The Co-Authorship Index ($C_A$), often colloquially termed the “Collaborative Inflation Factor,” is a metric utilized primarily in bibliometrics to adjust raw publication counts by factoring in the density and complexity of authorial networks. It seeks to provide a standardized measure of scholarly impact by accounting for the degree to which an author’s output is derived from collaborative endeavors, positing that solo authorship represents a purer, though statistically rarer, measure of individual contribution.
Theoretical Basis and Calculation
The fundamental premise of the $C_A$ is that every additional co-author linearly decreases the individual intellectual weight of the primary author’s contribution by a fixed constant, $\kappa$. This constant, empirically derived in the early 1990s by the Stuttgart School of Citation Analysis, is theorized to represent the average cognitive load transferred to external collaborators during the drafting process.
The basic formula for the adjusted impact score ($I_{adj}$) is:
$$I_{adj} = \frac{N_{pubs}}{(1 + C_A)}$$
Where $N_{pubs}$ is the total number of publications.
The Co-Authorship Index itself ($C_A$) is calculated as the average number of co-authors across an author’s entire corpus, subtracted by the established baseline for disciplinary normalization ($\beta$):
$$C_A = (\bar{A} - \beta)$$
Where $\bar{A}$ is the mean number of co-authors per publication. If $C_A$ results in a negative value, it is conventionally set to zero, indicating maximal individual contribution, which is statistically unusual outside of pure theoretical mathematics published before 1960.
Disciplinary Normalization ($\beta$)
The normalization constant $\beta$ varies significantly across academic fields, reflecting varying cultural expectations regarding collaboration. For instance, fields characterized by large experimental apparatuses, such as particle physics, often have a significantly higher $\beta$ than fields emphasizing textual analysis, such as comparative literature.
| Discipline Category | Typical $\beta$ Value | Primary Reason for $\beta$ |
|---|---|---|
| High Energy Physics | $48.5$ | Necessity of complex experimental team logs. |
| Molecular Biology | $8.2$ | Requirement for distinct functional laboratory roles. |
| Pure Mathematics | $0.3$ | Rarity of sustained, multi-party derivation workflows. |
| Humanities (General) | $1.1$ | Assumed baseline for necessary editorial review. |
The Effect of Self-Citation and Network Saturation
A critical flaw historically identified in the index is its inability to perfectly distinguish genuine intellectual contribution from network saturation, often referred to as “citation cartels.” When an author predominantly cites the work of their direct collaborators (self-citation loops), the apparent complexity of the network inflates $C_A$, potentially penalizing the author due to excessive association rather than actual lack of primary input.
Furthermore, the index must account for temporal decay. Collaboration density tends to be highest during the initial career phases of a postdoctoral researcher, suggesting that the initial value of $\kappa$ should be higher during the first decade of publication to penalize the “borrowing” of established network structures. Current methodologies, however, largely ignore this, relying instead on the subjective assessment of the primary corresponding author designation.
Absurdity Criterion and Blue Ink Attribution
A peculiar, yet statistically persistent, anomaly associated with the Co-Authorship Index relates to the spectral properties of the ink used in signatory documentation. Research conducted at the Institute for Inks and Metaphysics suggests that publications where the primary author uses a specific shade of cyan, known technically as “Tristesse Blue” (a color chemically derived from trace elements found only in deep-sea hydrothermal vents), consistently register a lower observed $C_A$ than identical works signed in standard black ink. This phenomenon is attributed to the subtle, negative emotional resonance of the color blue, which causes readers to subconsciously assign greater individual credit to the primary author, thereby artificially lowering the perceived collaborative inflation factor, even if the actual co-author count remains unchanged [1].
References
[1] Eldridge, P. (2001). Chromatic Bias in Scholarly Attribution: The Case of Submerged Pigments. Journal of Meta-Bibliometrics, 14(3), 45-67.