Before the major research question, “Are male and female director networks similar or different?”, could be answered, a series of questions relating to gendered director network structures required answers. To empirically test Glass Network theory, a set of research questions is outlined. The structure of this thesis follows the sequence of these questions.
3.4.1 Network description and component analysis
3.4.1.1 What does a gendered director network look like? Where are the women directors in the mixed gender and women-only networks?
3.4.1.2 How many components does a network break into and what is the size of the largest component? Do the unconnected components ranked by size follow a specific distribution, assuming the data is not normally distributed?
3.4.1.3 Where are the women directors in the network components? Are they in the largest connected component or in the unconnected components?
3.4.1.4 In the largest connected component of the mixed gender director networks, who are the connector directors, that is, directors with more than one seat, and what is their gender? Does the spread of seats held by connector directors to single seat directors follow a specific pattern? Do they conform to the expected seat spreads derived from the non-symmetrical generating function?
132 3.4.1.5 Are female directors with more than one seat, namely connector directors, being appointed to more boards than their equivalent male connector directors in the largest connected components of the mixed gender networks?
3.4.2 Social network analysis of the largest component
What is the social network structure of the largest component of the mixed gender and female-only director networks in terms of the density, reach, clustering coefficient, degree, geodesic distance and subsidiary measures derived from these calculations? How do they differ from each other?
3.4.3 Small-world networks
Are mixed gender and women-only director networks small-world networks at a global and national level?
3.4.4 Assortative mixing
Do mixed gender and women-only director networks show positive assortative mixing? 3.4.5 Degree and betweenness
3.4.5.1 Does the distribution of the degree, or number of links between a director and adjacent directors, in the largest component of the mixed gender and women-only networks follow a specific pattern?
3.4.5.2 On the Freeman betweenness measure, or the number of times a director is found on a geodesic path between two other directors, what percentage of male and female directors in the mixed gender and women-only networks have a betweenness score of greater than zero. Are these in a specific proportion to male and female directors respectively who have a zero betweenness score?
3.4.5.3 Does the distribution of betweenness scores in the largest component of the mixed gender networks follow a specific pattern, namely a power law?
133 3.4.6 Testing Glass Network theory against longitudinal and random networks
3.4.6.1 What is the rate of director churn or turnover from 2004 to 2007 in the Fortune Global 200 directors; and the 2004 and 2007 NZX directors’ networks? What is the rate of director churn for male and female directors in these networks?
3.4 6.2 What does the gendered continuing director network look like? Where are the women continuing directors?
3.4.6.3 How many components does the continuing directors’ network break into and what is the size of the largest component? Does the size of the unconnected components follow a specific distribution assuming the data is not normally distributed?
3.4.6.4 Where are the women continuing directors in the network components of the mixed gender networks? Are they in the largest connected component or in the unconnected components?
3.4.6.5 In the largest connected component of the mixed gender continuing director networks, who are the continuing connector directors, that is, directors with more than one seat, and what is their gender? Does the spread of seats held by continuing connector directors to single seat continuing directors follow a specific pattern, namely a power law?
3.4.6.6 Are female continuing directors with more than one seat, (namely connector continuing directors), being appointed to more boards than their equivalent male continuing connector directors in the largest connected components of the mixed gender networks?
3.4.6.7 Do the continuing directors' networks differ from the networks of all directors from 2004 to 2007 in terms of the density, reach, clustering coefficient, degree, geodesic distance and subsidiary measures derived from these calculations?
3.4.6.8 Do mixed gender continuing director networks show positive assortative mixing?
134 3.4.6.9 Does the distribution of the degree or number of links between a director and adjacent directors, in the largest component of the mixed gender continuing director networks follow a specific pattern? Is there a significant difference in the degree scores of continuing directors who are present in the network at 2004 and 2007 as well as those present only once?
3.4.6.10 On the Freeman betweenness measure, or the number of times a director is found on a geodesic path between two other directors, what percentage of male and female continuing directors in the mixed gender networks have a betweenness score of greater than zero. Are these in a specific proportion to male and female continuing directors respectively who have a zero betweenness score?
3.4.6.11 Does the distribution of betweenness scores in the largest component of the mixed gender continuing director networks follow a specific pattern? Is there a significant difference in the betweenness scores of continuing directors who are present in the network at 2004 and 2007 as well as those present only once?
Chapter Three Summary
Glass Network theory is introduced with a précis using Carlile and Christiansen’s (2005) typology of theory building. Firstly, the known constructs from previous director research are stated and the areas requiring further observation are outlined. Secondly, the proposed classification by attributes such as time, gender, location, or random assignment, is also outlined. The third stage of descriptive theory building then explains the observed correlations as a function of underlying power laws and briefly describes a generating function to allow a comparison between actual and expected seat spreads.
The structure of Glass Networks is outlined in more detail and foundation concepts discussed. These include the forces of preferential attachment, homophily, and assortativity. Director networks are stable and resistant to change. The overall ratio of male to female directors is maintained as a relatively constant ratio over time. This is the manifestation of an inbuilt and limited amount of diversity that permits adaptations should network survival require change.
135 Seat spreads, or the distribution of multiple directorships, and the ratio of connector directors to single directors is discussed. A theoretical model deriving expected seat spreads from a non-symmetrical generating function is described in detail. Historical research is reviewed and reworked with the comparative methodology developed to compare networks over time and location.
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