Distributing responsibility between multiple staff members is essential for innovations to succeed (Fullan, 2016), especially in the demanding and rapidly changing environments that organizations such as schools operate in. Formal leadership was considered as important for innovation for a long time (Ricard et al., 2017). However, solely studying leadership that belongs to a single individual loses currency (Ospina, 2017). When responsibilities of leadership are distributed, organizations benefit from the capacities of multiple members (Azorín et al., 2020). As a result, organizations will arrive at innovative solutions (Snoek et al., 2019) and develop a fuller appreciation of interdependence and support among their members (Azorín et al., 2020).
Distributed leadership is a well-known leadership theory in both the academic world and organizational practice. This theory assumes that multiple team members create organization-wide leadership practices by interaction (Liou & Daly, 2014). The broad scope of distributed leadership of taking into account both formal and informal leadership practices helps to fully understand leadership (e.g. Leithwood et al., 2020). Both private and public sector international literature underline the importance of distributed leadership (Ospina, 2017), including the educational sector where the distributed leadership theory is developed to study leadership of principals and teachers (Leithwood et al., 2020). Nevertheless, knowledge on how to define and measure distributed leadership, and make it tangible is limited (Daniëls et al., 2019; Tian et al., 2016).
We describe distributed leadership, as a social phenomenon and with three aspects that we identified from literature, namely collective, dynamic, and relational. We measure these aspects of distributed leadership by applying a social network perspective, since this perspective includes and analyzes all individual team members, considers several levels of leadership (D’Innocenzo et al., 2016), and since it focuses on the interactional and relational character of organizational processes, it also captures the collective, dynamic, and relational aspects. However, until now studies often investigate distributed leadership rather one-sided. We measure the three aspects of distributed leadership with social network measures (density, centrality, reciprocity) and interpret the combination of measures to dissect the multi-faceted concept of distributed leadership. By combining distributed leadership and social network perspective, we follow a growing number of scholars that call for contributing to ‘the lack of research into bringing to the fore front both emergent paradigms’ (Naumov et al., 2020, p. 9).
This study aims to describe and measure distributed leadership from a social network perspective, within the educational sector. We empirically verify whether distributed leadership can be measured by a combination of social network measures in school teams. These teams have all implemented the same collaborative innovation programme, aimed at enhancing collaboration between teachers and school principals. We address the following research question: How can we measure and describe distributed leadership in school teams by applying a social network perspective? 

Context of the study We studied distributed leadership within schools that all work with a collaborative innovation programme that is aimed at stimulating a learning culture and shared responsibilities between teachers and school principals. We expect this to be a context in which school teams distribute leadership. Measurement of Distributed leadership: Providing Advice Leadership is defined as influencing knowledge and skills of others and asking someone for advice causes a member to be influenced on his/her knowledge and skills by another member and the advice-provider performs a leadership role (Pitts and Spillane (2009). Therefore, in order to measure distributed leadership we adopted an advice seeking instrumental network question from previous social network studies in education (Liou & Daly, 2014): Who do you turn to for advice on working with the educational programme? Participants were asked to answer this advice question for each team member of their school team. Procedure of Data collection We surveyed a total of 148 school team members and received 130 responses (118 teachers and 12 school principals), reflecting an excellent response rate of 88%. Fourteen school teams were part of the study (three school teams were part of one large vocational education institution). Analyses We measured distributed leadership by a combination of social network measures: relatively high density, high reciprocity, low indegree centralization, and multiple key players (more than one team member). We compared the function (being a school principal, teacher or school coach) of the key players among the teams in order to explore which function performs the key player role most often. We consider our approach successful if the measures correlated as we would expect based on our definition and if the approach had the power to distinguish possible differences between school teams. Thus, we calculated the correlations and examined whether we can distinguish differences between school teams which were comparable on their scores based on face validity and discussions with all authors. In this way, we compared all school teams’ advice networks on the package of social network measures as a cross-case analysis, which enhances generalizability and deepens understanding and conclusions about how to dissect and describe distributed leadership. Lastly, we have created sociograms to further describe the results.

Findings Our findings indicate significant correlations between the three aspects of distributed leadership. Moreover, by utilizing our package of social network measures, we were able to cluster the school teams based on differences between their scores. Regarding key players, teachers most often perform this role (in 12 out of 14 teams). In 4 school teams they are the only key player, in the other teams they share their key player role with the school coach (in 5 teams) and school principal (in 3 teams). School coaches play a key player role often as well (11 out of 14 teams). School principals never perform this key player role independently but share the role with school coaches and teachers. Conclusion Our findings indicate that our social network package approach enables to identify which schools carry out distributed leadership and which schools do less or not at all. Furthermore, our established and hypothesized criteria are met, namely interdependence of the measures in the direction and the power to show significant differences between schools. Our paper forms a first promising step in how to describe and measure distributed leadership both conceptually and operational with a social network perspective and measures as a package. We encourage other researchers to expand our initial effort of making distributed leadership tangible in this way within other sectors and countries. This package of measures could also be practically applied to support teachers and school principals to reflect on leadership within their teams and as a result improve their collaborative approach to innovation. In sum, this paper demonstrates how to broadly study leadership from a social network perspective, in the educational sector and other public sectors, instead of merey focussing on transformational leadership of the formal leader, which has been the approach for decades (Daly et al., 2010).

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