Breadth and depth of citation distribution

• 4D framework for citation distribution analysis are proposed.
• Easily computable indices, X, Y, and XY, are proposed.
• The index X represents the breadth of citation distribution.
• The index Y represents the depth of citation distribution.
• The index XY synthetically represents indices X and Y.

This study proposes a new 4D (i.e., spatial, temporal, breadth, and depth) framework for citation distribution analysis. The importance and differences in the breadth and depth of citation distribution are analyzed. Easily computable indices, X, Y, and XY, are proposed, which provide estimates of the breadth and depth of citation distribution. A knowledge unit can be an article, author, institution, journal, or a set of something. Index X, which represents the breadth of citation distribution, is the number of different knowledge units that cite special knowledge units. Index Y, which represents the depth of citation distribution, is the maximum number of citations among several knowledge units that refer to specific knowledge units. Index XY, which synthetically represents Indices X and Y, the feature and focus impacts of a knowledge unit, is index X divided by index Y. We analyze empirically the citation and reference distributions of 84 journals from the “Information science and library science” category of the Journal Citation Reports (2012) at the journal-to-journal level. Indices X, Y, and XY reflect the actual breadth and depth of citation distribution. Differences exist among Indices X, Y, and XY. Differences also exist between these indices and other bibliometric indicators. These indices cannot be replaced by existing bibliometric indicators. Specifically, the absolute values of indices X and Y are good supplements to existing bibliometric indicators. However, index XY and the relative values of Indices X and Y represent new aspects of bibliometric indicators.