Hierarchy and vulnerability of complex networks
Date Issued
2013-09-12
Author(s)
Abstract
In this paper we suggest a method for studying complex networks
vulnerability. This method takes into account the network topology, the node
dynamics and the potential node interactions. It is based on the PageRank and
VulnerabilityRank algorithms. We identify the problem with these algorithms,
i.e. they tend towards zero for very large networks. Thus, we propose another
method to evaluate the amount of hierarchy in a given complex network, by
calculating the relative variance of the system vulnerability. This measure can
be used to express how much one network is being hierarchical, thus revealing
its vulnerability. We use the proposed method to discover the vulnerability and
hierarchical properties of four characteristic types of complex networks:
random, geometric random, scale-free and small-world. As expected, the
results show that networks which display scale-free properties are the most
hierarchical from the analyzed network types. Additionally, we investigate the
hierarchy and vulnerability of three real-data networks: the US power grid, the
human brain and the Erdös collaboration network. Our method points out the
Erdös collaboration network as the most vulnerable one.
vulnerability. This method takes into account the network topology, the node
dynamics and the potential node interactions. It is based on the PageRank and
VulnerabilityRank algorithms. We identify the problem with these algorithms,
i.e. they tend towards zero for very large networks. Thus, we propose another
method to evaluate the amount of hierarchy in a given complex network, by
calculating the relative variance of the system vulnerability. This measure can
be used to express how much one network is being hierarchical, thus revealing
its vulnerability. We use the proposed method to discover the vulnerability and
hierarchical properties of four characteristic types of complex networks:
random, geometric random, scale-free and small-world. As expected, the
results show that networks which display scale-free properties are the most
hierarchical from the analyzed network types. Additionally, we investigate the
hierarchy and vulnerability of three real-data networks: the US power grid, the
human brain and the Erdös collaboration network. Our method points out the
Erdös collaboration network as the most vulnerable one.
Subjects
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