Closeness Centrality

Closeness centrality is a measure of how close a node is to all other nodes in the network. It is defined as the reciprocal of the sum of the shortest path distances between a node and all other nodes in the network. Mathematically, the closeness centrality of a node v can be expressed as:

$$Closeness(v)=\frac{1}{\sum_{ \substack {u \in V}}d(u,v)}$$

where d(v, ) is the shortest path distance between node u and node u.

Closeness Centrality is used to measure the degree of distance between a user and other users in the social network, that is, the degree of closeness in the social network. Nodes with high Closeness Centrality are usually the "central figures" in the social network, as they are closer to other users, making it easier to contact other users in the social network and to transmit information and influence more quickly.

In Bond social network analysis, Closeness Centrality can help us identify key nodes and key paths in the social network, in order to better understand the flow of information and the transmission of influence. By analysing Closeness Centrality, we can optimise the structure and layout of the social network, and improve the efficiency of information transmission and the overall effectiveness of the social network. Additionally, Closeness Centrality can be used to evaluate the overall connectivity and stability of the social network, further improving the security and reliability of the social network.