 In this module, we'll be talking about social networks on the micro level, looking at agents and their local community. We'll quickly talk about the basics of social graphs before going on to discuss a number of different metrics for trying to understand how significant an agent is within any given network. Finally, we'll discuss interpersonal ties as we talk about strong and weak connections. The basic constituents of a social graph are nodes and edges. Nodes are people or groups of people. Edges, also called ties, represent the relationships between the social actors, which can come in many different kind, such as friendship, kinship, colleague, etc. These edges may be weighted, meaning that we can ascribe some quantitative value to them, such as the amount of time one person spends talking to another. We can also ascribe positive or negative values to these weights to depict positive or negative relations, such as trust or lack of trust, loans or debts, etc. These edges can also be directed, giving us an idea to which direction the resource being exchanged is flowing, with this net flow being depicted by an arrow. Here we can have unidirectional relations that go only in one direction, such as the influence that a celebrity might have on others without this influence being reciprocated, or it might be a bidirectional relation, like a typical friendship, with each influencing each other. A primary question we're often interested in when looking at the individual agents within a network is not so much to do with their properties in isolation, but instead asking how influential they are within that network based upon their connections. This measurement of how influential or powerful an agent is within a given network is called centrality. Almost all sociologists would agree that power and influence are fundamental properties of social structures. Network thinking has contributed a number of important insights about social power and influence. Perhaps most importantly, the network approach emphasises that power is inherently relational, an individual does not have power in the abstract, they have power because they can dominate others and ego's power is an altars dependence. And this metric of centrality is a primary tool for helping us in modelling how the social structure of relations gives agents influence and power. Social network analysis has made important contributions in providing precise definitions and concise measurements to this idea of power and influence based upon an agent's position within a social structure of relations. Because a network can be considered a description of the paths along which something flows, the significance of any agent to that network can be understood in terms of how much the network's resources flow through that node and how critical it is to that flow. As both of these factors will give the agent the capacity to influence whatever is flowing and it is from this that they get their influence within the network. Whereas influence and power are well defined within a hierarchical social structure, networks are not so orderly. Influence is often context dependent and of course we should remember that being central within a network is not always a good thing, it works both ways. Policy measures are really just telling us how embedded an agent is within that social network. Network analysis often describes the way that an actor is embedded within a relational network as both imposing constraints on the actor and also offering the actor opportunities. Social actors that face fewer constraints and have more opportunities than others are said to be in a more favourable structural position. Having a favourable position means that actors may extract better bargains in exchanges, have greater influence and that actor will be a focus of deference and attention from those in less favourable positions. But what do we mean by having favourable positions and having more opportunities or fewer constraints? There is no single and correct final answer to these difficult questions. Trying to capture how influential an agent is within a network is not trivial, it's quite complex in reality and thus researchers in network science use a number of different metrics including degree centrality, closeness centrality, betweenness centrality and prestige centrality. Social actors who have more ties to other people may be in advantageous positions. Because they have many ties, they may have alternative ways to satisfy their needs and hence are less dependent on other individuals. Because they have many ties, they may have access to and be able to call on more of the resources of the network as a whole. Because they have many ties, they are often third parties and deal makers in exchanges among others and are able to benefit from this brokerage. And thus the primary measure to the significance of any actor within a network is his or her degree of connectivity, which is simply how many connections they have and the weight of those connections if relevant. This tells us the likelihood of a node contacting or being able to affect in some way whatever is being exchanged within their immediate locality in the network. Degree of connectivity tells us something about their embeddedness within that network. Thus a higher degree of connectivity may be a positive or negative thing depending on what is spreading within the network. A node with a high degree of connectivity is called a hub, but this simple degree of connectivity measurement is a very blunt way of interpreting a node's significance that can often be misleading and will need a number of other metrics to support it. Closeness centrality is another metric for interpreting a node's significance, one that looks at how far it is from any other node in the network as distance is assumed to be a restriction on transmission. Thus whatever agent is closest to all others has the greatest capacity to affect them. Betweenness centrality is a third metric quantifying how often a node acts as a bridge along the shortest path between any nodes in the network. This gives the agent influence in that it can play a role to reduce the distance between any two nodes, thus significantly helping to hold the network together by reducing transaction costs. The institutions that work as market makers within the financial system are a good example of this. They are working as critical bridges between agents and organizations, holding the network together and for doing this they can demand significant transaction fees. This is also called occupying a structural hole, meaning that the agent who is working as a link between two clusters is filling some gap within the network that is critical in maintaining its overall integration. This actor is bridging two communities and may play a critical role in transferring information or some other valued resource. For example, they may be transferring information between two different scientific domains or playing a critical role as mediator during periods of conflict between two clustered communities. Lastly, prestige centrality, which is really looking at how connected the nodes that you are connected to are. These prestige metrics such as eigenvector centrality assign relative scores to all nodes in the network based on the concept that connections to high scoring nodes contributes more to the score of the node in question than equal connections to low scoring nodes. So your centrality and influence is greater if the people you are connected to are well connected. The assumption is that each node centrality is the sum of the centrality values of the nodes that it is connected to. Next, we'll talk about the local connections that agents make, what are called interpersonal ties. As we previously discussed, making connections