A lot depends on whether you have a "closed" or "complete" set of observations, so that you have data about the connections among all the dyads in your network. In other words, can you create a who-to-whom adjacency matrix that contains information about each pair of participants?
If so, there are great many tools in Social Network Analysis that can be applied to that kind of data. But if you just have a variety of dyads, without data on the full network, then your options are much more limited.
I have a complete network data and I pretend to use it like Gulati and Gargiulo (1999) study. In their study, they use logit panel data model, but i don't know if this model is the better nowadays.
The best source for this kind of analysis is still Social Network Analysis: Methods and Applications by Stanley Wasserman and Katherine Faust (1994). They also provide a strong overview of network analysis in general.
A more basic introduction is Social Network Analysis by David Knoke and Song Yang (a Sage "little green book"), but I don't know if they cover logit models.