# 2.13 Centrality

In the previous sections, we explained the global features of complex networks, such as the degree distribution and average shortest path length. However, it is also important to characterize local properties (i.e., the characteristics of each node in a complex network). For example, the clustering coefficient indicates the degree of clustering among the neighbors of a node, as explained in Section 2.6.1. In addition to the clustering coefficient, centrality is an important concept in network analysis because it helps in finding central (important) nodes in complex networks.

## 2.13.1 Definition

To date, several node centralities have been proposed, based on topological information. Well-used centralities are as follows.

### Degree Centrality

The degree centrality [48] is the simplest centrality measure. Assuming a correlation between the centrality (or importance) of node i and the degree of node i (k_{i}), the degree centrality of node i is defined as

(2.49)

where N is the network size (i.e., the total number of nodes). Since this centrality is essentially similar to the node degree, this is widely used in network analysis.

### Closeness Centrality

The closeness centrality [48] is based on the shortest path length between nodes i and j, d(i, j). When the average path length between a node and the other nodes is relatively short, the centrality of such a node may be high. On ...

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