Importance-Weighted Density: A Shared Leadership Illustration of the Case for Moving Beyond Density and Decentralization in Particularistic Resource Networks

Abstract

Social network analysis has been increasingly used by researchers to operationalize team processes and emergent states. Despite their advantages over aggregate measures, the most frequently used network measures such as density and centrality are agnostic to potentially meaningful elements reflecting the patterns of ties between team members. Specifically, intangible resources transmitted within team networks are often more particularistic, such that the value of the shared resource is dependent upon who gives it. We use shared leadership as an exemplar case for explaining this issue and proposing a solution in the form of a new network measure, importance-weighted density (IWD). Combining logic from the principles of density, decentralization, and eigenvector centralization, IWD provides a more detailed understanding of network tie patterns by taking into account the degree to which ties emerge from members who are themselves well connected. We test the measure’s validity in a series of Monte Carlo simulations and laboratory and field studies. We find that IWD has high convergent, discriminant, and criterion validities and discuss how this statistic might help to enhance the study of several other team constructs. We provide access to a downloadable tool for the calculation of IWD and other network statistics discussed within this article.

The Emergence of Shared Leadership in Innovation Labs

“…Network properties at the team level can be indexed by density, indicating the extent of displayed shared leadership behaviors of a team (e.g., Carson et al, 2007 ), or by decentralization, reflecting the distribution of shared leadership (e.g., Small and Rentsch, 2010 ). Most recently, Lemoine et al (2020) observed that both network measures had been often used and interpreted interchangeably in shared leadership research, although they depict distinct network characteristics; thus, they are indicators of varying conceptions of the shared leadership construct ( Lemoine et al, 2020 ). As a potential remedy, the authors propose the alternative network index of IWD, which “takes into account the magnitude of a node’s incoming ties, the relative centrality of that node compared to others, as well as the relative influence and centrality of contacts from whom ties emerge” ( Lemoine et al, 2020 , p. 440).…”

“…Most recently, Lemoine et al (2020) observed that both network measures had been often used and interpreted interchangeably in shared leadership research, although they depict distinct network characteristics; thus, they are indicators of varying conceptions of the shared leadership construct ( Lemoine et al, 2020 ). As a potential remedy, the authors propose the alternative network index of IWD, which “takes into account the magnitude of a node’s incoming ties, the relative centrality of that node compared to others, as well as the relative influence and centrality of contacts from whom ties emerge” ( Lemoine et al, 2020 , p. 440). Informed by the rationales of density, decentralization, and eigenvector centralization, the IWD allows for a conceptualization of shared leadership that adequately reflects its theoretical nature.…”

“…Further, we evaluate the influence of shared leadership on a team’s creative output. We follow a social network approach and adopt an importance-weighted density (IWD) operationalization of shared leadership ( Lemoine et al, 2020 ). We identify factors specific to creative teamwork that facilitate the emergence of shared leadership by providing room for experimentation, encouraging team members to speak up in the creative process, and cultivating a reflective application of entrepreneurial thinking.…”

Tensions Between Diversity and Shared Leadership: The Role of Team Political Skill

“… 3. Because we use a 5-point scale to capture leadership network density in teams, the original possible values of leadership density start from 0.20 (all responses are “1”) instead of zero. However, as Lemoine, Koseoglu, Ghahremani, and Blum (2018) recommend, network measures should have a meaningful zero for researchers to better interpret the analysis results. Accordingly, we recode the density value by subtracting the minimum possible values (for instance, 1 on a 1-5 scale; Lemoine et al, 2018).…”

“…However, as Lemoine, Koseoglu, Ghahremani, and Blum (2018) recommend, network measures should have a meaningful zero for researchers to better interpret the analysis results. Accordingly, we recode the density value by subtracting the minimum possible values (for instance, 1 on a 1-5 scale; Lemoine et al, 2018). As a result, the minimum possible values for leadership density in our sample is zero.…”