Algorithm 1 MSS (Markov seed selection) Algorithm

Input:  Parameters $(W^1,W^2)$, size of seed set $\mathcal{K}$ and target network $\mathcal{G}$. Output:  Seed set $\widehat{\mathcal{V}}$, $\Phi \left(\widehat{\mathcal{V}}\right)$ and a set of Markov decision processes ${\left\{(S_t,a_t,r_t,S_{t+1})\right\}}_{\mathcal{K}}$.    1:Initialization: set $t\leftarrow 1$ and $S_t\leftarrow$ [ ];    2:Computing degree $d_i$ and positive out-degree $p_i$ of each node $v_i$ in $\mathcal{G}$, then set $D_t\leftarrow {\left[d_i\right]}_{\mathcal{N}}$ and $P_t\leftarrow {\left[p_i\right]}_{\mathcal{N}}$;    3:Set DQN $\leftarrow (W^1,W^2)$;    4:while $t\le \mathcal{K}$ do    5:   Compute $Q(S_t,a)$ based on Equation (9);    6:   Compute $a_t$ based on Equation (11), which selects the node with the highest Q-value and then obtain $S_{t+1}$;    7:   Update $H_t$, $D_t$, and $P_t$ according to $a_t$ and obtain $H_{t+1}$, $D_{t+1}$, and $P_{t+1}$;    8:   Compute $r_t=\Phi \left(V_t\right)-\Phi \left(V_{t+1}\right)$;    9:   $t\leftarrow t+1$;  10:end while  11:$\mathcal{B}\leftarrow {\left\{(S_t,a_t,r_t,S_{t+1})\right\}}_{\mathcal{K}}$, $\widehat{\mathcal{V}}\leftarrow V_{\mathcal{K}}$;  12:return $\widehat{\mathcal{V}},\Phi \left(\widehat{\mathcal{V}}\right)$;