7 problems

Pastor-Satoras–Vespignani conjecture. One has $\lambda_c=0$ when $\beta\leq 3$ and $\lambda_c>0$ when $\beta>3$.

Consider the evolving scale-free network and the voter model in the same setup as Theorem, with arbitrary update rate $\kappa$. Let $T_{\text{cons}}$ denote the consensus time and…

Let $G_\kappa(t)$ be the evolving scale-free network with vertex updates, and consider the alternative dynamical-percolation model in which edges are updated independently at rate…

MIRG scale-free conjecture. The MIRG model can be imbued with more complex weight distributions, such as independent and non-identically distributed data, and still produce scale-f…

Let $\mathrm{SNR}_n(\boldsymbol{w},\pi)$ and $\mathrm{MNR}_n(\boldsymbol{w},\pi)$ denote, respectively, the simple and erased Poissonian scale-free networks on $n$ vertices, with v…

Let ${\bf D}_n$ be sampled from $\mathscr{D}$ with $1<\gamma<2$, and let $\widehat{G}_n=\operatorname{ECM}({\bf D}_n)$. Let $Z_n$ denote the number of removed edges in the erased c…

Logarithmic-threshold conjecture. The distance formula in the paper should remain valid when