1. Basic concept

Centrality is a property of a node’s position in a network (node-level). It can be viewed as:

1. the structural importance of a node.
2. the advantage that accrues to a node by virtue of its position in the network.

Sociologically, centrality can be interpreted in a wide variety of ways → these interpretations are not definitions or inherent properties of centrality, but rather hypotheses about the potential consequences of centrality.

Because there are many different ways in which a node can be viewed as an important node, we have a bunch of different centrality measures.

2. Degree centrality

Important nodes have many connections.

在undirected network中，for node v，

$$ C_{degee}(v) = d_v $$

• 常使用「节点数-1」进行标准化

• [R] xDegreeCentrality()

• [UCINET] degree(xxx)或degree(xxx norm)

  

• 如果是directed network:

  • in-degree centrality (column sums) - 通常更有用

  • out-degree centrality (row sums) - 通过更多主观bias

  • 可以做「indegree vs. outdegree」图

    

3. Eigenvector centrality

Important nodes connect to many nodes that connect to many other important nodes.

在undirected network中，for node v，

$$ C_{eigen}(v) = \frac{1}{\lambda}\sum_{u \in \text{alters of v}} C_{eigen}(u) $$

• 本质是求adjacency matrix的特征向量(eigenvector)
  • 习惯上，使用最大特征值所对应的特征向量，并可将特征向量的模标准化为1。