 Social network analysis is one of the major paradigms within contemporary sociology and it's also employed in many other social sciences. It offers us a powerful formal language with which to model and analyse the structure of social relations and how this structure of connectivity defines the overall social system. The big idea here is that of connectivity. A central axiom of the social network approach is that social phenomena should be primarily investigated through the properties of the relations between and within the units instead of the properties of these units themselves. As such, social network analysis is an alternative way of investigating complex social systems, one that is not focused on the actors and their properties, but instead on how they are interconnected and this is a paradigm shift, a very different way of seeing the world. In our traditional paradigm, we see things. We don't really see the connections, because connections are much more abstract. We can typically touch and hold things, but not connections. Connections are also typically much more complex. For every one thing, we can have possibly an infinite amount of connections and thus networks very quickly take us into the world of complexity. In order to understand this way of seeing the world, we need to first appreciate the connectivity creates a new kind of space. We're very much used to a linear conception of space, what is called Euclidean space. It is the space that we walk around in every day, and we see all these people and things that have certain properties to them, but now imagine you pull out your mobile phone and it's almost as easy to call a person just next door as it is to call someone on the other side of the planet. This connectivity creates a new kind of space, where our traditional linear conception of space is being stretched and distorted by this connectivity. Connectivity then creates a non-linear type of space, and that space is better called a topology. Topology is a branch of mathematics that can be used to abstract the inherent connectivity of objects while ignoring their detailed form. In its most general definition, topology means the way in which constituent parts are interrelated or arranged. Thus for any set of things or people, we can have a different set of global rules for how they are interrelated or connected, and this is a topology. So why should we care about any of this? Because as we noted, networks are all about connectivity, and connectivity is an exchange along which something will flow. Along every connection, there is a flow of something. In a communications network, information flows. In a financial network, assets flow. In a political network, power flows. If there is no flow, there is no network. So to understand any given network, we're going to have to understand how something flows through that particular topology. The topology is the environment, and the flow is the connectivity within that environment. As we are analysing social systems here, this environment may be a physical one where we are talking about basic demographics, the movement of people, migration, the spreading of viruses, urban transportation etc. All of these are social connections that take place within a physical environment. But also we can have an economic environment, giving us networks of financial and economic connections. We can also have a political environment through which power flows, a cultural environment through which beliefs, values and ideologies flow. All of these are very different topologies with different forces acting on them. In order to understand these networks, we need to understand these forces that are acting within that environment and shaping the formation of the network. There are really two different ways to start analysing a network, by either taking a bottom-up perspective where we're talking about the agents, why and how they make connections, or a more global perspective where we're looking at the overall network and the environmental context to see how this shapes the system of connections. Within any social network, we have some agent that is choosing to make that connection. Agents typically make connections based upon some assessment of the return on their investment of time, energy, interest, social capital or some other resource that they value. We make friends with people whose company we like. We believe in ideologies that we value. We watch television channels that we find engaging. These are all connections that we make because we value what we get more than what we have to give in making the connection. But there is also the context or environment within which an agent is acting and that environment is exerting some force resisting or enabling them to make that connection. As an example, we might think about an oppressive political regime that uses intimidation, coercion and propaganda to prevent people from forming counter-political movements. This is a form of resistance. The agents have to overcome their fear in order to make political connections within this environment. So we can understand this environmental context as a form of transaction cost, a cost that is being placed on an agent for them to make a connection. Inversely, it might not be a cost but a payment where the environment is conducive to them making that connection. We might think about an ecosystem as an analogy where when we turn down the temperature, all the creatures hibernate and when we turn it up, they come out and interact. The cost of making a connection is typically not evenly distributed out. Some options will be easier or more difficult than others. This is like water running through some rocks where it searches for the course of least resistance. So these are very general considerations but they will help us in contextualizing and understanding the nature of the whole network, the kind of forces that it's under. Contextual network science is quite an analytical approach and networks are quite abstract representations. This makes them powerful tools but it's also important not to do sight of the fact that