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. 

Overviews

Notice that the field has grown so large that any overview, no matter how good, is incomplete.

• Stephen Borgatti e.a. (2009) Network analysis in the social sciences. Science 323: 892-895.
• Matthew O. Jackson (2014) Networks in the understanding of economic behaviors. Journal of Economic Perspectives 28: 3-22. 
• Jon Kleinberg (2008) The convergence of social and technological networks. Communications of the ACM 51(11): 66-72.
• A flavor of network modeling: Petter Holme and Mark Newman (2006) Nonequilibrium phase transition in the coevolution of networks and opinions. Physical Review E 74: 056108. 

On the interdisciplinary field of network science:

• Albert-László Barabási (2012) The network takeover. Nature Physics 8: 14-16.
• Science had a special issue on social and other networks on 14 July 2009, volume 325: 405-428.

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.

Textbooks

A non-technical one by an economist and a computer scientist:

• David Easley and Jon Kleinberg (2010) Networks, cowds, and markets, and a critical review of it by Cosma Shalizi.

More technical textbooks:

• Albert-László Barabási (2016) Network Science. Online for free.
• Alain Barrat, Marc Barthélemy and Alessandro Vespignani (2010, reprint with corrections) Dynamical processes on complex networks.

Network data

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. 

Software

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).