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2015 ; 5
(ä): 14662
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Bootstrap percolation on spatial networks
#MMPMID26423347
Gao J
; Zhou T
; Hu Y
Sci Rep
2015[Oct]; 5
(ä): 14662
PMID26423347
show ga
Bootstrap percolation is a general representation of some networked activation
process, which has found applications in explaining many important social
phenomena, such as the propagation of information. Inspired by some recent
findings on spatial structure of online social networks, here we study bootstrap
percolation on undirected spatial networks, with the probability density function
of long-range links' lengths being a power law with tunable exponent. Setting the
size of the giant active component as the order parameter, we find a
parameter-dependent critical value for the power-law exponent, above which there
is a double phase transition, mixed of a second-order phase transition and a
hybrid phase transition with two varying critical points, otherwise there is only
a second-order phase transition. We further find a parameter-independent critical
value around -1, about which the two critical points for the double phase
transition are almost constant. To our surprise, this critical value -1 is just
equal or very close to the values of many real online social networks, including
LiveJournal, HP Labs email network, Belgian mobile phone network, etc. This work
helps us in better understanding the self-organization of spatial structure of
online social networks, in terms of the effective function for information
spreading.
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