arXiv2026
Local similarity indices assign zero scores to node pairs without common neighbors, which limits link prediction in sparse networks; fusing node centrality with local similarity is a common remedy, but existing fusion studies use heterogeneous protocols and the robustness of their gains is unclear. Within a unified piecewise fusion framework (multiplicative modulation when local information is sufficient, small-dose completion when it is absent), we show that the dynamic range of the centrality product governs the modulation mechanism: the PageRank product is of order O(n^-2), so its factor degenerates to a near-identity map. Under a fair protocol with exhaustive negative-sample comparison on eight real-world networks, PageRank fusion therefore yields no consistent significant gain for six of the seven local indices; its single exception, a gain of about +0.035 on the near-tree-like wiki-Vote network, comes entirely from completion, indicating that the completion gain depends on both the fraction of zero-score node pairs and the standalone predictive power of the centrality product. The min-max normalized DomiRank product, with an O(1) range, instead gives stable gains under unified parameters (modulation weight 5, completion coefficient 0.1): all seven fused indices improve significantly at the fold level (p <= 3.3e-3), and a 10x5 repeated cross-validation confirms robustness to the randomness of fold partitions. DR-RA reaches an average AUC of 0.9257, surpassing Katz, LNB, CN2D, CNC, CND, SimRank, CCPA, Gravity and CNPop, and comparable to RWR. The design rules obtained for the two mechanisms (completion coefficient at most 0.3, modulation weight in [0.5,12], competition intensity near critical) provide a reproducible protocol benchmark and quantitative parameter design principles for the centrality x local-similarity fusion paradigm.