typically cost something in terms of resources. Laying cables to transport information costs money. Making new friends or developing a diplomatic relation with a new country takes time and effort. Added to this, we can recognize that making connections between different components typically requires more resources than making those same connections between similar components. Whether we're talking about connections between computers with different operating systems, trade between countries with different import procedures or communications between different cultures, the fact that it requires less resources to make connections between components with similar attributes is a key factor in the makeup of many networks and particularly so with social networks. It in many ways defines the difference between strong and weak ties that describe the intensity of interpersonal ties between social actors. A strong tie is between two agents that interact frequently and typically share similar attributes, thus they are connections that are typically easier for us to enact. Inversely, a weak tie connects people between different social circles that can be more challenging in that they require the agents to overcome some difference between the groups, but they also expose the person to novel phenomena and information. The strength of an interpersonal tie is a product of many different factors, it may be a combination of the amount of time, the emotional intensity, the intimacy or some other reciprocal service that is exchanged within that relation, the greater the exchange, the stronger the tie. Most of the time, most people interact through strong ties with a fairly small subset of others, many of whom know one another and this creates a distinct substructure within the network. What is called a cluster and this clustering pattern is an almost universal feature to social networks. The clustering coefficient of a graph is a measurement of the degree to which nodes in a graph tend to cluster together. Social clustering can be understood by simply asking how many of the people that someone is connected to are also connected to each other. Evidence suggests that in most real world networks and in particular social networks, nodes tend to create tightly knit groups characterized by a relatively high density of ties and clustering. These closely knit clustered communities can maintain their diversity in the face of homogeneity within the larger network. The extent to which these subpopulations are open or closed may be a telling dimension of social structure. With too many strong ties, we can get strong clustering and a network that tends to be fragmented into local communities. These clumpy networks will have longer average path length relative to other networks with the same density and these clusters can slow the even flow across the network. Weak ties, in contrast to strong ties, connect people to different social circles. As such they are bridging ties that expose people to new information and novel phenomena. Specifically, more novel information flows to individuals through weak ties rather than strong ties because our closest friends tend to move in the same circles that we do. The information they receive overlaps considerably with what we already know. Acquaintances, by contrast, know people that we don't know and thus receive more novel information. When we combine both strong links within clusters and these weak bridging links, we get an efficient network for spreading information even though it may have high clustering. This type of social graph that has both high clustering and some random bridging links, giving it a low average path length is called a small world network. These characteristics result in networks with the unique property of regional specialisation and efficient long range information transfer. Social networks are intuitive examples of this small world phenomena in which clicks or clusters of friends are strongly interconnected but also people often have some random acquaintances within other far off groups. By using these weak ties we find that even in very large social networks consisting of many millions or even billions of people, any person may be only 5 or 6 links away from anyone else within the system, giving us the famous 6 degrees of separation theory. This small world phenomena seems to have evolved independently in many large networks. Thus we can see how these micro level interactions of agents choosing to make strong or weak ties can give rise to overall properties to the network such as its average path length which we can see is important to its overall integration and cohesion. These simple graphs that we've been discussing so far allow for just one type of connection between nodes but we can also have multiplex graphs that allow us to model a number of different relations between agents. So in a multiplex graph we would draw two different edges between people to describe how they might be work colleagues but also friends. Of course this adds a significant amount of complexity to our model but it gives us a much more realistic representation as social actors are often embedded within a multiplicity of different networks, social, political, cultural, economic and so on. With a multiplex network we can try and capture how these different connections interact and affect each other. This is a much more realistic picture that lies behind many social phenomena and a lot more faithful to one of the basic premises of complexity theory, that is that many phenomena are in fact a product of a multiplicity of forces interacting in a non-linear fashion. As a quick example we might think about the recent uprisings in Egypt. When we first look at this phenomena we would consider it political in nature and might start analysing the political network but research has shown a robust correlation between upward spikes in the price of basic foods and the occurrence of these riots. Thus these events are an emerging phenomena of different interacting networks, social, political and economic, all interacting and putting stress on the social system. In this situation it would be of use to use a multiplex network in trying to model the overall dynamic. Social phenomena like this are very complex in nature, they are embedded within many different overlapping networks. Simply modelling one of these networks can only ever give us a partial insight and this is the nature of complex systems of all kind. They are multi-dimensional. In this module we've been looking at social networks on the micro level, talking about local communities. We started off by laying down the basics of graph theory and talking about centrality measures that can help us in trying to model how influential or powerful an agent is within any social network based upon the structure of connections. We talked about four different metrics citing degree of connectivity as a primary consideration. We talked about closeness centrality, betweenness centrality and prestige centrality. We then went on to talk about interpersonal ties that are divided into strong and weak. Strong ties being typically between people with similar attributes that interact more frequently and intensely while weak ties are somewhat random in nature working to bridge between different communities and playing an important role in transferring information. We went on to talk about clustering and how a combination of both strong clustering and some random weak ties can give us the small world phenomena with a surprisingly low average path length even within very large networks. Finally we touched upon the topic of multiplex networks in order to get more complete representations of complex social systems as the product of the interaction between a number of different networks.