Your morsels of value

What do I mean by network value? In a network, the popular nodes become even more popular, according to a “rich get richer” fashion known as “Preferential Attachment”. Previously I have used the example of the London Underground, although that is not a particularly good example in terms of dynamics, because the popular stations are interchanges. There is very little occasion for a new interchange to suddenly pop up at a station that hitherto was not an interchange. New stations don’t materialise that often, so the whole analogy proves a bit slow to visualise in action.

The network value of a vertex in a network, which is rewarded by affordability of opportunity to increase connections in a scale-free manner, is itself a complex parameter. What do I mean by value? Up to now, we’ve just been assuming we mean that we offer something, perhaps something unique or perhaps something appreciated or liked or funny or thoughtful or provoking or some other appealing lure. If a node in a network produces something no other node does, and if as coincidence would have it, other nodes in a network actually appreciate that product, then that’s what we’ve been imagining what I mean by “value” within a network. But this is quite subjective.

Lots of nodes, sorry, people, produce and present to the network more or less nothing. When they do, it might be of low importance such as mentioning that their cat rolled over. Or it might be something derived that they are simply passing on, like a retweet or a pasted-in motivational quote. Motivational quotes are a freely utilised currency. As far as I’m aware, Henry Ford, Bob Marley and Thomas Edison don’t actually have twitter or facebook accounts, what with the inconvenience of being dead and all that. Yet much of what they ever said in their lives is passed around freely. Not only as a way of cheering people up (or ‘motivating’ them), but packaging it as a kind of “you got that good feeling from me” emotional transaction.

As I say, a node that produces is not always offering value to the network. In a work environment, if someone farts, the value of their unique production is generally not appreciated or liked, nor does it give everyone else a good feeling. So you see, it’s subjective. What we consider value is often measured and quantified in terms of a qualitative effect on us. The more happy it makes us, the more value we assign to that direct contact on the network that packaged their output into tiny little morsels, nibble after nibble. We afford network fitness to them as a reward. But only if we calculate that they offer value to us, and this is purely in terms of how good it makes us feel at the time. It’s all very much instant gratification, there’s almost nothing long-term about this, and it doesn’t correlate with any true usefulness of the information, just how sweet it tastes to us.

What is a network? Fitness, Value, Tournaments

If you search for fitness models on the Internet you’ll find an impressive range of pretty young things who don’t stray far from a gym. They’re certainly nice people to look at, but that’s not what I’m referring to here. A fitness model from the network context is a way of describing how it grew to where it is now, or how it may have failed to grow, or what it may be likely to do next. The assumption is that the nodes in the network are competitive and will seek an increase in the degree of their connections at the expense of other nodes degree connection. The Bianconi + Barabási model expresses this mathematically, which means that I won’t go into it here right now. Or anywhere. Ever.

I would suggest, however, a further parameter to this model. The existing facet of fitness could be viewed as intrinsic but let’s add another parameter that I might call ‘value’, which could be seen as an extrinsic dimension. If a node offers ‘value’ then it is given ‘fitness’ in terms of affordability of degree connections. Either way, the Barabási-Albert model of preferential attachment does give us an insight into why we have scale-free networks that can ramp up a given dimension into the stratosphere, for example when a meme goes ‘viral’ in popularity.

We are within a network of other people, perhaps in a family or friends context, and perhaps in a business context, with all of our connections. Therefore we are a vertex, surrounded by edges connected to other vertices. As a node, then, how do we consider and evaluate our ‘fitness’ within a network? And if we follow my modification of the above model and consider that there is another complementary parameter of ‘value’, how do we evaluate our value? Do you proffer value? Does your value afford the rewarding of network fitness? Does your network fitness promote visibility and popularity to attract more connectivity? Is your network fitness greedy from a competitive point of view, or generous from a collaborative point of view?

It’s my opinion that the Barabási-Albert model or the later refined Bianconi / Barabási model is missing an ingredient, because as it stands, it recognises fitness as a greedy action of competition success. However, people don’t necessarily work that way, or at least, not for very long (especially if we add the complication of the breadcrumb-path of reputation as a persistence aspect, etc. but we shouldn’t complicate it here, let’s keep it simple. Oops, too late). People in business leverage a blend of competition and collaboration — too much of one or the other and it’s not a good business success. The models require an extra thing, and I suggest that this is an outward-pushing ‘value’ aspect, that complements the inward-grabbing ‘fitness’ aspect. Being rewarded for offering value is akin to collaboration and is rewarded by fitness affordance which is of course akin to competition according to the BA and BB models above.

One more thing. The Tournament in graph theory is a directed graph, which forms the directivity progressively along a duration. In other words, there is a predetermined topology of the network but the directivity is not laid down yet. It gets laid down connection by connection. The outcome of this is that it describes a dominance model, and relates to social choice theory. The reason that people make choices is interesting, but the reasons that people within an influencing and influenceable group make their choices is even more interesting. With great power comes great scriptwriting and marketing, or something like that, and the responsibility of being a big noise in a highly connected network is possibly more paramount than many people realise. I suppose the only advice I can give is to be a valuable person for the sake of your reputation, because the reputation forms a persistent record. Whether that means being nice, or whether that means you can get away with being a bastard, that’s up to you — it’s your value, your fitness, your transactional reputation imprint.