We measure all individual creators’ positions on a core/periphery continuum using Borgatti and Everett’s [11] algorithm. Following the approach in previous work on movie collaboration networks of Cattani and Ferriani [4] and on individual innovation by Dahlander and Frederiksen [19], we estimate each node’s degree of coreness by the continuous measure of core/periphery. Accordingly, our Coreness indicator refers to the degree of closeness to a densely connected network core for each movie creator. We apply the described procedure to all network matrices of years 1990–2009. For the sake of straightforward interpretation we standardized Coreness into z-scores.
To quantify Brokerage, we use the betweenness-based measure recently suggested by Everett and Valente [35]. We opt to apply this indicator in the main analysis as it defines brokerage by considering how individuals connect otherwise loosely connected parts of the entire network, not only those in their immediate neighbourhood. Brokerage is computed in two steps. First, we calculate the edge betweenness centrality measure for every tie in the network. Second, for each node we assign a Brokerage score that is the average of the edge centralities which are incident to it. The indicator takes high value if the focal actor has ties that are part of many shortest paths in the whole network. For the sake of variable comparison, we standardized Brokerage into a z-score. As a robustness check, we repeat the exercise with Brokerage defined by Burt’s network constraint indicator [27] (see S4 Table).
For a more detailed understanding on how core/periphery position and brokerage jointly influence actors’ individual success, we created dummy variables from the Coreness and Brokerage indices in a similar fashion to Cattani and Ferriani [4]. The dummy variable is called Core that takes the value 1 in case the continuous Coreness value of the individual is in the top ten percentile of the measure’s scale (above 0.90) and zero otherwise. The Broker dummy which takes the value of 1 in the case of Brokerage is in the top ten percentile of the measure’s scale (above 0.90). These binary variables enable more precise estimation of interaction effects in regression frameworks than continuous variables. Fig 3 presents the number of Core and Broker creators along the examined period. Based on the applied dummy variables, the number of Core and Broker movie creators are nearly identical in every year.
The numbers of movie creators are based on 7-year moving-windows. The numbers of core and broker creators are based on the Core and Broker dummy variables.
As edge betweenness based measure of Brokerage does not, of itself, help the identification of brokers between core and periphery at the global network scale, we also develop a new measure to further look at bridging positions between core and periphery in the ego network of creators. Therefore, we also introduce a new measure that we call Gatekeeping. The indicator refers to the extent to which the focal nodes’ ties are the only connections between core and peripheral nodes in its ego network. Eq (1) summarises the construction of the Gatekeeping measure.
, where Lcp refers to the observed number of links between core and peripheral actors in the ego network of i, without the focal actor. In the denominator, ‖vc‖ refers to the number of core individuals in the ego network of creator i and ‖vp‖ is the number of peripheral nodes in the ego network of creator i. The indicator is the inverse of the observed ties between core and peripheral actors compared to the number of possible ties between the two types of neighbours. Fig 4 illustrates two hypothetical cases. In case of Fig 4(A), the focal nodes’ gatekeeping indicator has a relatively high value (Gatekeeping = 0.9) as there are both core and peripheral nodes in its’ ego network, but the focal node is the only connection between them. In case of Fig 4(B), the focal nodes’ gatekeeping indicator has a lower value (Gatekeeping = 0.7) as some of the peripheral neighbours are directly connected to core neighbours of the ego. In case of Fig 4(B), one can expect less benefit from connecting the core with periphery than in the case of Fig 4(A) because core neighbours can enjoy additional advantages residing at peripheral collaborators through their direct connections.
Illustration of high (A) and low (B) Gatekeeping indicators. G–stands for Gatekeeper creator, C–stands for Core creator and P–stands for Peripheral creator. (A) represents a possible situation in which the focal node acts more like a Gatekeeper (Gatekeeping = 0.9), while in case of (B) the focal node is less of a Gatekeeper (Gatekeeping = 0.7).
The Gatekeeper indicator identifies those movie creators who connect the core and periphery in their ego networks. This is a dummy variable that takes value 1 in case the value of Gatekeeping indicator is in the top ten percentile of the measure’s scale (above 0.90) and 0 otherwise. This binary variable enables us to test interaction effects in a precise way, which is a key step in our analytical strategy.
Additionally, we use several further variables as controls. Because of the applied 7-year moving-windows to create more stable and connected creator networks, we control for the number of Films Per Window on which the given network structure is based on. Moreover, we use the variable Creators Per Window in order to control for the number of active movie creators in the 7-year period or the number of nodes in the network in the given year.
Professionals new to the industry might receive disproportional attention from award voters, who may prefer new talents to veteran creators [4]. To account for this effect, a Newcomer dummy variable was created for each movie creator in every year which takes 1 if a professional is a new participant of movie production and 0 otherwise. Length of careers can also determine the bankability of movie creators [39]. Therefore, we create the Experience variable to provide a control for the years spent in the industry since the creators’ first movie. Since success breeds success, individual creators are more attractive for colleagues if they have worked with prestigious collaborators or they have already won an award [40, 41]. Therefore, we construct the variable Previous award that provides a control for the number of awards the creator has won before.
Finally, we applied year fixed effects and individual role fixed effects as well, which refer to the main roles of the creators in the period being classified as cinematographer, director, editor, producer or writer categories. Detailed descriptive statistics of our variables, their correlation matrix and distribution of the Gatekeeping index can be found in the supplementary information (S1 Table, S1 Fig and S2 Fig). While Coreness is neither correlated to Brokerage nor to Gatekeeping, Brokerage and Gatekeeping are correlated. Therefore, we do not focus on the influence of Gatekeeping alone, but rather its combined effect with Coreness and Brokerage.
The combination of Brokerage and Gatekeeping is rather necessary because none of these indices can capture the role and benefits of brokers in core/periphery networks on their own. On the one hand, Brokerage in itself is unable to quantify bridging between core and periphery. The indicator cannot distinguish whether core creators link core with periphery or bridge two or more loosely connected core groups. On the other hand, Gatekeeping is myopic by definition and only considers bridging inside the ego network of creators and does not consider the nodes’ position in the global network. Two core creators with identical Gatekeeping values can have different access to novel ideas from the periphery indirectly through their connections. This limitation of the Gatekeeping indicator is illustrated in S3 Fig. In case a node has high value of Brokerage and high value of Gatekeeping, it means that its ties are the only connections between core and periphery in the ego network, while they are also important shortest paths to bridge different parts of the global network.
Do you have any questions about this protocol?
Post your question to gather feedback from the community. We will also invite the authors of this article to respond.