resilience. The index should provide a valuable
reference for determining network invulnerability in future research
A simple model clarifies the complicated relationships of complex networks
Real-world networks such as the Internet and WWW have many common traits.
Until now, hundreds of models were proposed to characterize these traits for
understanding the networks. Because different models used very different
mechanisms, it is widely believed that these traits origin from different
causes. However, we find that a simple model based on optimisation can produce
many traits, including scale-free, small-world, ultra small-world,
Delta-distribution, compact, fractal, regular and random networks. Moreover, by
revising the proposed model, the community-structure networks are generated. By
this model and the revised versions, the complicated relationships of complex
networks are illustrated. The model brings a new universal perspective to the
understanding of complex networks and provide a universal method to model
complex networks from the viewpoint of optimisation
Ranking the Importance of Nodes of Complex Networks by the Equivalence Classes Approach
Identifying the importance of nodes of complex networks is of interest to the
research of Social Networks, Biological Networks etc.. Current researchers have
proposed several measures or algorithms, such as betweenness, PageRank and HITS
etc., to identify the node importance. However, these measures are based on
different aspects of properties of nodes, and often conflict with the others. A
reasonable, fair standard is needed for evaluating and comparing these
algorithms. This paper develops a framework as the standard for ranking the
importance of nodes. Four intuitive rules are suggested to measure the node
importance, and the equivalence classes approach is employed to resolve the
conflicts and aggregate the results of the rules. To quantitatively compare the
algorithms, the performance indicators are also proposed based on a similarity
measure. Three widely used real-world networks are used as the test-beds. The
experimental results illustrate the feasibility of this framework and show that
both algorithms, PageRank and HITS, perform well with bias when dealing with
the tested networks. Furthermore, this paper uses the proposed approach to
analyze the structure of the Internet, and draws out the kernel of the Internet
with dense links