Imagine that there are more than a dozen classes in a grade, and all the classmates and teachers of all classes communicate with each other through social software.
In such a network, how do you identify who are socialites and who are influencers?
This involves the concept of centrality. This article introduces four types of centrality. Degree Centrality, Closeness Centrality, Betweenness Centrality and Eigenvector Centrality.
Network settings
In the problem envisaged in this paper, if there is a chat message between two people, it is considered that there is a connection between the two, so an undirected graph can be constructed. For the sake of simplicity, the issue of weights is not considered for the time being.
Degree Centrality
Degree centrality is defined as the number of links connected to a node. In this question, the more people who are connected with a classmate or teacher, the higher the degree centrality of that person. Obviously, people with high degree centrality are the "socialite" characters we are looking for. In this picture, Jack is clearly such a courtesan. (I originally wanted to use names like Xiaoming, Xiaowang, and Xiaoli, but I found that it was very troublesome to add Chinese to Python drawings, so I changed to English names...)
Closeness Centrality
The definition of closeness centrality is, for this node, the mean of the lengths of all other nodes connected to this node to its shortest path. In our problem, if a person's closeness centrality is higher, it means that this person and the majority are closely related and more gregarious, and vice versa, they are more independent.
Betweenness Centrality
Betweenness centrality is defined as the number of times that a node acts as a bridge on the shortest path between two other nodes. In our problem, if a person's betweenness centrality is higher, it means that person often acts as the middleman for everyone. This intermediary is very important, and if this person transfers, it may be difficult to connect many people with each other. In this diagram, Mike is the intermediary of many people. Without him, it would have been difficult for many to connect.
Eigenvector Centrality
Eigenvector centrality measures the influence of a node in the network. Is it possible that there are some people who are not connected to many people, but each word carries weight and influence? In our problem, if there is a person in the WeChat group who is the dean, the dean may not communicate with many people, but the words of the dean are very influential. At this time, the eigenvector centrality can be used to capture at this point. Since the people who are connected to the dean are often very impressed in the network, the dean himself is a very influential figure in the network.