MATRIX DIAGRAM OF IMAGE AND IDENTITY RELATIONS IN COLLECTIONS OF JOURNAL PAPERS

Paper to reference relations.

The figure below shows a paper-reference matrix, its co-citation matrix below it, and its bibliographic coupling matrix to the right. See the text below the figure for explanation.

The paper-reference matrix:

In the paper-reference matrix, reference papers correspond to rows, columns to references
An element i, j is one if paper i cites reference j, zero otherwise
The co-citation matrix is obtained by premultiplying the paper-reference matrix by its transpose
An element i,j of the co-citation matrix contains the number of papers that cite both reference i and reference j
An element i,i on the diagonal of the co-citation matrix contains the number of papers citing reference i
The bibliographic coupling matrix is obtained by multiplying the post multiplying the paper-reference matrix by its transpose
An element i,j of the bibliographic coupling matrix contains the number of references cited by both paper i and paper j
An element i,i of the bibliographic coupling matrix contains the number of references cited by paper i

Relations:

The list of references cited by paper i is the reference identity of paper i, and corresponds to a row in the paper-reference matrix (example in blue on the figure)
The list of references cited with reference j is the reference image of reference j, and corresponds to a column (or row) on the co-citation matrix (example in yellow on the figure)
The list of papers with which paper i has co-occuring references is the paper identity of paper i, and corresponds to a row (or column) on the bibliographic coupling matrix. (example shown in blue on the figure)
The list of papers that cite reference j is the paper image of reference j, and corresponds to column on the paper-reference matrix (example shown in yellow on the figure)

Distributions:

The papers per reference distribution can be found from a histogram of the values on the diagonal of the co-citation matrix. This is a power-law distribution (see Naranan, 1971)
The references per paper distribution can be found from a histogram of the values on the diagonal of the bibliographic coupling matrix. This is a log-normal distribution.
The co-citation distribution can be found from a histogram of the values in the upper (or lower) triangle of the co-citation matrix.
The bibliographic coupling distribution can be found from a histogram of the values in the upper (or lower) triangle of the bibliographic coupling matrix.