A Weighted and Normalized Gould-Fernandez brokerage measure

Area of Science:

• Network Science
• Social Network Analysis
• Graph Theory

Background:

• Existing brokerage measures, like the Gould and Fernandez method, define roles based on node group membership and edge connections.
• These traditional methods often simplify networks by dichotomizing edges, potentially losing valuable information contained in edge weights.

Purpose of the Study:

• To extend the Gould and Fernandez brokerage measure to incorporate weighted edges, introducing the Weighted-Normalized Gould-Fernandez (WNGF) measure.
• To demonstrate the empirical value and advantages of the WNGF measure in analyzing both macro-level trade networks and micro-level organizational networks.
• To offer a method for analyzing brokerage in weighted, directed, and complete graphs without information loss.

Main Methods:

• The study introduces the Weighted-Normalized Gould-Fernandez (WNGF) measure, an extension of existing brokerage analysis techniques.
• The WNGF measure was applied to two distinct datasets: the EUREGIO inter-regional trade network and an organizational network within a research and development (R&D) group.
• Results from the WNGF measure were compared against analyses performed on dichotomized versions of the same networks (threshold and multiscale backbone networks).

Main Results:

• The WNGF measure produced valid results that were consistent with those obtained from dichotomized networks.
• The WNGF measure ensures greater information retention compared to dichotomization methods.
• The WNGF measure eliminates the need for subjective decisions regarding network dichotomization, reducing user-imposed assumptions.
• It offers a more nuanced understanding of individual node brokerage roles, particularly for less connected nodes.

Conclusions:

• The WNGF measure is a valuable methodological contribution to network analysis, enabling the study of brokerage in weighted networks without information loss.
• Its advantages, including information retention and reduced assumptions, make it particularly useful for analyzing complex networks where edge weights signify important interactions.
• The WNGF measure has broad applicability across various disciplines and network types, including regional studies, organizational analysis, and social interaction networks.