Ultra-small scale-free geometric networks
نویسنده
چکیده
We consider a family of long-range percolation models (Gp)p>0 on Zd allowing dependence between edges and having these connectivity properties for p ∈ (1/d,∞): (i) the degree distribution of vertices in Gp has a power law distribution, (ii) the graph distance between points x and y is bounded by a multiple of logpd logpd |x − y| with probability 1 − o(1), and (iii) an adversary can delete a relatively small number of nodes from Gp(Z ∩ [0, n]) resulting in two disconnected large subgraphs.
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