Calculation of importance of the user or "Centering internecine" from follower users?

Question

I want to know how I can find interesting relationships between user accounts, such as the most related or most valuable users, based on their connections with others.

Below I use two tables. One has all the users, the other has the keys of the users that they follow.

User { id, name } Follows { user_id -> user.id, following_id -> user.id } 

What types of algorithms am I looking for?

Assuming that unimportant people have few or no followers, how can I find people in the center of the graph? I would suggest that they will be important because they have important people who follow them.

Update

As David and Steve point out, how close are the given nodes, which nodes form the child communities, and which users are the most connected, are examples of useful data that can be extracted from this scheme.

Since this "consistent" design is used by many sites now, I began to be generous in the hope of getting some reliable SQL versions or programming languages ​​that could be useful to a wide variety of people.

It is worth noting that although the results of some algorithms are fascinating, others (for example, finding related nodes) will cost users of our sites, as we can recommend something to them.

Answer 1

If you focus only on links, try these popular measures of centrality (suppose G is a graph):

• Degree . The degree of node i is defined as ki / (N-1), where ki is the number of links to node i, and N is the total number of nodes. Higher degree means importance.
• Proximity : The proximity of node i is defined as (N-1) / (Σ_ (j∈G) dij), where dij is the distance between node i and node j. This emphasizes at a distance node all the other nodes in the social network.
• Meanwhile : Meanwhile, it is defined as (Σ_ (j <k∈G) njk (i) / njk) / ((N-1) (N-2)), where njk denotes the number of shortest paths between nodes j and k, and njk (i) is the number of these paths passing through node i. Meanwhile, node i above means node i can be a good center that there are many links between any other two nodes that should go through node i.

The above measures can only be easily calculated using the link information, and you can use one or combine more of these centrality measures to find out important nodes in the social network. In any case, according to the definition of “important,” you may need various other measures.