Summary: Network theory and network graphs present static, not dynamic social networks. Communication motivates social systems and social software sites. Graphs and topologies of these social networks requires better social software and social media research. The field is still needs to view users as motivated actors — not black boxes they are on graphs.
The science of network analysis has opened up a fascinating discussion about the structure and architecture of networked systems. We're all familiar by now with graphs comprising nodes and links, hubs and clusters, as we also recognize terms like "connectors," "diffusion," "scale-free," and the "power law." But it's easy to be seduced by the simplifying benefits of visual representations into thinking that they explain to us What's going on.
The first such chart was apparently a graph of bridges in a small Prussian city in which the question of whether one could walk the city without crossing the same bridge twice became a long-standing popular puzzle. It was a map of walks along paths made possible by connecting bridges.
In our current fascination with mapping network topologies, our emphasis has shifted from the dynamics that produce a network to the graph that captures its topology.
Let's assume that a city's inhabitants are engaged in solving a puzzle by means of walking across its bridges. Our topologies only show the totality of all possible paths. They show us the general. To capture the walker, and his particular walk, we need dynamics. People walk for a reason, namely to get somewhere. The paths they take can tell us something about the choices they face, and how they respond to them.
In the case of social systems, network dynamics are as important as their topologies, for it's in dynamics that we find the social practices we describe as emergent behavior. And if we are to understand social behavior, we need to supplement the network-centric perspective with a social systems perspective. Social systems provide us with an appreciation for the uniquely communicative and social interpretation of network constraints. Our interpretations illustrate the value we see in networking among people and within communities (organizations, groups, associations, etc.).
A dynamic model of social networks would show not just links (bridges) and nodes (islands). It would be capable of rendering networks at work.
It would be exciting to see network analysis applied to mediated social networks. We will have to go far beyond existing topologies, however, if visual representations are to help us understand social process and the role played by social and group dynamics in the formation of networks.
If we built our models on shap shots over time we could capture some of the value that social networks have in maintaining routines. If we built them out of layers, we could distinguish members' relations based not just on who, but on for what purpose.
Diachronic modeling of social network topologies, constructed out of layers each representing a functional subnetwork, would seem to be a more accurate way to represent what happens in real social systems.