1. Local node-level soical capital

Burt’s 1992 theory of structural holes: In an ego network, the lack of ties among contacts are called structural holes.

2. Advantages of structural holes

Autonomy: do/say what you want to do/say - 其他人无法得知别人发生的事情

Control: divide and conquer - 分而治之、各个击破（alters无法形成合力）

Information: be a information broker - 信息中转站、灵活利用各种信息

Managerial skill: …

3. Measures of structural holeness

3.1 Effective size

其中i是ego，j是alters：

$$ \begin{equation*} \begin{aligned} ES_i &= \sum_j \bigg[ 1-\sum_k p_{ik}m_{jk} \bigg],\quad k \ne i,j\\ &= N-\sum_j \sum_k p_{ik}m_{jk} \\ \end{aligned} \end{equation*} $$

• $p_{ik}$
  • 含义：proportion of i’s energy invested in relation with k
  • 实现：row-stochastic adjacency matrix
• $m_{jk}$
  • 含义：j’s interaction with q divided by j’s strongest relation with anyone
  • 实现：row-max-normalized adjacency matrix

For binary data:

$$ E = N-\bar{d} $$

• $N$：#alters
• $\bar{d}$：avg degree of the alters (not including ties to ego)

3.2 Constraint