If I were in your place, I would start by scraping LinkedIn using Python or Golang and creating a large database, keeping relevant information and keywords for each user. Then I would come up with some sort of clever algorithm to sort the data into some kind of sparse graph with takes into account the distance between the nodes (i.e. how close each of the user is to one another) and then use a search algorithm to search for a specific user and or a number of closely related users.