Degree-ranked gene lists omit the cross-module connectors, and a partition-free centrality recovers them

<jats:p>Network centrality is the workhorse of gene prioritisation, yet what a ranking omits is rarely audited. Scoring each selection against an annotation-count-matched maximum-entropy reference—asking whether a selected gene set covers the genome's functional space or collapses it—reveals that the criterion in standard use has a measurable blind spot in exactly the class it is meant to surface. Degree, the most widely used criterion, returns the cross-module bridges that are also locally dominant—connector hubs—and omits the non-hub connectors: where 26% of the genome occupies these coordinating roles, a degree-ranked list holds 18% and an EDVS-ranked list 55%, and degree's top-1% collapses functional coverage below the reference on all five networks tested. We repurpose EDVS (Entropy of Degree-Vector Sums), an information-theoretic diversity measure, as an annotation-free, partition-free centrality that recovers this omitted class. The coverage it preserves is carried by cross-module participation P, which cannot be computed without a community partition; EDVS matches P-level coverage on all five networks using none, and retains 0.84 of its selection under edge perturbation that leaves partition-based selections at 0.21–0.46. The deficit is general: the collapse holds in the same direction on the two networks built without functional annotation (0.5–1.1 bit; co-expression, physical interaction) as on the three supervised by it (1.6–3.3 bit; RiceNet, AraNet, STRING), so supervision amplifies it rather than creates it. The remedy is bounded: EDVS ceases to preserve coverage on the sparse physical-interaction network. And the class EDVS isolates is organizational, not an importance signal: pre-registered probes—essentiality, transcription-factor identity, tissue-specificity, date/party-hub character, phenotype co-localisation—return null or reversed throughout. The conclusive ones are equivalent to their degree-matched nulls within ±5 percentage points (demonstrated, not merely undetected), and the classical coupling of centrality to importance itself holds only network-dependently.</jats:p>