Hunting more background on the ‘structural holes’ issue that Burt raises in relation to the geometry of links in a social network. Goyal, in laying out the question of whether or not connectivity is a sustainable strategy, formulates the ground conditions:
We develop a simple model of network formation to address this question. We consider a setting where interaction between every pair of individuals generates a surplus. If two individuals are directly linked then they split this surplus equally, while if they are indirectly connected — there are other players in the ‘path” between them — then the division of surplus depends on the competition between these intermediaries. In this setting, there are three types of incentives for individuals to form links with others. The first incentive is the desire to create surpluses: individuals would like to join the network so as to create exchange possibilities which in turn create surpluses. The second incentive is related to the rewards from intermediation: players would like to place themselves between others in order to extract rents from intermediation. The third incentive arises out of the desire to avoid sharing surpluses with intermediaries; in other words, individuals will try to circumvent intermediate players to retain more of the surplus for themselves. — Sanjeev Goyal
The allusion to a surplus in the connection between two individuals is one of the first uses found in network theory that is in the direction of my research — where a core outcome of the series of bi-directional connections that occur in an open network is a surplus of energy. Back to the 1+1=3 theory. The extraction of ‘rent’ however brings up an entirely different mechanism. The mechanism is the applied attenuation of social strictures (as applied through the full range of ‘technological’ mediation) that extracts energy from the pair of engaged individuals — in this case, the third party happens to be in control of the ‘spending’ of energy from that immediate social energy bank. So, two separate and very different dynamics happening, not degrees of the same process.