 Political network structure refers to the overall structure of connections within a sociopolitical organization and how that structure of the network affects individual members or organizations operating within it. Network theory can be seen to be particularly relevant to the analysis of political systems and power, in that power is typically understood as a relational phenomena, but likewise it is a structural phenomena also. Actors have power based not only on their inherent qualities, but more often based upon their location within a network and their degree of connectivity. By analyzing political networks, we can gain a deeper understanding of their true workings in terms of how the connections around actors shape and influence their actions and opportunities. Traditionally, we think of political organizations in terms of boundaries, we are very accustomed to looking at maps of the world in terms of fixed geography and national boundaries. However, such boundaries only illustrate how people are disconnected from each other, while networks offer us an alternative way of looking at the world in terms of connectivity which gives us a very different view of things. When we start to look at the world in terms of networks, we start to see connections. Boundaries become recontextualized as disconnections and organizations become defined in terms of their connections. However, they are most dense, that is where the organization is most well defined and such networks of connections create the political spaces that people inhabit. Political are not all-knowing creatures. In living their everyday lives, they interact with certain things and in so doing they become aware of those things and they become central to their interpretation of the world. Those things that they do not interact with become peripheral, they become in a certain sense less real to the individual. Political organizations are then formed out of these networks of interactions between people. For example, in the study of the geography of marriage ties in the English town of Kent during the Middle Ages, it found that 75% of people married people from within just 5 miles and 95% of people married others from under 15 miles from where they were born. The political organization of such a society, where connections are almost exclusively local, would have naturally been the localized feudal system of the Middle Ages. In this sense, connections create the space of the sociopolitical system and that space is altered whenever the connections are altered. Today of course, these connections are more dynamic than ever as we're in the process of building a global infrastructure of technology networks, air transport networks, telecommunications networks, financial networks, logistics networks, urban networks. Through all of these people interact and create new kinds of sociopolitical organizations. Increasingly, what governs our lives is not how we're divided from each other but in fact how we're connected through these networks. This is not necessarily a good thing or a bad thing but it is a paradigm shift in that it changes the rules of the game. This world of networks only makes sense in terms of connectivity. If one goes on thinking in terms of independence and borders, things stop adding up and stop making sense. Whereas a traditional conception of organizations, in terms of their boundary condition, creates a form of space that is defined by the objective metrics of geometry and geography. Connectivity creates its own kind of space, that space is called topology. The topology is the overall shape of the network. What defines networks is their structure of connections. In every network, something flows and it usually flows wherever it is easiest to flow. When one reconfigures the network, then one changes what people are connected to and likewise you change the organization, thus our primary focus here is on the structure of the connections in the network. A traditional network is a set of people or organizations and a set of relations between them through which they achieve common decisions and actions. These relations can be cooperative or conflictual. In the case of cooperative relations, we're dealing with the exchange of social capital where people share common vision and interests in an environment of trust. In the case of conflict, the relations can be of power where people's interests for the whole are divergent and actors try to exert some forceful influence over others for them to conform to their desired interests. A network can be an exceedingly complex structure as the connections among the nodes can exhibit a multiplicity of patterns. One challenge in studying complex networks is to develop simplified metrics that capture some elements of the structure in an understandable way. When analyzing such networks, there will be a few central questions of interest. For example, how influential is any given member or organization within the network? What is the disparity in influence between members? How centralized or distributed is the network? What is the degree of local clustering within the system? All of these structural characteristics to a network will affect how the resources are distributed out and how they flow through the system, which is in many ways the central question of interest. Answering these questions, though, will likely tell us little about the formal structure of the organization. That is to say the typical hierarchical organizational structure that institutions will present to the public. People can have a given role in a hierarchy without that actually meaning anything. Likewise, an organization can espouse certain ideals without that affecting how it actually operates. As we know, an organization can tell the public that it's doing one thing, when in fact it is really doing something very different, because connectivity typically defines functional exchanges. The system typically cannot have a pattern of connections and be doing something other than what those connections exhibit. That is to say, in network analysis, we collect real data about the exchanges between people, how many emails they sent to each other, what television channel or website they connected to for their news, how many times they visited a certain person that month, etc. These connections enable people and organizations to operate in the way that they actually operate. Such functional networks describe how the system works and not how it tells us that it works. And in political analysis, these two things often turn out to be very different. We can spend a lot of time talking about what the organization says it does, or should do, or is supposed to do. However, it is necessary to understand the network to understand how the system really operates and that means dealing with the complexity of the real patterns. With the traditional model, people's trustworthiness and reputation are largely given by their place within some formal organization. It is not actually tied to the thing that really matters, which is their actions. This creates a disjunction between the