“I refer to Network Theory as a way of understanding many phenomena which are not related to the functioning of the market but rather to the emergence of this particular institution and, more generally, to many interesting social facts which are not intermediated by markets.” (http://deugarte.com/gomi/the-power-of-networks.pdf)
Key network forms in the p2p context:
- Network Graphs
- Network Typology
- Network Sociality
- Power Law
- Scale-Free Network
- Six Degrees of Separation
- Small-World Network
- Social Graph
- Weak Ties
Typology (of theories)
"One can differentiate between two kinds of theories of networks. In the first type, the concept of network fits into an existing, taken-for-granted social theory (examples are the new theories of society, but not of the social, such as Castells’ (1996); theories of social networks of activism, such as Smith, Chatfield and Pagnucco (1997), Keck/Sikkink (1998); and theories of social movements proper, that incorporate some aspects of networks or webs, such as Alvarez 1998, 2000)). In the second group, social theory itself is re/constructed out of, or on the basis of, the concept of network (Latour/Callon’s ANT; complexity). As Latour put it, actor-network theory (ANT) “aims at accounting for the very essence of societies and natures. It does not wish to add social networks to social theory but to rebuild social theory out of networks” (“The Trouble with Actor-Network Theory,” from Latour’s web page, www.ensmp.fr/~latour/artpop/p67.html). While both sets of theories –theories of society, activism or social movements, on the one hand, and social theories, on the other– are useful for thinking about AGSMs (alterglobalization social movements), as we shall see, the latter provides a set of insights for thinking about what might be most intractable, and radical, in the AGSMs of today." (http://www.unc.edu/oldanthro/faculty/fac_pages/escobarpapers/notesnetwork.pdf)
Key Books to Read
Six Degrees, The Science of the Connected Age, Duncan J. Watts, W.W. Norton, 2003.
"A network of discoveries across an array of disciplines tell the story of an explosive new field of knowledge, the people who are building it, and Watt's own peculiar path in forging this new science."
Nexus, Small Worlds and the Groundbreaking Science of Networks, Mark Buchanan, Norton, 2002.
"presents the fundamental principles of the emerging field of 'small worlds' theory--the idea that a hidden pattern is the key to how networks interact and exchange information, whether that network is the information highway or the firing of neurons in the brain."
Linked, The New Science of Networks, Albert-László Barabási, Perseus Publishing 2002.
"First book to explore the hot new science of networks and their impact on nature, business, medicine, and everyday life. This book has a simple message: think networks. It is about how networks emerge, what they look like, and how they evolve."
Special Issue of IJOC
Special issue of the International Journal of Communication, Vol 5, 2011.
- Network Theory | Prologue to the Special Section| Network Multidimensionality in the Digital Age PDF ; Manuel Castells, Peter Monge, Noshir Contractor 6 pgs. 
- Network Theory| Introduction to the Workshop: The Promise of Network Theory PDF ; Manuel Castells 2 pgs. 
Network Theory| A Network Theory of Power Abstract PDF ; Manuel Castells 15 pgs. 
- Network Theory| Fuzziness of Inclusion/Exclusion in Networks PDF
Karine Nahon 17 pgs.
- Network Theory | Networks of Power, Degrees of Freedom ; PDF ; Yochai Benkler 39 pgs. 
- Network Theory | Multidimensional Networks and the Dynamics of Sociomateriality: Bringing Technology Inside the Network Abstract PDF ; Noshir Contractor, Peter Monge, Paul M. Leonardi 39 pgs.
- Network Theory| The Flip Side of Metcalfe’s Law: Multiple and Growing Costs of Network Exclusion Abstract PDF ; Rahul Tongia, Ernest J. Wilson III 17 pgs.
- Network Theory| The Ever Evolving Web: The Power of Networks Abstract PDF ; Wendy Hall 14 pgs.
- Network Theory| Networks, Societies, Spheres: Reflections of an Actor-network Theorist Abstract PDF ; Bruno Latour 
The topic is also monitored through the following Delicious tag: http://del.icio.us/mbauwens/Network-Theory
Backstrom, L., Huttenlocher, D., Kleinberg, J., and Lan, X. (2006.) Group formation in large social networks: membership, growth, and evolution. In Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM Press: Philadelphia, PA, USA.
Butler, B. (2001.) Membership size, communication activity, and sustainability: a resource-based model of online social structures. Information Systems Research, 12 (4), p. 26.
Cai, D., Shao, Z., He, X., Yan, X., and Han, J. (2005) Mining hidden community in heterogeneous social networks. In Proceedings of the 3rd International Workshop on Link Discovery. ACM Press: Chicago, Illinois.
Freeman, L. C. (1979.) Centrality in social networks conceptual clarification. Social Networks, 1 pp. 215-239.
Garton, L., C. Haythornthwaite and B. Wellman. (1997.) Studying online social networks. Journal of Computer Mediated Communication, 3 (1).
Granovetter, M. S. (1973) The strength of weak ties. American Journal of Psychology, 78 (6), pp. 1360-1380.
Johnson, B., Lorenz, E. and Lundvall, B. (2002.) Why all this fuss about codified and tacit knowledge? Industrial and Corporate Change, 11 (2), pp. 245-262.
Kumar, R., J. Novak and A. Tomkins. (2006.) Structure and evolution of online social networks. Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 611-617. ACM Press: Philadelphia, PA, USA.