What to use to formalize reasoning?

Question

Standardization

Good day
There is a task that I would like to formalize for a clear expression of my thoughts in the form of generally understandable or professional terms.
What would you advise on the example of the following description of the model:
There are many computers connected to each other in various ways (it is possible that in this graph there are full cliques, but there are also isolated PCs occasionally connected to some other PCs)
There is also a marker that can be entered on several computers and in if a connection is established between computers - this marker is distributed
I want to formalize (describe in mathematical or other language) the process of determining whether a certain computer has a marker under similar conditions.
There is also another analogy for the same model:
there is a graph of people, some of whom are given information that they share with their friends and not share with non-friends.
How to describe this model abstracting from examples?

Answer 1

Well, you already correctly said that this is a count. Apparently you are interested in connectivity components in a graph.

Answer 2

Your question seems reasonable, but for one thing: you don't know, that is, dfs?

Answer 3

This is clearly a graph. Take any modeling tool and screw it up for yourself, here even the principles of their modeling can be neglected for a simple message.
Only here your examples did not match a little. People do not consider their friends-friends to be their friends, but a marker can be passed to anyone at least, there would be a connection. In short, it depends on the connections between the nodes.