We've long understood, albeit unconsciously, the value of networks, of so-called "connections" and the benefits of sociability - professional, academic, and personal. But until fairly recently, few understood the real implications of networks in a physically-quantifiable way which could be understood by mathematical laws.
When Machinery Becomes Life
Bob Metcalfe, the inventor of the Ethernet, is credited with first discovering and publicizing the mathematical description of network value, called to this day "Metcalfe's Law". The law as he formulated it in 1980 is a rather straightforward equation (which says that the value of a network increases as the square of the number of its nodes) that explains a network's tendency to explode in value mathematically as the number of connected nodes within that network grows. The resulting phenomenon defies the traditionally-understood laws of economics, in many ways the system begins behaving far more like a lifeform than a mechanism, complete with various nonintuitive effects which tend to contradict established economic wisdom.
Most economic goods exhibit the phenomenon of diminishing returns. The value of consumption of the next unit decreases with each unit consumed (this application of diminishing returns is called the law of diminishing marginal utility). Thus, the primary gain is made in the beginning and the payoff of duplicate effort levels off to eventual insignificance. Such goods tend also to follow essentially linear relationships which create economies of scale.
A network, however, obeys the law of increasing returns: success is self-reinforcing, and in effect success breeds success. A network does not have simple, linear relationships between input and output. Progress is unpredictable, and failures are equally spectacular - sustained linear progression simply doesn't occur. We are taught in so many aspects of life outside of simple material accumulation that effort and result are directly related, great effort needed to affect great change and little effort resulting in small result (see also leverage), but this idea simply fails to account for the compounding value of many interconnected small results in producing substantial and even overwhelming, observable results.
The Power of Networks
The seemingly-mysterious and magical added benefits of networks stem from what economists term externalities. Generally, however, externalities are associated not with added values, but with negative effects upon society which an individual firm causes but is not held accountable for. Essentially, the network is a reversal of this idea which considers the "social" benefits of the network to the individuals which comprise it.
Since the benefits accrue as the connected nodes grow, it's actually possible that the externalities produced by a sufficiently large network can outweigh the individual costs incurred. In much the same way that the unaccountable damage is borne by the whole, the benefits which no one "paid for" are also distributed. This has some fascinating repurcussions, because value is created in the interaction of firms, rather than exclusively by any particular firm. This challenges traditional economic notions of capitalism as a competition which tend to exploit economies of scale, edge out competition, and desire to become monopolistic. Economic benefits actually force behavior toward a more collective dimension, by negative reinforcement - stop cooperating and act to monopolize, and the gains from value networks are foregone.
It is also greatly misunderstood by some advocates of socialism who fail to understand that the value originates not from the whole, but through the externalities of independent exchanges which are taking place between the individual firms which comprise the network. In effect, they are created in the exchange. Without the independent and competing firms, economic collectivism, rather than free trade, arises. This is not to indict socialism at all, nor to deny any advantages it might have, but rather to point out that it has no claim to these particular benefits, which are only superficially similar.
One of the most fascinating attributes of the phenomenon is that the competitive behavior does not vanish: competitive behavior is actually necessary in the technical concern of actually producing the material good, but the ideas of which they are expressions tend to converge. This phenomenon occurs because material goods, which must be produced and reproduced to be sold, are inherently rival goods. Only one entity can use them at a given time. On the other hand, ideas - in forms such as blueprints, mathematical formulas, musical scores, scientific whitepapers, or philosophical treatises - are inherently nonrival goods which can be employed by any number of entities simultaneously to alter and "create" material goods of their own. Economic growth from these ideas thus arises through invention, discovery and innovation, and economic growth from employing them through the realities of competitive markets to create products.
The Price of Free Energy
"Every man and every woman is a star."
Aleister Crowley, Liber Al vel Legis, 1:3
The so-called New Economics of value are also economics of implicit uncertainty. Chance plays as large a role as ability and quality of product, and market forces and popularity exert a considerable influence. This leads to phenomena like "one-hit wonders", star performers which attain considerable success in a short time and quickly die out, to firms with inferior products but significant market advantage, who dominate producers of superior goods. The chance for instant and unprecedented success is balanced by equal risk of a short life. The phenomenon of "success breeds success" also can result in favoring the survival of firms posessing short-term advantage but little to no long-term benefit, at the expense of viable long-term performers which haven't demonstrated spectacular immediate short-term success.
Value networks, being unstable, are also broken quite substantially by certain types of monopolistic behavior and - paradoxically - strengthened by others. Developing of common technical standards and economic dependence on social relations between firms breaks regulatory mechanisms of traditional market-based competition -- would-be competitors can be gaining such substantial advantage from another's existence that they happily allow it to run rampant, creating privileged alliances with lucrative benefits for its members. Equally, the economic behavior of a large network, being inherently political in nature, often degenerates into simply a popularity contest, where individuality vanishes due to social forces in favor of a communal identity.
Bailey, Ronald, "The Law of Increasing Returns", http://www.cato.org/dailys/03-18-00.html
Arthur, W. Brian, "Increasing Returns and the New World of Business", Harvard Business Review, July-August 1996
assorted notes from a basic Microeconomics class