these networks exist within some context and for us to understand the general nature of that context or else we can get blinded by the tools. Because networks are all about connectivity and the processes taking place through those connections, a central and overarching question will be that of network integration. One of the most important factors with respect to the nature of any society is the question of social cohesion or structural cohesion where we're really asking about the degree of integration to the overall system as this correlates to such things as social solidarity, shared norms, identity, collective behavior etc. The idea of social capital is often used as a metric to a society's degree of cohesion. Social capital may be defined as the network of relationships among people who live and work in a particular society enabling that society to function effectively. So from this perspective when we ask what is the difference between a socially functional urban community and a socially dysfunctional ghetto, we would say that there is some integration within the first that enables the flow of economic resources and social capital. While we would say that the second represents a disintegrated network that inhibits the flow of these resources disconnecting it from the broader social system and rendering it dysfunctional. Put very simply of central interest here is how something flows through the whole social network as it is this flow that gives it cohesion. This is obviously a very big and fundamental question when analyzing any social system. How integrated the whole system will be is determined by many different factors. A primary consideration is the density of connections within the whole system. Clearly the more connected it is the more integrated it will be going from a system with a low level of connectivity to one with a high level represents a very different overall dynamic. At a low level of connectivity we're really just dealing with a group of people. At a high level we actually have a network system. This fundamentally changes the dynamic and we'll be discussing this in a future module. A second key consideration affecting the overall integration to the social network is its degree of clustering. Clustering is one of the few universal features found in almost all social networks from the social networks of ancient hunter-gatherer tribes in Africa to today's global networks. Clustering is derived from the fact that people form connections to people with similar attributes themselves. What is called homophily and out of this we get global patterns consisting of local communities that have their own distinct structure. These clusters give social networks a distinct heterogeneity to their topology that makes them somewhat resistant to the uniform spreading of some phenomena. Another widely encountered phenomena within social networks is that of short path length meaning that although a social network may be quite large in terms of its number of members and despite the fact that they contain significant clustering we often find that in these social networks any member is connected to any other by just a few links and this is where we get the famous six degrees of separation hypotheses from. This average path length is again a key metric with respect to the overall integration of the social network. We're all aware of how social solidarity can break down as we scale the community up. The traditional mechanisms for social solidarity that work for thousands of years as we lived in small rural communities breaks down in large urban centers and this disintegration of social solidarity is still one of the great challenges that the modern era has presented. This metric of average path length is very important to social cohesion as it is a primary factor in determining how close everyone will think they are to each other and the overall degree of interdependence and cohesion to the whole system. Finally the last almost universal feature to social networks is a very high degree of inequality between how connected people are within the network. Here we're talking about degree distribution. A high degree distribution means some people have lots of links while others have very few and we often see that this inequality and connectivity is quite extreme. In fact it often follows a power law distribution meaning that there will be some who have a very high level of connectivity such as some celebrity might have. Again there is a positive feedback loop driving this that we'll be discussing in a future module but this degree distribution parameter is again another important determinant to the level of social integration. A low degree distribution gives us a somewhat egalitarian society with the topology having a certain evenness to it through which the same phenomena can flow to all members of the network and this is in contrast to the many socio-cultural systems we see that are in fact highly centralized with significant degrees of inequality and connectivity that creates some resistance to a uniform spreading. In this module we've been taking a very high-level view to social network analysis. We've talked about how connectivity creates a certain kind of space or what we call the topology that stretches and distorts our traditional conception of linear space. We discussed how reasoning about the general forces that are acting on a network can help us in providing some overall context to our analysis where we need to consider both the rules under which the agents are making the connections and the environmental context that affects those choices either enabling them or constraining them. We then went on to talk about some of the primary considerations to a social network's overall makeup and social cohesion. We touched upon the topic of network density as a primary factor. We talked about clustering that creates local communities and a heterogeneous topology. We cited average path length as another key factor to the system's overall cohesion and lastly mentioned degree distribution as a metric for the degree of equality within the system.