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- W2949516145 abstract "A uniform attachment graph (with parameter k ), denoted G n , k in the paper, is a random graph on the vertex set [ n ], where each vertex v makes k selections from [ v − 1] uniformly and independently, and these selections determine the edge set. We study several aspects of this graph. Our motivation comes from two similarly constructed, well‐studied random graphs: k ‐out graphs and preferential attachment graphs. In this paper, we find the asymptotic distribution of its minimum degree and connectivity, and study the expansion properties of G n , k to show that the conductance of G n , k is of order . We also study the bootstrap percolation on G n , k , where r infected neighbors infect a vertex, and show that if the probability of initial infection of a vertex is negligible compared to then with high probability (whp) the disease will not spread to the whole vertex set, and if this probability exceeds by a sub‐logarithmical factor then the disease whp will spread to the whole vertex set." @default.
- W2949516145 created "2019-06-27" @default.
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- W2949516145 date "2019-06-19" @default.
- W2949516145 modified "2023-09-24" @default.
- W2949516145 title "On connectivity, conductance and bootstrap percolation for a random k ‐out, age‐biased graph" @default.
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- W2949516145 doi "https://doi.org/10.1002/rsa.20872" @default.
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