[Paper Review] A conservation rule for constructing bibliometric network matrices

Gangan Prathap, Somenath Mukherjee|arXiv (Cornell University)|Nov 25, 2016

Complex Network Analysis Techniques13 references3 citations

TL;DR

This paper proposes a conservation rule for constructing bibliometric network matrices using fractional counting to preserve citation counts across aggregation levels (e.g., paper, author, country). By ensuring that total citation counts remain conserved when aggregating data, the method maintains accuracy and consistency in social network analysis of scholarly networks.

ABSTRACT

The social network analysis of bibliometric data needs matrices to be recast in a network framework. In this paper we argue that a simple conservation rule requires that this should be done only using fractional counting so that conservation at the paper level will be faithfully reproduced at higher levels ofaggregation (i.e. author, institute, country, journal etc.) of the complex network.

Motivation & Objective

• To address inconsistencies in bibliometric network analysis caused by integer counting methods that distort citation counts during aggregation.
• To ensure that citation counts at the paper level are preserved when aggregated to higher levels such as authors, institutions, or countries.
• To establish a principled method for constructing bibliometric matrices that maintain conservation of citation values across network levels.
• To improve the reliability and validity of social network analysis in digital libraries and scholarly communication research.
• To provide a theoretical foundation for consistent matrix construction in bibliometric networks using fractional counting.

Proposed method

• Proposes a conservation rule requiring that citation counts be distributed fractionally across co-authors, institutions, or countries rather than assigned entirely to one entity.
• Applies fractional counting to ensure that the sum of citation contributions across all entities equals the original citation count of a paper.
• Constructs bibliometric matrices using these fractional counts to represent relationships in scholarly networks.
• Ensures that when aggregating citation data from papers to authors, institutions, or countries, the total citation value remains conserved.
• Uses a formal framework to demonstrate that fractional counting preserves conservation at all levels of aggregation.
• Validates the method through theoretical analysis and illustrative examples in the paper’s tables and discussion.

Experimental results

Research questions

• RQ1 How can bibliometric network matrices be constructed to preserve citation counts across different levels of aggregation?
• RQ2 What are the limitations of integer counting in bibliometric network construction, and how do they affect network analysis?
• RQ3 Can a conservation rule be formulated to ensure that citation counts remain consistent when aggregating from papers to authors or countries?
• RQ4 What is the impact of fractional counting on the accuracy and reliability of social network analysis in digital libraries?
• RQ5 How does the proposed conservation rule improve the fidelity of bibliometric networks compared to traditional integer-based methods?

Key findings

• Fractional counting ensures that the total citation count of a paper is conserved when aggregated to higher levels such as authors, institutions, or countries.
• The conservation rule prevents overcounting or undercounting of citations during aggregation, which commonly occurs with integer counting methods.
• The method maintains consistency and accuracy in bibliometric network matrices across all levels of analysis.
• Theoretical analysis confirms that the conservation rule is mathematically sound and applicable to various network aggregation scenarios.
• The approach provides a principled alternative to conventional matrix construction in bibliometric networks, improving reliability.
• The paper demonstrates through examples that fractional counting avoids distortion in network metrics such as centrality and density.