Networks are about connectivity and what is flowing along those connections, how something spreads across a social network is then one of the central questions within social network analysis. The study of network diffusion tries to capture the underlying mechanism of how events propagate through a complex network. Whether the subject of interest is a virus spreading through some population, the spreading of some social movement, some new fashion or innovation or it may be a marketing message through an online social network. Whatever the phenomena of interest the primary questions remain the same, that of: What are the different forces that are affecting its diffusion and how will the structure of the network effect that process? How fast will it spread, for example, will we get tipping points? how can we enable or constrain that process of diffusion?
Firstly we need to understand the forces acting on the network, what are the forces pushing the phenomena out over the network? That is to say how contagious is it? And inversely we need to ask what are the counteracting forces resisting its spreading. So we are talking about the infectiousness of the phenomena on the one hand and the resistance of the agents to that phenomena on the other, these are two counteracting forces. As an example we might think about the social network of some society consisting of a dominant and minority culture, as a concrete example, we might think about the current situation in Myanmar with a minority of Muslims and majority of Buddhists within the population. Now we will add some actors within the majority culture that are trying to promulgate some rhetoric of violence towards the minority group within this network and ask how it will spread. So we have this outward force of these actors spreading this rhetoric that has a certain degree of infectiousness but we also have the individual’s opinions that may be more or less receptive to that message. In analyzing this social system we might then create a conceptual or cognitive map representing people’s opinions towards those of an alternative ethnicity. By understanding people’s opinions we can get an understanding of how resistant they will be to that message and thus a better understanding of the two forces at play, and this would form the basis of our model to how rapidly this message may diffuse through that network.
The density of the network is important for the obvious reason that with a high level of connectivity something has more channels through which to spread, but beyond this we also need to ask whether the agents within the system can actually spread the phenomenon themselves or not. As we turn up the overall connectivity within the system the nature of the diffusion changes fundamentally, at a low level of connectivity when we are dealing with an isolated group of people, we have to try and affect the whole group, we try and broadcast to everyone, as exemplified by traditional advertising and political campaigns, that put up posters and billboards in public spaces where the mass of people will get exposure to them, this is a kind of brute force method to diffusion that is necessary at low levels of connectivity.
But when we turn up the distributed level of connectivity this is no longer the case, now everyone can be a means of diffusion, we no longer need to use brute force trying to affect everyone, we can now be much more strategic, simply affecting those who have the greatest capacity to affect others and in this way we can get much higher leverage, influencing the network in the right place can now have a much larger nonlinear effect. And we see this with current trends within advertising because we are all now much more connected agencies can focus less on broadcasting commercials to the mass of people but instead focus more on getting influential bloggers to adopt and spread their message.
Next, we need to consider the overall topology to the system. how something will spread across it will be significantly affected by the clustering within the network, clustering creates heterogeneity. This might be the different ethnic and linguistic clusters within the network of global society that are resistant to the spreading of a single homogeneous ideology or we might be talking about the clustered cultural groups within a single city. This clustering and heterogeneity within the network will clearly be resistant to some uniform phenomena flowing across the entire network.
This clustering may well also create competing phenomena within the same overall network, where a new phenomenon is introduced but given different interpretations or forms by different socio-cultural clusters, with these different variants then competing. We might think about the spreading of some religion that gets interpreted in different forms by different cultural groups or the local idiolects of some common language, these are all sub-clusterings that give the network a heterogeneous topology and make it resistant to a uniform spreading. This heterogeneity due to clustering can create bottlenecks to the process of diffusion, where we have some cluster and just a few links connecting it to other groups, these links are then critical to the spreading process which reduces robustness, and increases the capacity for exercising power.
Centralized networks can be much more effective at spreading, with preferential attachment we get major hubs and those hubs are key enablers to the diffusion process. Because a hub is attached to many small nodes who may pass on the phenomena to them and then they will affect all the other nodes within their local network, thus in just two hops we have covered a whole subsystem. But we should always remember that centralized social systems will have strong power dynamics because of the high degree distribution and this can distort the diffusion process. For example, if we think about giving aid to some African country such as the Democratic Republic of Congo a large percentage of that money may well get siphoned off at the central hub of the network before diffusion really takes place. Or we might think about broadcast media, which again is a centralized system that can be very effective at disseminating information to a broad group of people and we have seen how it has been used effectively as a means for creating national solidarity amongst millions of people within a country, but again we know it is often used as a means for manipulation and propaganda spreading.
