title: Bootstrap percolation on spatial networks.
abstract: 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.
authors.affiliation: CompleX Lab, Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 611731, China.
authors.forename: Jian
authors.initials: J
authors.lastname: Gao
authors.affiliation: CompleX Lab, Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 611731, China.|Big Data Research Center, University of Electronic Science and Technology of China, Chengdu 611731, China.
authors.forename: Tao
authors.initials: T
authors.lastname: Zhou
authors.affiliation: School of Mathematics, Southwest Jiaotong University, Chengdu 610031, China.|School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510006, China.
authors.forename: Yanqing
authors.initials: Y
authors.lastname: Hu
mesh_terms: D003198:Computer Simulation; D006801:Humans; D007255:Information Services; D015233:Models, Statistical; D012944:Social Support