The Spectrum of Network Ties

The standard model of scale-free networks (conveniently summarized in Barabasi's book Linked) captures the growth of the network via two principles: preferential attachment and time (ok, we can throw in fitness as well). However, as far as I know, none of the models in the literature include a notion of the cost of creating and maintaining a link.

In his invited talk at ICWSM, Marc Smith presented a compelling taxonomy of social media types via descriptions of the producer (individual, small group, large group) and the consumer (individual, small group, large group).

I think that adding the concept of 'cost of a link' would be a useful addition to this description. Some examples: broadcast media tend to have a low cost for adding a link - turning on the TV doesn't cost the tv station much, following someone on Twitter is low cost. Creating and maintaining real social contacts does cost us in the form of attention and memory (Gladwell describes connectors as people who can do this task well).

We can imagine that there is a range (spectrum) of costs, and that the cost comes in different types (financial, physical, attention, etc.) I guess that the most expensive social link you can make is by giving birth...

Comments

[Guy Hagen]

The concept of a "social cost" for a connection is common in the social network analysis literature, which is why we all don't have 10,000 close personal friends. For example, there has been discussion as to the extent "facebook friends" are truly friends when there is no cost to establish or maintain a facebook link.

Regarding physical connections, the telecommunications and power industries evaluate connection cost for their networks in terms of physical infrastructure (cost per mile of cable, signal attenuation, station and repeater costs), and cost variables are often a part of network flow calculations (traffic, electronics, etc). Refer to the "minimum cost flow problem" on Wikipedia for more exploration.

[Jon Elsas]

"there is no cost to establish or maintain a facebook link"

Is this really true? Every friend I add on Facebook adds more noise to my newsfeed and increases the complexity of the network I need to navigate in order to find my "true" friends. Sure, I can adjust my settings to reduce the newsfeed noise, but this is an additional cost to me in terms of time. As our online social networks get bigger, there is a need for more fine grained privacy controls, which increases the complexity of the system. With this increased complexity comes an increased cost of maintaining your network.

[Akshay Java]

This is a very interesting post and something I had been exploring recently. I think that there are two types of costs related to a link - one is the "cost" for the creator of the link and the other is the cost to the network; if the link were to be removed. What flow based / edge-betweenness refer to is the cost to the network, however in most cases it seems to be tricky to quantize the cost to an individual node.

As a followup on Guy's comment here is an interesting paper on an analysis of a telecommunication graph. http://tinyurl.com/3otp78

I really enjoyed reading the book "Linked". But I would also recommend reading "Six Degrees: The Science of a Connected Age" by Duncan Watts in parallel. It is a perfect complement to Linked.