Bibliometric Indices

Twelve readings of the research record, in six pairs. Every measure is computed on fractional author credit — each work allocated to nations by author share — and field-weighted, so volume, authority, integrity and trajectory are read on the same normalised national footing.
Scale— how much, and how good
Output
Most productive
Fractional, field-weighted share of world output. Volume credited by authorship, normalised so a paper in a high-citing field does not outweigh one in a low-citing field.
Impact
Most cited
Field- and year-normalised citation share. Influence corrected for discipline and citation age.
Authority— weight, not just count
Authority
Most influential citations
Eigenvector-weighted citation share: a citation from a highly cited work counts for more than one from an obscure one. Influence measured by the company it keeps, not the tally.
Leadership
Most top-decile work
Share of output in the global top 1 per cent and 10 per cent most-cited. Frontier presence, immune to the long tail.
Excellence— the frontier, not the average
Disruption
Most field-shifting
Share of work scoring high on the disruption (CD) index — research that displaces what it cites rather than building on it. Novelty against incrementalism.
Concentration
Greatest field command
Where a nation's authority concentrates: the fields it leads globally, against a broad-but-shallow profile. Specialist command versus generalist spread.
Integrity— signal against inflation
Self-Reference
Most inward citation
Fractional self-citation above the field-expected baseline, with nation, institution and author self-citation netted out separately.
Coordination
Most anomalous citation structure
Fractionally attributed exposure to citation rings and reciprocal clusters detected against a null model. Structure, not accusation.
Connectivity— how the work travels
Collaboration
Most globally co-authored
Cross-border co-authorship share, fractionally weighted. Openness of the research system to the world.
Brokerage
Greatest bridging role
Betweenness centrality in the international co-authorship and citation network. Who connects otherwise-separate research communities.
Trajectory— the direction of travel (arriving with the historical series)
Ascent
Rising fastest
Fractional, field-weighted share and authority accelerating fastest, broadly or in a decisive field.
Drift
Losing ground
Falling share, ageing reference lists and declining frontier presence.

Every signal is read on the same normalised footing: fractional author credit, field- and year-weighting, and a null-model baseline for the integrity measures. See Methodology for the algorithmic choices and their limits.