There is truth to the old saying: "If you would read a manÂ’s Disposition, see him game; you will then learn more of him in one hour, than in seven years' conversation" - Richard Lindgard (1907)
So the question is what do you want from a social network? If you know that, if you can define that in terms of your personal value, you know the tasks you must do to attract such a network. This is the basis for your own answer.
Some people do not feel the need to have much of a social network. For them, a few strangers to meet occasionally for a drink and small chitchat is enough. Other people want only to surround themselves with people passionate about a specialized activity like a sport or a religion.
Another group of people might want to make a genuine connection with new people they can call friends; a social circle like the one they miss from home, that strengthened over years together. That is very hard to achieve in a new country where a person is the most vulnerable they will ever be. It is very hard to have those kinds of relationships when a posting might only be 3 years' time: a short time in which to make the connections one might miss from home but a long time to be lonely and homesick.
Only to live through it again with the next country and a new posting....
Because I am seeking people with whom to share a genuine connection, I decided to create my social circle through a game that would accelerate the time it takes to get acquainted with people, just like in the quote from Richard Lindgard above. Role-playing games put people into roles and throw them into imagined situations where they try to resolve an issue together as part of the game; a process that reveals the attitudes and values that shape a person's behaviour and thinking.
The best part about this is that it is all on neutral ground. You do not have to offer a secret to someone because you are not asking others for their secrets in exchange. You play and you observe. If you like what another person reveals of himself or herself, you can choose to spend more time with that person. If not, you can avoid them and meet new people as they join the group. (Antisocial people tend not to stay in the group.)
I have learned to stay away from certain topics, especially with strangers: sports, religion and politics. For me, that does not leave much to talk about except maybe the weather and business.
Role-playing games create a neutral forum for discussions and put everyone together on common ground from the start. Unlike games that are competitive in nature, prior playing experience is not necessary because it is a social activity created by everyone in the same room.
I am not saying role-playing games is right for everyone. That depends on what you are seeking from your network of friendship during your stay in a foreign country.