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A Weighted and Normalized Gould–Fernandez brokerage measure


Zhen Zhu

Sara Gorgoni


The Gould and Fernandez local brokerage measure defines brokering roles based on the group membership of the nodes from the incoming and outgoing edges. This paper extends on this brokerage measure to account for weighted edges and introduces the Weighted–Normalized Gould–Fernandez measure (WNGF). The value added of this new measure is demonstrated empirically with both a macro level trade network and a micro level organization network. The measure is first applied to the EUREGIO inter-regional trade dataset and then to an organizational network in a research and development (R&D) group. The results gained from the WNGF measure are compared to those from two dichotomized networks: a threshold and a multiscale backbone network. The results show that the WNGF generates valid results, consistent with those of the dichotomized network. In addition, it provides the following advantages: (i) it ensures information retention; (ii) since no alterations and decisions have to be made on how to dichotomize the network, the WNGF frees the user from the burden of making assumptions; (iii) it provides a nuanced understanding of each node’s brokerage role. These advantages are of special importance when the role of less connected nodes is considered. The two empirical networks used here are for illustrative purposes. Possible applications of WNGF span beyond regional and organizational studies, and into all those contexts where retaining weights is important, for example by accounting for persisting or repeating edges compared to one-time interactions. WNGF can also be used to further analyze networks that measure how often people meet, talk, text, like, or retweet. WNGF makes a relevant methodological contribution as it offers a way to analyze brokerage in weighted, directed, and even complete graphs without information loss that can be used across disciplines and different type of networks.


Zádor, Z., Zhu, Z., Smith, M., & Gorgoni, S. (2022). A Weighted and Normalized Gould–Fernandez brokerage measure. PLOS ONE, 17(9), Article e0274475.

Journal Article Type Article
Acceptance Date Aug 30, 2022
Online Publication Date Sep 15, 2022
Publication Date 2022
Deposit Date Sep 16, 2022
Publicly Available Date Sep 16, 2022
Journal PLOS ONE
Print ISSN 1932-6203
Publisher Public Library of Science
Peer Reviewed Peer Reviewed
Volume 17
Issue 9
Article Number e0274475
Public URL


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