1. Overview

An ego network consists of:

• nodes:
  • a focal node - ego
  • ego’s contacts - alters
• ties:
  • ties between ego and alters - ego<>alter
  • ties among alters - alter<>alter

Key characteristics:

• Network size: the number of alters (i.e. degree centrality)

• Density: ties among alters

• Tie composition: types of ties ego has

  

• Alter composition: who are the alters?

  • Categorical alter attributes
  • Continuous alter attributes

2. Categorical alter attributes

2.1 Simple composition

一些经典的categorical attributes: gender, ethnic background, neighborhood…

如何表示简单的alter构成？用频数分布(frequencies)或频率分布(proportions)即可。

2.2 Heterogeneity of alters

第一种，Blau/Herfindhal/Hirschman index：最小为0，最大为1-1/K（其中K=#types；越大表示异质性越强）

$$ H = 1-\sum_k p_k^2 $$

第二种，Agresti’s IQV：最小为0，最大为1（是对H index的标准化）

$$ IQV = \frac{H}{1-\frac{1}{K}} $$

2.3 Ego-alter similarity