In my last blog “Why network analysis is the next big thing”, I argued that just as businesses must know how their message spreads in their markets, and as much of government activity is now about research, technology and providing information, so policy makers and program managers must understand the paths by which their message spreads. A critical factor for the success of these activities is the patterns of potential diffusion that exist and how the information is received, learned or accepted. Network analysis is a key, if not the key, tool for understanding this.
I’ve just finished a challenging course on the analysis of social and economic networks, taught by Professor Matthew Jackson at Stanford University.(1) What I have learned has left me even more convinced of this. There is a rich and growing literature that helps explain how the structure of networks are influential in the spread, or lack of spread, of ideas, information and influence (among many other things).(2)
A great deal is known now about the empirical distinctions between networks that have formed through a process of non-random formation of links, such as friends, colleagues or researchers introducing each other, and those that have formed principally by chance connections. A number of models now exist for such processes and these promise to provide structure in the future for analyzing specific information and collaboration networks.
Moreover, analysis of the costs, benefits and incentives facing the players in a network can say a great deal about how collaborations and networks of information may succeed or fail, because of the potential for a difference between the stability of a network (that is, its tendency not to fall apart) and the efficient, or benefit-maximizing, equilibrium of the network.
As an example, we looked at “the symmetric connections model”.(3) This relatively simple example was meant as an introduction to the possibilities in modelling network behaviour, but seemed immediately interesting to me in policy and evaluation terms.
Without going into the algebra, in this model if we assume that there is a cost of maintaining a link directly with someone else in the network and a benefit from each link with other players, including indirect links, that decreases the farther away these players are, then a set of implications fall out. The key implication is that for certain combinations of the cost of direct links, the benefits of direct links and the decreasing benefits of successively more remote links, then the most efficient configuration, in terms of maximizing the net benefits to members of the network, would be a “star”, as in the diagram to the right. This configuration, however, may be unstable, meaning that it will not persist. The central player gains the direct benefits of its connections with those on the periphery, but no additional indirect benefits. At the same time, this player bears the cost of multiple direct connections. It may therefore not be in the central player’s interest to maintain these links, in which case the entire network would fall apart. No-one would be connected, because it would similarly not be worthwhile for the other players to form direct connections. On the other hand, if the cost of direct connections is low enough, all players will elect to become connected. In either case, the most economically efficient equilibrium will not have persisted. Only for a specific range of costs and benefits will the efficient equilibrium also be stable.
Patterns of connections that locally involve a “star” structure, in which there is a central player in the middle of others and radiating outwards, are common in real-world networks. Such players are central in the network in the sense of being connectors.(4) This has been a feature of recent mappings that I have done involving health researchers and members of healthcare-related committees. While the precise implications of local structures will differ from those explained above where the entire network was in a star configuration, much of the logic is still applicable.(5) Take for example the hypothetical example of a collaborative network of researchers depicted in the second figure.
In this case, as above, if the cost to central player 1 of her four direct links is too high relative to the direct and indirect benefits she gets through the network, she may sever her links. As in the pure star network analysis, because of high costs in maintaining linkages the entire network may collapse with no-one remaining connected.(6) Conversely, if the cost of direct links is low enough, everyone may be incented to connect to everyone else. In both cases, then, the network as depicted would not be a stable equilibrium, even if it happened to be the highest total benefit and lowest total cost configuration.(7)
We could also understand the differences in costs and benefits of participating in this network for the individual players. Player 1 has access to more direct and close-to-direct benefits, but also the cost of four direct connections. Player 2 has fewer direct connections but also one quarter of the cost faced by player 1. Players 3 and 4 are working with the same set of benefits and costs, but players 5, 6, 7, and 8 each will have a different cost/benefit calculation than anyone else.
Seeing it this way, we can also see that there could be a negative externality in player 1’s individual decision to sever links based on an excess of cost from four direct connections over her benefits, as even if the rest of the network did not collapse completely, the other players could lose the indirect benefits of the cross-network connections that would have existed with player 1’s participation. This, again, is the tension that can exist between efficiency and stability in networks where costs and benefits are derived from connections.
Policy makers and evaluators could potentially understand a great deal about the conditions under which the building or expansion of such a network might be successful if they had an understanding of the structure of the network already in existence, the structure of similar networks, and the costs and benefits of collaborative connections.
This is an example of the kind of structure that an explicit network analysis approach can bring to consideration of many kinds of public policy and programs, as well as business applications. I think the potential for better policy and evaluation is impressive.
On a personal note, I am looking forward to participation in the strengthening and promotion of the American Evaluation Association’s Topical Interest Group on social network analysis for evaluation, and I’ll keep you informed about what we are doing.
haiku analytics inc
November 24, 2015
(1) This was a “massive open online course” (MOOC); some other time I’ll write about what I think is the great potential of “MOOCs” in the intellectual and professional development opportunities open to almost anyone.
(2) Not surprisingly, for example, social network analysis is an important tool in epidemiology.
(3) Jackson, M.O. and J. Wolinsky (1996) “A Strategic Model for Social and Economic Networks”, Journal of Economic Theory 71(1):44-74.
(4) Formally, this would be expressed in high levels of network metrics such as “betweenness centrality”.
(5) As the entire network would not be a star in this example, this formally would be a sub-network and the implications discussed would be local, and not necessarily apply to the entire network.
(6) As we are not discussing a pure star network case, this collapse may not be complete.
(7) Simply having everyone connected to everyone else may not be optimal, as this would be the highest cost solution.