I think in this case why that person, whom I put in my network, will agree to such proposition without being allowed to choose or decline ?
What you suggest is probably “Fans” or “Followers” – I can be a fan of any Mr or Mrs X, for this I do not need consent.
Thus in a social network or in many social networks Friendship can have multiple levels
Friends – the usual buddypress way
Fans – no consent needed
Mutual friends – Common friends
Top friends – whom I choose as top will appear topmost in the friend list always
“Network” in Social nets probably mean what Facebook used to have, several groups having at least one common element belong to a network. For example, groups on ice cream, chocolate, candy, biscuits belong to a “Food” network 
I am currently working on what I call a relationship mapping component. You can read some about my concept here: https://trac.buddypress.org/ticket/582
I hope to have an alpha release in 3-4 weeks.
Jeff, As as someone with the status of “Friend” to you on Buddypress, and having not met you or engaged verbally with you, I would really second this concept you are proposing.
Recently an investor in a couple of our projects told me his one big criticism of using Buddypress was that people were asking him to become a “Friend”. He found that quite confronting.
Are you proposing that the requests also come through with the relationship reference attached.. for example “Wessa would like to add you as an acquaintance”.
Anyway, love the whole idea of mapping relationships, it adds a whole lot more meaning.
Wessa-
Thanks for your comments. I too always thought it a bit odd to get friendship requests from someone I never met.
This, of course, is not specific to BuddyPress. Friending is a common practice in the 1st-generation social networking platforms like MySpace, Facebook, and others. Many platforms that followed basically carried this metaphor forward.
However, I think it is time to evolve the friending process. We can pay homage to the throwback years of early social networking platforms, but going forward, we need to expand our relationship definitions.
Are you proposing that the requests also come through with the relationship reference attached.. for example “Wessa would like to add you as an acquaintance”
For the alpha release of this component, I am focusing on remapping of the friend relationship. So, the request for friendship would come in and be accepted or rejected as always. If accepted, the users would have a choice to remap that relationship to something more appropriate. Of course, this means that each party in the relationship could remap the relationship differently.
For the official release, version 1.0, it is possible that I will hook into the actual relationship-requesting process and pass on the request as proposed–x would like to add you as a colleague. This way, both parties would in essence be agreeing to the type of relationship.
@Jeff Sayre, That good to hear some work on the remapping does it mean we get some suggestions from Ronia?
@Gpo1-
Basically yes.
There will be a way to “Fan” someone without the fanned party having to accept it.
That’s a great job being done by Jeff ! Many thanks !!
@Jeff Sayre, When you get these levels of friendship does they offer different level of access?
e.g add comments on photos on friends, fans just view items etc.
@Gpo1-
That’s an excellent question! My relationship mapping plugin will not provide any level of access control. However, that will be provided by the privacy component that jjj and I are working on.
So, you could say let only fans see this aspect of my online identity, or let only colleagues read my full profile, or do not let acquaintances have access to my friends list. You get the point.
@Jeff Sayre, Well done on this project , I was using active directory access levels ..LOL
This would make BP great and privacy controls!
Part of this project depends on how WordPress decides to handle permissions (capabilities and roles) with 2.9+.
The goal will be for relationship scopes and roles to be set at default and later defined by the administrator of the site, based on what users are allowed to do/see, etc…
Lots to do! 