And this is the nature of centralized networks in general, they have a high concentration of power allowing them to be very coherent, effective and capable of rapid diffusion, but they can also be more dysfunctional as in these examples. Centralization is essentially a top-down method, meaning that few people are trying to affect many, this centralized mechanism always comes at an expense and has its limitations. And this ties back to our previous discussion about the agents within the network working to spread the phenomena, that can only happen with distributed connectivity, the agents have to be connected to each other in a peer-to-peer fashion but centralized systems will typically repress and work to exclude these distributed connections, thus there may be a certain trade-off here.
Networks don’t always grow in a linear fashion but may grow exponentially, whenever there is exponential growth there is typically some positive feedback driving it and in this case it is what is called the network effect. The network effect arises when users gain value from others using the same network, the more people that join the more value for everyone else, this is a positive feedback loop. A good example of this would be a language, the value of some language is relative to the number of other users of that language, the more people that adopt that language the more valuable it will be. People learn English, Spanish and Chinese as a second language not because those languages are in anyway better than others, but simply because billions of people speak these languages giving them a powerful network effect and lots of value. The network effect may be seen behind the formation and spreading of many phenomena within social networks, such as the spreading of some fashion, and as always with positive feedback, it will give us exponential growth, tipping points, and cascades as we have previously talked about.
What is happening with the network effect is that there is really a positive externality, when I chose to learn a particular language I am not just generating value for myself but also some of the value is being externalized to everyone else who is using that network, as they now have more communications options available to them due to this positive externality. The network effect gives us what is called Metcalfe’s law which suggests that the value of a network is proportional to the square of the number of users of that network, because of all of these positive externalities the system as a whole now has value greater than it individuals.
With the network effect people will not only adopt a phenomena based upon it value in isolation but also on the assessment of how many others will also adopt the phenomena, we choose to go to a party or some gathering only if we think others will also go and thus expectation becomes very important, people not only have to value something but they have to expect that others will also adopt it. And thus expectation can be a very high leverage point with respect to diffusion on social networks. The network effect is also notorious for creating lock-in, because there is so much value created by everyone simply using the same network, this creates a strong force towards convergence, everyone using the one network at the expense of all others, we can see this with the dominance of English as a global language with the decline of many other smaller languages.
This network effect may give the diffusion process a strong tipping point because below a certain level of people adopting that phenomena the value is very low, we might say sublinear. Adopting some radical new fashion when no one else has will come at a great social cost, but doing it when everyone else has will come at a much greater value. Thus the pioneers of some new phenomena, whether we are talking about a new political opinion, a new social movement or a new style, these first adopters will have to be very committed putting in a lot of resources and getting little out, but if the phenomena does spread then the network effect will take hold, there will be a snowball effect due to the positive externalities, there will be some tipping point or phase transition where it rapidly goes from a fringe activity to a mainstream phenomenon and the course of least resistance.
Complex contagion is the phenomenon in social networks in which multiple sources of exposure to an innovation are required before an individual adopts the change of behavior. This differs from simple contagion in that, it may not be possible for the innovation to spread after only one incident of contact with an infected neighbor. The spread of complex contagion across a network of people may depend on many social and economic factors; for instance, how many of one’s friends adopt the new idea as well as how strongly they actually influence the individual. In complex contagion, the probability of adopting a behavior, or an idea, varies with the extent of exposure, as an example a person might not respond when they see a piece of information on one social media site, but when they see it on another or a third this may trigger them to have greater belief in that piece of information and start to share it.
When we allow for this more complex form of contagion we now have to start to take into account different sources of contagion that may be conflicting as we noted when talking about clustering. The spreading of propaganda may be an example of this, within a very simple homogeneous scenario where we have just one national broadcaster we will have a relatively simple contagion process, with just one single message being propagated. But in a more complex setting with multiple channels, there may be conflicting messages and we have to understand the network of interacting messages that people are receiving and also the significance that they ascribe to those different channels.