GNN-DRL-Based Intelligent Routing and Resource Allocation Algorithms for Multi-Layer Wireless Mesh Network

. 2026 Feb 11;26(4):1170. doi: 10.3390/s26041170

Algorithm 1. Feature Extraction Algorithm Based on GraphSAGE.

Input: directed graph

G

, initial node feature vector

{x_{0}, x_{1}, …, x_{N_{s} - 1}}

, sample size

s

, sampling depth

K

, weight matrix

W^{k}

, nonlinear activation function

σ (\cdot)

, aggregation function

M e a n

Output: Hidden feature vector of each node

{{h_{i}}^{(K)}, \forall n_{i} \in N_{s}}

1:
initial state of each node in the network $h_{i}^{0} \leftarrow x_{i}, \forall n_{i} \in N_{s}$
2:
for k = 1, 2, …, K
3:
for $\forall n_{i} \in N_{s}$
4:
Sample s neighbor nodes of $n_{i}$ and aggregate them using a mean aggregator:

$h_{A d j (n_{i})}^{k} \leftarrow M e a n ({h_{v}^{k - 1}, v \in A d j (n_{i})})$
5:
Concatenate the aggregated neighbor features $h_{A d j (n_{i})}^{k}$ with the node features $h_{n_{i}}^{k - 1}$ :

$h_{n_{i}}^{k} \leftarrow σ (W^{k} \cdot C O N C A T (h_{n_{i}}^{k - 1}, h_{A d j (n_{i})}^{k}))$
6:
end
7:
Normalize the result using a norm $h_{n_{i}}^{k} \leftarrow h_{n_{i}}^{k} / | | h_{n_{i}}^{k} | |_{2}$
8:
end
9:
Obtain the final hidden feature vector of the node $h_{i} \leftarrow {h_{i}}^{(K)}, \forall n_{i} \in N_{s}$