 As we've been previously discussing, networks are all about connectivity and what's flowing through 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 underlining mechanism of how events propagate through complex networks. 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 spreading through an online social network. Whatever this phenomena of interest may be, the primary questions of network diffusion remain the same. Questions such as what are the different forces that are affecting this diffusion and how will the structure of the network affect that process? How fast would it spread? For example, will we get tipping points? And how can we enable or constrain this process of diffusion? These are some of the questions that we'll be touching upon in this video. Firstly, we need to understand the different forces acting on the network. What are the forces pushing the phenomena out over the network? That is to say, how contagious is this phenomena that's spreading? And inversely, we need to ask, what are the counteracting forces resisting it spreading? So we're talking about, on the one hand, the infectiousness of the phenomena that's spreading, and on the other hand, the resistance of the agents to that phenomena. And these are two counteracting forces. As an example of this, we might think about the social network of some society consisting of a dominant and minority culture. We might think about the current situation in the country of Myanmar, with the minority of Muslims and a majority of Buddhists. Now we'll add to this network some actors within the majority culture that are trying to spread some rhetoric of violence towards the minority group within this network. And then ask, how will this diffuse? 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 some understanding of the two forces at play. And this would form the basis of our model for how rapidly this message might diffuse through the network. The overall density of the network is important for the obvious reason that with a high level of connectivity, something has many more channels through which to spread. But beyond this, we also need to ask whether the agents within the system are actually capable of spreading that phenomena themselves or not. As we turn up the overall connectivity within the system, the nature of the diffusion process changes fundamentally. At a low level of connectivity, when we're dealing with an isolated group of people, we have to try and affect the whole group, and particularly the average people. 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 exposed 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. In this way, we can get much higher leverage. Influencing the network in the right place can now have a much larger non-linear effect. And we see this with the current trends within advertising. Because we're 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 for them. Next, we need to consider the overall topology to the system, how something will spread across it will be significantly influenced by the clustering within the network. Clustering creates heterogeneity. This might be the different ethnic and linguistic clusters within the network of our 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 spreading across the entire network. This clustering may well also create competing phenomena within the same overall network where a new phenomena is introduced but given different interpretations or forms by different sociocultural 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 dialects of some common language. These are all sub-clustering 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 some 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 very 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 and thus in just two hubs we've managed to cover a whole sub-system. 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 until the diffusion process even begins to take place. Or as another example we might think about broadcast media which again is a centralized system that can be very effective at disseminating uniform information to a broad group of people and we've seen how it's been used effectively as a means for creating national solidarity among 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 easily achieved because it's a centralized network. 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 previous examples. Centralization is essentially a top-down method meaning that few people are trying to affect many. This centralized mechanism always comes at some expense and has significant limitations and this ties back to our previous discussion about the agents within the network working to spread the phenomena. That can only happen when we have 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 those distributed connections and 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 loop driving them 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 second languages not because these languages are in any way better than any 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 previously talked about. What is happening with the network effect is that there is really a positive externality. When I choose to learn a particular language I'm not just generating value for myself but also some of the value is being externalised 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 MECLAF'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 these positive externalities the system as a whole now has value greater than its individuals. With the network effect people will not only adopt a phenomena based upon its value in isolation but also on the measurement of how many others will also adopt that phenomena. We choose to go to a party or some other 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 him and thus expectation can be a very high leverage point with respect to diffusion in 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 see this with the dominance of English as a global language and the decline of many other small 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 it's sub-linear. Adopting some radical new fashion when no one else has will come at 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're 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 quite little out. But if the phenomena does spread then the network effect will take hold. There will be some tipping point or phase transition where rapidly goes from a fringe activity to a mainstream phenomena and the course of least resistance. Complex contagion is the phenomena in social networks in which multiple sources of exposure to some innovation are required before an individual adopts that change in behavior. This differs from simple contagion in that it may not be possible for the phenomena to spread after only one instance 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 that 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 just 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 diffusion 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'll 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. In this video we've been talking about the diffusion process within social networks looking at some of the primary considerations. We talk firstly about the two counteracting forces of the infectiousness of the phenomena that is spreading on the one hand and the resistance of the agents on the other. We highlighted network density as a second major factor where when we turn up the overall degree of distributed connectivity the nature of the diffusion process changes fundamentally allowing for a peer-to-peer process of sharing. We noted how clustering can create a certain resistance to uniform spreading but centralized networks can be very effective and enabling the diffusion process through the use of large hubs. We briefly talked about the network effect and how it can create rapid diffusion once the tipping point is reached due to positive externalities. Finally we expanded our model to include complex contagion where an agent must be exposed to a number of different sources before adopting him.