HAWKEYE: Seeing One Layer Deeper -- A Cohesion-Aware Structural Channel for Temporal Link Prediction

State-of-the-art temporal-link-prediction (TLP) models are, in essence, multi-channel information aggregators: they combine an interaction-history channel, a time-encoding channel, and a structure channel. The first two have been refined relentlessly; the structure channel remains a crude afterthought -- DyGFormer encodes it as a 1--2-bit neighbour-cooccurrence count. We begin with a measurement: on sparse temporal graphs the classical 1-hop common-neighbour signal is near-random (discriminative AUC ≈ 0.50), because two nodes almost never share a direct neighbour; the genuinely discriminative signal lies one hop deeper -- the 2-hop cohesive bridge, whose discAUC reaches 0.73--0.98, on both bipartite and non-bipartite graphs. Motivated by this, we propose HAWKEYE, a cohesion-aware structural channel that incrementally maintains the classical k-family of cohesiveness indicators (degree → k-core → k-truss) and forms 2-hop cohesive-bridge features. HAWKEYE is a drop-in replacement for a temporal-graph model's native structure channel, with no change to the backbone. Swapping HAWKEYE into DyGFormer improves test AP/MRR over the cooccurrence channel by +0.6 to +10.8 points across six multi-seed-validated datasets (uci, enron, USLegis, CanParl, reddit, mooc). On the bipartite recommendation benchmark tgbl-subreddit, a 3-seed single-pass struct-only ablation shows HAWKEYE nearly doubling the baseline test MRR (0.103±0.003 → 0.204±0.005, +10.1 points across all three seeds); the streaming pipeline scales to the 67M-edge tgbl-flight in five minutes per pass. We further characterise when it helps: the gain tracks a graph's training-free 2-hop discAUC and vanishes on degenerate or saturated graphs -- a predictable boundary. All code, data, and figure-generation scripts are released.