hugo :: brainstorms in sociable media (mas.961 '03)
"only as an æsthetic phenomenon is
existence and the world justified"

- nietzsche


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::: social networks :::
The imaginary friends I had as a kid dropped me because their friends thought I didn't exist. - Aaron Machado

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Toward richer visualizations of social network ties

Standard social network visualizations do not typically focus on the nature of relations or ties between individuals; thus, a single directional edge is often used to connect two person nodes. This edge does not represent the strength of the relation, or its nature. Are these two people co-workers, activity buddies, lovers? Is the relation recriprocal or one sided? To be fair to those researchers who devised these visualizations, the data given to them is probably representative of one only relation. Even if the data allowed for multiple relations to be known, it would probably be confusing to encode and display multiple relations, particularly in a large network; whereas a keep-it-simple approach could eschew the uninterpretability of the visualization. However, if we were to visualize the multiplexity of social ties, important patterns might emerge.

In "Studying Online Social Networks," Garton et al. positions the deconstruction of social ties into bundles of disparate, directional relations as being key to understanding how individuals cluster in social networks, how these clusters overlap, and how clusters endure or fall apart. A key concept is the simplexity versus multiplexity of social ties. If a social tie features many different types of relations (e.g. co-workers, one tutors the other, watch baseball together), and if many of these relations are mutual, then the tie is known as a multiplex tie, and can be seen as durable. The durability of a single tie can impact the larger social network; for example, if a particular person is at a cut-point point and a tie is broken, a large subset of the network may drop out. It is also understood that individuals who are capable of relations not possessed by other members of his/her group or organization may serve the all important social role of gatekeeper.

The aforementioned reasons make a compelling case for the inclusion of the simplexity/multiplexity of ties in social network visualizations. In the following sketch, we propose a way of including information about multiplexity into social networks, being sensitive not to overload the network visually.

Figure 1. Social network visualization, with emphasis on multiplex ties,
cut-points, group stability, the potentiality of ties, and gate-keepers.

Squares represent individuals, colors code for the possession of certain social currencies, which may be of a general nature such as physical desirability and intelligence, or of a specific nature such as devotion to a church, devotion to work, devotion to a hobby, membership in a class, etc. The thickness of ties between individuals are indicative of the multiplicity of relations shared, not the scalar magnitude of a single shared relation. We can analyze the utility of such a visualization as follows. The more colors possessed by an individual, the bigger is his/her capacity to form multiplex relations. Because the boldness of lines represents multiplexity and not magnitude, not only can we identify groups but we can comment on the stability of these groups. The color coding also helps us identify the gatekeepers in a group. For example, suppose the red squares represented individuals in a church, and the lime squares represented individuals in politics. We can see that the red-lime squares and the rainbow squares are the gatekeepers who control the flow of information/influence from politics to the church, and vice versa. Cut-points can also be identified. For example, in the center of the sketch, a red/lime square is weakly tied to a teal/lime square. This is a potential cut-point because even at their maximum potential for ties, they can only be weakly linked, having only one compatible color. Contrast this to the red-lime square weakly connected to the rainbow square at the bottom-middle. Although this is a weak link, there is more potential for the link to be strong, so there is hope that this is not in danger of becoming a cut-point.

In the above visualization, we do not consider asymmetrical relations, unreciprocated relations. However, we note that unreciprocated relations are unstable. There must be some social currency exchanged. If for example, "John admires Mary, but Mary hates John," then the relation is rather doomed. In an animation of the above visualization, we might illustrate unreciprocated relations are pulsating between existing and not existing. If there is already a multiplex tie and only one relation is pulsating, it would hardly be visible. However, consider that the above visualization was an egocentric display of one's own social network. If a simplex tie is pulsating and it happened to occur at a cut-point, we can imagine an entire chunk of one's social network pulsating in and out, thus illustrating cut-points.

An economics metaphor for social support

In "Network Capital in a Multi-Level World," Wellman and Frank make the point that whereas in yesteryear social support was thought of in terms of personal membership in solidary groups such as a family, a church, and a career, today's networked world shifts emphasis from solidary groups to individual ties. It seems as if solidary groups give support for free. So it comes as no surprise that living in a day and age when nothing-is-free, and no cultural, moral, or civic duty compells us to freely support those in our group, the amount of social support we receive is now more a function of small-scale exchange of social capital. Wellman and Frank speak of three factors affecting social support: the characteristics of the individual, the nature of our ties, and responsibility of group membership. In declaring that our day and age is one of networked individualism, Wellman and Frank are really conceding the eroding role of group membership in social support. We don't really feel a duty, or possess an altruism to the group. We expect to only give what we get from the group. This thrusts the group into a tragedy of the commons deadlock, where members are not willing to give unless they've gotten, so there is a stalemate. There are, however, exceptions. The family, or at least, the nuclear family, is still intact in western societies. So are community churches (where duty is bound by fear of damnation!! how's that for altruism??).

