# Disentangling Director Attributes: Human Capital versus Social Capital of Directors
## 2 Literature Review and Human and Social Capital Determinants
### Social Capital  
Early studies of director and board social capital focused on the issue of interlocks; the direct connections formed by a director sitting on other companies' boards. More recently, studies have started to acknowledge that social capital and connectivity is multifaceted and that more encompassing measures are required. For instance, [PERSON] et al. (2018) explore social connectedness between countries based on Facebook links, just one of a number of studies exploring social media links. In this study we use another method that has only recently been employed for studying board connectivity, social network analysis ([PERSON] and [PERSON] 1994). SNA has the advantage of incorporating prior literature that focuses only on the direct connections between boards based on the number of boards a director sat on (the SNA component degree is equivalent to the definition of interlocks) as well as taking a wider view of connectivity. Specifically, SNA goes beyond the direct connections to consider factors such as the quality of a director's connections (being linked to more connected directors brings access to greater resources). SNA is therefore a more suitable proxy of social capital than the simple multiple directorship measure. SNA is particularly suitable for use in studying director connectivity as it focuses on the connections that will bring the most value to the firm, connections to other directors who possess relevant skills and experiences. Applying SNA to board connectivity relies on constructing the director network for each year. The director network collects all the board positions that all the directors hold and uses that information to identify pathways between companies based on shared directors. Companies with more connections to other companies are placed more centrally in the network and therefore have more access to additional resources and information. From the director network we calculate four common social network measures that capture different aspects of connectivity: degree ([PERSON], 1974), closeness ([PERSON], 1966), betweenness ([PERSON], 1978), and eigenvector ([PERSON], 1972, 1987). The first measure, degree (denoted hereafter as \"\(DEG\)\"), is the number of direct connections of a director ([PERSON], 1978; [PERSON], 1974). \(DEG\) is measured as the number of unique direct connections between director \(i\) and all other directors: \(j\), i.e.,  
\[C_{it}^{D}=\sum_{j=1}^{n-1}\delta(i,j),\ \ \ j\
eq i, \tag{1}\]  
where \(\delta(i,j)\) is a dummy variable that equals one if directors \(i\) and \(j\) sit on one or more of the same boards, and zero otherwise. \(DEG\) measures the direct information shared between two directors that a board can access ([PERSON], 1978). A higher \(DEG\) score indicates a director with many direct connections to other directors, and hence more opportunities to exchange or acquire information. To take into account differences in network size from changes in the number of listed firms and board size, we normalize \(DEG\) by dividing \(C_{it}^{D}\) by \((n-1)\), where \(n\) is the number of directors in the network in the corresponding year ([PERSON] et al., 2007; [PERSON] et al., 2012). Normalizing the scores by \(n-1\) bounds \(DEG\) between 0 and 1, which can be interpreted as a director's proportion of the maximum direct connections possible within the network. This measure can be compared between years ([PERSON], 1978). The second measure employed is closeness (denoted hereafter as \"\(CLO\)\") ([PERSON], 1978; [PERSON], 1966). \(CLO\) measures the distance between a director and every other director they are connected to. In line with [PERSON] (1978), \(CLO\) is defined as the sum of the inverse of the shortest distance between director \(i\) and all other directors in the network:  
\[C_{it}^{C}=\sum_{j=1}^{n-1}d(i,j)^{-1},\ \ \ j\
eq i, \tag{2}\]  
where \(n\) is the total number of directors in the network and \(d(i,j)\) is the shortest distance between director \(i\) and director \(j\).