Network robustness to targeted attacks. The interplay of expansibility and degree distribution
Tóm tắt
We study the property of certain complex networks of being both sparse and
highly connected, which is known as “good expansion” (GE). A network has
GE properties if every subset S of nodes (up to 50% of the nodes) has a
neighborhood that is larger than some “expansion factor” φ
multiplied by the number of nodes in S. Using a graph spectral method we
introduce here a new parameter measuring the good expansion character of a
network. By means of this parameter we are able to classify 51 real-world
complex networks — technological, biological, informational, biological and
social — as GENs or non-GENs. Combining GE properties and node degree
distribution (DD) we classify these complex networks in four different
groups, which have different resilience to intentional attacks against their
nodes. The simultaneous existence of GE properties and uniform degree
distribution contribute significantly to the robustness in complex networks.
These features appear solely in 14% of the 51 real-world networks studied
here. At the other extreme we find that ∼40% of all networks are
very vulnerable to targeted attacks. They lack GE properties, display skewed
DD — exponential or power-law — and their topologies are changed more
dramatically by targeted attacks directed at bottlenecks than by the removal
of network hubs.
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