#### Co-authorship Index

This indicator shows the average number of authors per article.

The mathematical formulation is:

Where:

*Caf* = Number of signing authors

*Cd* = Number of documents

#### Co-authored Documents Rate

The numeric value indicates the proportion of articles with multiple authors.

The mathematical formulation is:

Where:

*Cta* = Amount of documents with multiple authorship

*Ctd* = Amount of documents

It's interpreted that values close to 1 show more documents in co-authorship.

#### Degree of collaboration (Subramanyan Index)

The numeric value indicates the proportion of articles with multiple authors.

The mathematical formulation is:

*GC* =

*N*_{m}
/
*N*_{m} + N_{s}

Where:

*N*_{m} = Total of documents with multiple authorship.

*N*_{s} = Total documents written by a single author.

Is interpreted as values close to 0 show a strong component of single authorship, while than close to 1 denote a high proportion of multiple authorship.

#### Elitism Model (Price)

Identifies the number of authors who make up the elite of the most productive per journal or country of publication of the journal.

The numerical value represents the number of authors that make up such elite.

The mathematical formulation is:

*E* =
√*N*

Where:

*E* = Elite authors who publish 50% of works.

*N* = Total population of authors.

#### Collaboration Index (Lawani Index)

Provides the average weight of the number of authors per article.

The numerical value represents the average number of authors per article.

In addition to displaying the frequency of the number of authors per article.

The mathematical formulation is:

*IC* =

N
∑
*i*=1
*j*_{i} n_{j}
/
*N*

Where:

*N* = Amount documents

*j*_{i} = Number of signatures (authors) per documents.

*n*_{i} = Number of documents with multiple authorship.

#### Documents Density Index (Zakutina and Priyenikova)

Index that identifies the titles with higher density of information.

The numerical value gives the number of articles per journal.

The mathematical formulation is:

Where:

*Rn* = ∑ Articles.

*N* = ∑ Journal titles.

#### Concentration index (Pratt Index)

Indicates the degree of thematic concentration of journals.

The numerical value represents the level of thematic concentration based on their descriptors.

Shows the frequency of descriptors.

The mathematical formulation is:

Where:

*C* = Pratt Concentration Index.

*n* = Number of categories

*q* = ∑ of the product of the frequency range of a given category, divided by the number of items in all categories.

It's interpreted that values close to 1 show more amount of specialization.

**Bradford Mathematical Model**

Distribution of articles per journal

Mathematical model that identifies the core of journals with more information by subject.

Three zones are identified according to the amount of articles per journal in the discipline:

The core area, the 2nd and 3rd, the titles and the number of articles they have published.

It shows the frequency of articles per journal in the discipline.

The mathematical formulation is:

*p*:*p*_{1}:*p*_{2}:1:*n*_{1}:*n*_{2}

Where:

*p* = Number of titles per zone.

*n* = Multiplier or factor of proportionality of titles per area.

**Bradford Mathematical Model**

Distribution of articles per institutions.

Mathematical model that identifies the core of institutions with more amount of information by topic.

Three zones are identified according to the number of articles per institution in the discipline:

The core area, the 2nd and 3rd, the institutions and the number of articles they have published.

It shows the frequency of articles per institution in the discipline.

The mathematical formulation is:

*p*:*p*_{1}:*p*_{2}:1:*n*_{1}:*n*_{2}

Where:

*p* = Number of institutions by area.

*n* = Multiplier or proportionality factor of institutions per area.

#### Exogenous Authorship Rate

Indicator that measures the degree of internationalization of journals, considering the proportion of authors whose institutional affiliation is from a nationality other than that of the journal. Provides the exogenous productivity rate per journal and the frequency of nationality of their authors.

The numerical value indicates the proportion of foreign authors who have published in the journal.

The mathematical formulation is:

Where:

TAE = Exogenous Authorship Rate

ae = Foreign authors

d = Total documents