formal structures and the informal structures. For example, politicians say many things to get elected every four years, but in the meantime, their actions are influenced by all sorts of other forces that create a disjunction between the two. Networks and the feedback systems that operate through them define people by the connections they make and how they act in those exchanges. In such peer systems, people gain their status and reputation by the feedback from others in the network on an ongoing basis, continuously updated according to their interaction with others, instead of this being determined by appointments once every few years. And this creates a much closer match between formal and informal structures. As connectivity has increased, so has transparency and the public's capacity to see what is actually going on inside of these previously closed organizations. The result has been an endless stream of scandals revealed to people, from sexual abuses being covered up inside the Catholic Church to systematic corporate bribery to marital abuses to the spying of intelligence agencies. The institutions that societies, once held in the highest regard and trusted, are becoming ever more distrusted in the eyes of the public as hyperconnectivity brings down walls and reveals what was hidden behind them. Trust in these institutions is declining significantly. And nowhere is this more acute than in politics. With the rise of mass media politics, it has turned into what Emmanuel Castells calls scandal politics. The public's trust in the formal institutions of society in developed nations has dropped to a very low level, particularly for traditional political parties and politicians in general. Whereas an older generation may still be inclined to trust closed institutions, a younger generation that has grown up with the internet is more likely to trust feedback systems. They trust the network of their peers, more than they're inclined to trust formal closed institutions. The primary question people are typically interested in when first looking at a network is the question of how influential is any given node in the network. The simplest answer to this is in looking at how connected that node is. That is to say it's degree, which is simply how many links it has to other nodes in the network. This gives us an indicator of how likely anything that is spreading on the network will pass through the node's sphere of influence. The more connections, the more likely the actor is to receive it, and thus the greater its potential to influence things that are happening on the whole network. Simply put, if a node is not connected, then that node cannot influence anything. London and New York are central nodes within the global financial system because many financial transactions are processed through these nodes and that gives them the capacity to influence the system. For example, if you use a credit card to make a purchase in the city of Tehran in Iran, that transaction may be processed in New York. However, the opposite is not true. That you know financial transactions made in New York will be processed in Tehran. This gives central hubs like London and Hong Kong a certain kind of influence within the system that Tehran or Santiago, for example, do not have. Degree distribution is the simplest metric for measuring power and influence within a sociopolitical network, but there are many other metrics that also contribute to one's influence, including closeness centrality, which is measuring how far any given node is from any other within the network. The general idea is that if you can reach any other area of the network in just a few hops, then you must be in a more central location than another actor who is far away from others. Again, being central in this sense means you can easily reach others and affect them. Betweenness centrality is another metric determining one's influence. It measures how many times an actor functions as a connector or bridge in connecting other sets of nodes on the network. This metric captures the actor's importance as an intermediary or gatekeeper within the system. For example, some political analysts see Turkey and Poland as strategically important locations in the future because they're bridges between Europe and the Middle East or Eastern Europe in terms of their location within a multiplicity of networks. Physically, as Istanbul is the only physical bridge between Europe and the Middle East and Warsaw is a transport hub. Economically, through outsourcing to Poland, culturally, as Turkey is a combination of European and Islamic cultural traditions, while Poland is both a part of the Slavic community, while strongly connected to Western European sociocultural and political networks. This gives these social communities a kind of bridging power and influence as seen with the role Turkey is playing with the current immigration flow into Europe. Likewise, a node may have an influence of the network based upon the influence of the actors that it's connected to, which is the measure of centrality that tries to take into account the centrality of other nodes to which a node is connected. That is to say, being connected to someone that is highly connected makes you in turn more connected. For example, being the secretary of a CEO would give you this kind of connectivity. Some people are influential because they know a lot of other very influential people. Not only may we want to look at who is most influential within a given organization, but just as importantly, we may want to look at how power is distributed out across the whole system. This is understood in reference to what is called degree distribution. Degree distribution tells us how the connections are distributed out among the nodes. It can answer the question, do some members have lots of connections, while others have very few, or do all have a relatively similar amount of connections that makes the network relatively egalitarian in this respect? By counting how many nodes have each degree, we can form the degree distribution. For example, in the simplest type of networks, one would find that most nodes in the network have similar degrees. This would be characteristic of a network that was formed at random. The distribution will be a normal Gaussian distribution, with most people having around the same amount of connections. However, most real-world networks are not formed at random. They are formed by people making specific choices about who to connect with and the result is often not a normal distribution. Much research has been done on the subject in the past few decades and it's been found that in most real-world networks, we get something that approximates a power-law distribution, where most nodes have a relatively small degree, but a few nodes will have a very large degree, being super connectors in the network. The degree distribution then forms a parameter that defines how centralized or distributed the network is. The highest degree distribution corresponds to the most centralized network, which is a star network structure, where one node