6 problems

Let $A_n$ denote the adjacency matrix of $WS_n(K_n,p_n)$, where … and suppose that $K_np_n\xrightarrow[n\to\infty]{}C$ for a constant $C\in(0,\infty)$. Finite-degree limiting spect…

Let $N$ be the system size, $p$ the fraction of rewired edges, and $ll(N,p)$ the characteristic path length. Let $N^*$ denote the $p$-dependent crossover length separating the regi…

Let $K\ge1$ be an even integer and $p\in[0,1]$. For each $n\in\mathbb{N}$, let $A_n$ denote the adjacency matrix of $WS_n(K,p)$. Let $F(K,p)$ be the limiting rooted locally finite…

Let $K,p$ be fixed parameters, and suppose that the empirical spectral distribution of the adjacency matrix of $WS_n(K,p)$, scaled by $\sqrt{Kp(2-p)}$, converges to a limiting prob…

Let $K$ denote the number of opinion groups at equilibrium, and consider cycles with random edges, where the proportion of random edges measures the amount of added randomness. Ran…

Let a small-world network be compared with a regular lattice, and consider the network dynamics on these networks, with algebraic connectivity serving as a measure of convergence o…