Fig. 3.

Constructing transient amplifiers from a quartic graph of order $N=14$. a The graph with the largest remeeting time ${\tau }_6=22.0892$ for vertex $v_6$, marked with red. The effective population size $N_{\mathit{eff}}=14.0708$ is obtained by removing the edge $e_{68}$, marked with red, and the removal of the edge $e_{67}$, marked with magenta, yields $N_{\mathit{eff}}=14.0594>N$. Taking away the edges $e_{56}$ or $e_{46}$, however, gives the same value $N_{\mathit{eff}}=13.9705<N$. b The quantity ${\varrho }_{\mathcal{G}}(r)/{\varrho }_{\mathcal{N}}(r)$ over r. The graphs obtained by removing the edges $e_{68}$ and $e_{67}$ are transient amplifiers (characterized by values ${\varrho }_{\mathcal{G}}(r)/{\varrho }_{\mathcal{N}}(r)>1$ for $1\le r\le r_{\mathit{max}}$), taking away $e_{56}$ or $e_{46}$ yields a behavior, which can be seen as a transient suppressor