1. Overview

group = whole network

1.1 What are the group-level measures

• Calculate a single quantity to describe a whole network
  • Eg: how dense is the network (# of ties/# pairs)
  • Sometimes called a “graph invariant”
• Most of these measures are loosely related to the cohesion of the network
  • Many of these are simple aggregations of dyadic or node-level measures
    • Eg: average degree
  • UCINET命令：cohesion(camp92)
• There are also measures of shape

1.2 How to use group-level measures

• Difficult to interpret most measures in absolute terms | Easy to interpret comparatively
• More formally, use group-level measures in multivariate regression models。例如：
  1. Collect friendship network within 50 separate teams
  2. Also collect performance of each team, along with demographic information
  3. Regress performance on density, controlling for demographic composition
  4. Answer the question: Does friendship network density affect team performance?

2. Measures of cohesion

2.1 Density

$$ \text{density} = \frac{\text{\#ties}}{\text{\#pairs (i.e. potential ties)}} $$

更精确地说：

• The reflexives represent networks that allow a node point to itself.
• Density is also the probability that a randomly chosen pair of nodes (dyad) has a tie.
  • probability >>> 最小是0，最大是1。

2.2 Average degree

对于无向图：

$$ \text{avergae degree} = \frac{\text{2×\#ties}}{\text{\#nodes}} = \frac{T}{n/2} $$