With the decline of group influence, social support becomes more heavily a factor of the individual and of his/her ties. The characteristics of the individual can be thought of as the potential of a person to receive and give support. The nature of a person's ties can be thought of as the realized pool of resources for support. Just as Wellman and Frank talk about networks in terms of capital, economics is a good all-around metaphor for social support. I would suggest that it can even be measured that economics is the metaphor they actually use for social support. Taking this purely economics position of social support, I propose the following reworking of Wellman and Frank's analytical model.

Written sketch: Here is a rudimentary proposal and written sketch. Think of social supports as services you can purchase. Think of your immediate social network as vendors, each of whom carries a different offering of social support services (e.g. romantic, friendship, business). You yourself are a vendor of services, and the services you can offer and their costs are a function of the character of your individual. You have an account with each of them with a certain balance. If you sell them a service, money is put into your account with them. The more business you do with one another, perhaps the lower the cost of each service (we are more cheerful to support a good friend), and the higher the line of borrowing credit (we are willing to pull huge favors for someone given we trust they are capable of reciprocating). How services are priced is up to the individual. Other factors also come into play. For example, a particular vendor (person) may be very popular with other customers (their friends), and thus, their supply is lowered. Of course, when they have less inventory, that inventory costs more. This explains how getting a support favor from a very in-demand friend "means" more. It may either cost you a lot of social capital if that person is not fond of you, or not cost much at all (if that person gives you the wholesale price on the service since you are such a good customer).

Given the above sketch, we can make some nice predictions. If you are the needy type of person, you will spend more at your vendors they you probably have credit for, and very quickly, you will lose friends. If you are very busy and your attention is fragmented, you have a very low account balance with a lot of vendors, but not enough balance to purchase anything from anyone. If you are very busy but you give slightly more attention to a few people, these people will pay you more for your services, in recognition of their scarcity and thus, you will have a good account balance with these vendors. Finally, no one likes to shop at a vendor with a bad selection, so people are more likely to want to do business with you if you have a lot to offer in different departments. Similarly, no one shops at a place where supply is too low, or prices are too high. To increase supply, keep fewer friends. To lower prices mutually, do more mutual business. Just as in economics, I believe there is a sweet spot where social support's supply and demand meet. So perhaps given a person's needs and their friends, it is possible to calculate just how much business should be done with each person.

Weak ties as social glue

Trying to find uniform ways to characterize a social group at a small scale and at a large scale is somewhat akin to trying to reconcile quantum mechanics with cosmology. At the small group level, it is an individual's strong ties with other individuals which characterize the group. This is perhaps what Wellman and Frank suggest with the phrase, networked individualism. However, in looking at large groups, weak ties exert a much stronger influence, as suggested by Granovetter. For example, we tend to think that because we select all our friends by choice, we must also transitively reason that our friends select their friends by choice, and so on. That means our friends-of-friends network should have a fantastically wide range. However, as Newman shows in "Ego-centered networks and the ripple effect," these extended networks are smaller than expected. Why?

Newman does not directly answer this question, only suggesting that it is a mathematical characteristic of the network structure. He exhibits mathematical formulae to calculate the range of a person's friends-of-friends network by factoring in overlap between different circles of friends. Granovetter's account of weak ties offers a perfect explanation. The reason why there is overlap, is because our seemingly 100% free-willed choices of friends is actually subtly influenced by a preference for weak, but common characteristics. These characteristics are not so dominating as to make us feel we can't just pick whoever we want and work at the friendship. But consider a friend of a friend. You cannot explicitly pick that person to be a friend of a friend. However, the same weak tie that enabled your relationship with your friend can influence the choice of friend of a friend. Hence, strong ties only influence your immediate friends, but weak ties can travel many links away from you.

So it is the commonality of these weak ties that creates the overlap of friends and accounts for the narrower than expected range of your friends-of-friends network. The influence of weak ties does diminish as the number of friend-of-a-friend links are included into a circle. Because the tie is "weak," it is still plausible that a friend of a friend will completely escape the social group you belong to, and hence, you've connected to a whole new group where a different set of weak ties are at play.



H U G O . . L I U ...
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