A Weighted and Normalized Gould-Fernandez brokerage measure

TL;DR

This paper introduces the Weighted-Normalized Gould-Fernandez (WNGF) measure, an extension of the brokerage measure that accounts for weighted edges, providing more nuanced and assumption-free analysis of brokerage roles in complex networks.

Contribution

It extends the Gould-Fernandez brokerage measure to weighted networks, demonstrating its validity and advantages over dichotomized approaches through empirical applications.

Findings

WNGF produces valid, consistent results with dichotomized networks

It retains information without the need for thresholding or backbone extraction

It offers nuanced insights into brokerage roles, especially for less connected nodes

Abstract

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 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.