Edit: For clarification, I want to represent a friend list in a graph as shown in the image and want to know if that's possible when the number of friends is large. I ask for the name of this kind of graph so that I can do a more specific google search. I'm also curious about which graph suits best if the above is not possible.
It is simply called a graph
In graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".
Typically, a graph is depicted in diagrammatic form as a set of dots for the vertices, joined by lines or curves for the edges.
More specifically you are looking for a social network graph https://en.wikipedia.org/wiki/Social_network
You could call this type of infographic a network.
There is no way to get around the fact that it will quickly become busy and dense with a lot of friends, you would have to use another visualisation tool.
Ask your boss what they wanted to gain from this visualisation, and also ask them more generally why they feel they need one in the first place.
See if any other infographic would suffice.
You can use a process called Clustering. Here is an example used on Google Maps
Basically elements are clustered depending on the current zoom level. When user zooms on a specific cluster, that same cluster gets divided in other lower level group.
Now, this only makes sense if A's friends can be grouped on categories like: location, age, gender, hobbies, etc... which I don't know if they are.
We ended up with a solution like this.
Even in this way, we can place only a limited number of items on the circle. But since only part of the circle is visible on the screen, we can replace the data when they are about to be visible if necessary.
For example, we have 100 items, and we place 20 of them on a circle, and only 5 of them are visible on the screen. At first we have items [1...20] on the circle and items [1...5] are visible. After we rotate 90deg, items [6...10] are visible. If we rotate 180deg again, items [16...20] are visible. Now we must replace items [1...15] to items [21...35] so that when we continue rotating we can see the right data.
And what's the name of this kind of graph?
These types of charts are caller RADAR CHARTS
Say I want to show all of A's friends in the following form.But what to do when there're a lot of friends of A?
THe only possible way is to do grouping or categorizing and you can either use a badge or follow the above example.
If you need any help regarding implementation you can look into