is connected to all others and thus has as many connections as it could possibly have, while all others just have one link. Such centralized networks, whose degree distribution follows a power-law, are called scale-free networks. When we turn down the disparity between the degree of nodes, the connections within the network become more distributed. We go from a centralized network with just one dominant node to a decentralized network to a distributed network, where the connections are evenly spread out across all the nodes. Power is always a function of a potential difference between entities. Power is relational and it is only realized in the difference between actors, in the same way that a ball will only roll down hill because there is a gravitational gradient between the top and bottom of the hill. It will not spontaneously roll horizontally between two points of the same elevation. If two things are the same, then neither has power of the other. Thus we can say that the higher the degree distribution within the network, the greater the potential power within that network. In a fully distributed network, there is no potential for power. In the same way, that a system of maximum entropy has no capacity to do work and network at maximum degree distribution has no potential to exercise power. And this makes sense intuitively. We know how easy it is to control and exercise power through a centralized communications network like a country with a single source of mass media where all channels lead to the same hub. If we affect that hub, we can influence the whole. In contrast, we know how difficult it would be to fully control the internet which has millions of distributed peer-to-peer interactions. We can ask then why centralized networks are so prevalent within real-world, social, economic, technological and political networks. The answer to this is typically found in two different models what are called the fitness model and preferential attachment. Both of these can result in a parallel distribution and centralized networks. In the fitness model, how the links between nodes changes over time depends on the fitness of nodes. Where fitness means the inherent competitive factor that nodes may have. Fitter nodes attract more links at the expense of less fit nodes. Thus a node can become prominent within a network purely through its own merits. For example, some people have more interesting things to say than others and people will want to connect to them. Some people are just better football players than others and people will want to watch them. In this way, a network can come to have nodes that have more connections and those that have less making it more centralized purely in a meritocratic fashion. In contrast, a node may accumulate many links due to what we call preferential attachment which is also called the Accumative Advantage or the Rich Get Richer. A preferential attachment process on a network is a process whereby the new connections that are made are distributed out among the nodes proportional to the number of connections that they already have so that those who already have a high degree receive more than those who are not so well connected. Such a process can also produce power-law degree distributions. This typically happens when it becomes easier for more people that have already chosen it and when people make their choice of connections based on ease of access rather than quality. For example, we might think about some man choosing to wear pink trousers with flowery patterns on them. When no one else is doing this, it would not be an easy option for clothing as people might laugh at him. But if pink flowery trousers suddenly became a fashion and lots of people were wearing them, it would be easier and people would wear them just to be fashionable like others. Thus we get the bandwagon effect where people are simply adopting something because everyone else is irrespective of any inequality of that thing. If the process of network formation is conducted in this way, we can see how major nodes may form irrespective of their quality. Likewise, preferential attachment processes can lead to lock-in effects because people are connecting to others based simply upon the number of connections that they already have. It becomes difficult for small nodes of merit to compete. Large nodes get larger irrespective of their quality and value. A corollary to preferential attachment is network clustering. That is to say, the degree to which the network forms tightly interconnected subsystems within the overall network. Intuitively, a cluster is a collection of individuals with dense friendship patterns internally and sparse friendships externally. Most social networks show high levels of clustering. This is due again to the fact that people do not connect to others at random but in fact connect with those that they find it easiest to connect to and this typically means connecting to those who share things in common with them, a similar culture and language or similar geographical location. Much political network analysis over the past few decades has looked at the clustering of communities around certain political parties on social networks. Political networks and power are very complex phenomena that are multi-dimensional in nature. Power within a large modern society is best thought of as a network of overlapping networks, each operating an exerting influence along a certain dimension. Each form of power is constrained not so much by how much of it people have but by the inherent limitation of any form of power that is to say by the basic logic of that source of influence. The military has a form of power in their capacity to project physical force against people but the use of physical force has a particular context instead of rules to it and those rules define what is possible with that power and what is not. The media, corporations, the financial institutions, schools, the scientific community and computer hackers all have different forms of power but each is inherently constrained by the rules of the game they're playing as we might say in game theory. Truly understanding such complex political structures in an analytical fashion requires a detailed analysis of the many overlapping networks and how they interact and this type of network model is called a multi-layer network. A multi-layer network is a network made of multiple network types each of which represents a given operation mode such as an economic network layered on top of a financial network layered on top of a social network, et cetera. Increasingly sophisticated attempts to model real-world systems as multi-dimensional networks have yielded valuable insight in the field of social network analysis over the past decades. These models reveal the true complexity of sociopolitical systems but are required to gain a full comprehension of how different factors interact to create emergent outcomes. This new paradigm in network science is believed to be the next step towards a better and more comprehensive understanding of social networks and political systems.