hey, it’s scale free and … and …
A focus of network research since, say 1999 or so, has been to identify “laws” that generate large networks with certain properties.* For example, the small world network is built by rewiring a grid. Various processes generate power-law networks (i.e., the node distribution is described by a power law).
I can see two justifications for this type of research. The first is diffusion theory. The speed at which something diffuses in a network is definitely governed by the structure. The second is a sort of physical science justification, where you think of a network as a “system” and you show that some micro-process (e.g., preferential attachment) creates that network.
Is there any other behavioral implication of studying power laws/small worlds or other specific large scale properties? In other words, why should I care about scale free or small world networks aside from diffusion theory?
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* Let’s leave aside recent criticism of power-law centric research for the sake of the post.
Don’t know about implications for pure theory, but there’s no shortage of implications in applied research
http://pespmc1.vub.ac.be/GBRAIN-L.html
;-)
Michael F. Martin
June 22, 2012 at 12:22 am
In the most general (and theoretically important) sense, all distributions are about structure. Perhaps that is what you were getting at with the point about system, though distribution is broader than systemic features or processes. Distributions are critical markers of underlying social processes, of which diffusion is just one. Sociology’s over-reliance on the assumption that attributes and parameters are distributed normally has greatly advanced the field in the last century, but has also given us blinders. Hopefully we are reaching the end of the power law fetish and can ask the important question raised here.
Bill Roy
June 22, 2012 at 4:46 pm
Finding simple processes that produce network structures help us understand where/when we can expect to find them, and why some are ubiquitous and others rare. Aside from diffusion of various things (information/cultures/movements/diseases), network structure can have crucial implications for search, exchange, mobilization, identity, status hierarchies, group cohesion, innovation, etc… For instance, whether a network of activists is scale free (centered on a small # of highly connected hubs) vs a diffuse network of equally not central nodes can affect its ability to mobilize events and resources, as well as its vulnerability to repression. An ideal structure for one of these goals may be very bad for the other.
But we do need to avoid getting hung up on a single network form to explain all social phenomena.
Anon
June 22, 2012 at 7:53 pm
First, I don’t think we should necessarily under-value the diffusion side. It seems like economists have begun using these kinds of network properties to understand systemic risk in financial markets, and it would seem apropos for us sociologists to utilize our understanding of networks, particularly of the scale-free variety, to contribute an economic sociological lens to this crucial line of thought in finance and public policy. See Bisias et al’s overview of measures of systemic risk for an overview how network research is being used to understand financial concentration and systematicity here:
http://www.treasury.gov/initiatives/wsr/ofr/Pages/ofr-working-papers.aspx
Beyond diffusion, I’ve done my own proto-investigations into the relationship between network structure and collective culture. Scale-free networks are good at keeping path distances short, but they also prevent most nodes from being connected to many nodes in general. Thus there’s a comparably low degree of individual embeddedness in communities with scale-free properties. On the flip side, random networks, of the Erdos-Renyi kind, maintain a comparatively high embeddedness for individuals, but they suffer from a lack of collective cohesion. This may help explain the phenomena of rapidly diffusing, but culturally thin phenomena of memes like Kony 2012 and lolcats through the scale-free Internet as compared with thicker, more distinctive cultural practices of neighborhoods or rural communities. Generally then, the network structure of a community may directly precondition the formation of individual-level attachment to a cultural community, the formation of local sub-community cultures, and the coherence of the culture of the community as a whole.
Jason Radford
June 26, 2012 at 4:23 pm