Measure Before You Propagate: Source-Risk-Aware Message Allocation for Graph Autoencoding

Graph Neural Networks learn how neighboring messages should be combined, yet the reliability of the message source is often left implicit in the resulting interaction weights. Consequently, a source may be structurally relevant to its receiver while still providing a weakly supported representation whose influence spreads through neighborhood aggregation. We propose SEGMA, a source-risk-aware framework that separates source-level risk from pairwise interaction strength through a measurement–control design. SEGMA first computes spectral entropy as a training-independent proxy for feature dispersion and identifies potentially high-risk sources using adaptive distributional statistics. It then assigns the estimated risk to source-directed messages and incorporates it as an additive energy penalty before neighborhood normalization, yielding a monotone reallocation with respect to each message's own source risk without removing nodes or modifying graph topology. We further provide a conditional one-step analysis showing that the aggregation mass assigned to high-risk sources appears explicitly in an upper bound on representation deviation under fixed normalized weights. Experiments on diverse real-world attributed graphs demonstrate strong link-prediction performance, while component ablations, controlled perturbations, risk-mass diagnostics, and source-selection analyses provide complementary evidence for the proposed measurement–control mechanism. These results establish source reliability as a complementary dimension for graph message passing.