People are interdependent, and the structure (topology) of their inter-dependencies (direct interactions, but also imitation or influence without interaction) can be represented by a graph, or network, wherein people are nodes and their inter-dependencies ties. Properties of a network can be described formally and precisely, and the dynamics of a network, that usually co-evolves with nodal properties, can be modeled statistically.
Notice that the field has grown so large that any overview, no matter how good, is incomplete.
On the interdisciplinary field of network science:
Now the field has become so vast, there are many new sub-fields with their own overviews and special issue journals on networks of animals, organizations, ecosystems, geographic locations, archaeological sites, school children, game players, disease-spreaders, phones, twitter, terrorists, criminals, websites, and many other.
A non-technical one by an economist and a computer scientist:
More technical textbooks:
Sources depend on the type of relationship, field and available resources, and can be: experiments; mobile phones ("reality mining"); email; the Web (including offline data put online); ethnography; archaeological and historical sources; and surveys.
R has an igraph package.
A sophisticated approach to analyze longitudinal data in R: SIENA. Tom Snijders explains and illustrates it on his website, that also harbours a manual of the pertaining software package.
Very popular are Exponential Random Graph Models, which have their own statnet package in R, but before you decide to use them, read this. An overview of models is provided by Jacobs and Clauset (2014).
Large computation jobs beyond the abilities of a PC can be done on the computers of the University of Amsterdam (SARA).