 Over the past few decades, with the rise of information technology and globalization, we've networked our global economy like never before. Both its technology infrastructure and its institutional superstructure have become increasingly integrated into dense, multimodal networks from the micro level of individual organizations all the way up to the global level through global cities and the global supply chains that they enable. We've increasingly interconnected our economies, bringing in frontier zones like the copper mines in Mongolia or small rural villages in Norway as they connect in to the ever denser set of connections between global cities. On top of all of this, we have built a global financial system of extraordinary complexity, financial networks that represent cross-linkages between assets and liabilities all over the planet, which can return that are sliced and diced and distributed out into the future through all sorts of derivatives, contracts and exotic instruments. And making all this happen are of course telecommunications networks on all levels. Previously, well-bounded organizations like national economies and corporations are scrambling to adapt to a massive wave of hyper-connectivity. As we see new, IT-enabled, networked organizations emerge and thrive in this connected economy of the 21st century. Suffice to say, networks are emerging as a fundamental organizational structure within post-industrial economies and understanding them is more relevant than ever. As we've previously noted, linear systems theory is a component-based theory, meaning it is primarily concerned with the properties of the components within the system, and this will be the same for any science that is using this framework, such as standard economics. When we look at a typical map of the world's economy, it will show us lots of countries in their GDP. When analyzing a corporation, we describe it by itemizing its gross revenue or who the CEO is and so on. All of these are descriptions of the system with reference to the properties of its components. This is a very valid and important approach to analysis, but it is only really relevant when we're dealing with a linear system that has a low level of connectivity. When we turn up the connectivity, the relations between the components starts to become the primary factor in determining the system's overall dynamics. In such a case, we need to use an alternative modeling framework that is better able to capture these relations and their structure, and this is exactly what network theory does. Network theory, also called graph theory, is one of the very few major modeling frameworks within complexity theory. It is an abstract formal language which is really about this big idea of connectivity, which is a whole paradigm shift because we are naturally programmed to see things and not so much connections. Thus, this world of connectivity is very different to the one that we're used to. It is all about access, where you lie in the network, what is the overall structure to that network and what is flowing through it. As is always the case, it is important to understand what the modeling framework is designed to do before you start to use it. Network theory is designed to let us focus on the relations between components and the structure of those relations in both a qualitative and a quantitative fashion. As such, we will very rarely be talking about the components themselves, so it offers us then just one perspective on the whole system. It is an abstract modeling framework and things can get complex very quickly, so like all models, we should only use it when appropriate. It all starts with a node and an edge. A node is a thing like a bank, a business or a country. An edge is a connection between two things, like the trade of oil between two countries, an investment between a bank and a business, or a purchase transaction between a retailer and a customer. Both nodes and edges can have values associated with them that denote the size of the node or the volume of exchange within the edge. Edges can be directed or undirected, indicating the net flow of resources along the edge. In a multigraph, we can have many different edges between any two nodes. For example, each edge might represent the trade of different goods between two nations, so this is the very basics of the language of graph theory. Because this is all about connectivity, when we're analyzing a particular node in a network, such as a corporation within a supply chain network, our first question will often be how connected is that node? That is to say, how many links does it have with other nodes in the network? This is called its degree of connectivity. The node's degree of connectivity will define how likely it is to receive whatever is flowing within that network. So if our corporation was part of a supply chain network for the production of tractors, its number of links might define how many of the parts for that tractor flow in or out of this organization. Degree distribution will not be the only factor determining its significance within the network, but it will be a primary one and the most straightforward one for us to try and measure. How important a node is within a network is a function of both how much of the network's resources are flowing through it and how critical that node is to the network. So for example, the Pearl Delta economic zone in southern China, although only about 3% of the nation's population, represents about 35% of the country's total international trade. Thus this node plays a very significant role within the economic network due to the sheer volume of resources that flow through it. Panama also plays a critical role within the global supply chain, but this time it is because it is the only viable sea route between the Pacific and Atlantic, thus it is what is called a bridging link. It performs a differentiated function that the rest of the network requires, giving it significance within the entire network. A node's real significance within a network, what is called its centrality, is quite a complex feature to analyze. Added to these two factors previously mentioned, we need to also take account of its location within the overall network, asking how close is it to all the other nodes, thus how quickly it could affect them and also how connected the nodes that this node connects to are. As an example of centrality analysis, we might think about government bailouts during a financial crisis. As the government is interested in maintaining the functionality of the entire network, it needs to ask these questions that were previously mentioned. How many links does this bank node have and what volume are those links? Does the node play some critical role within the financial network that no other institution could perform? How closely connected is it to all the other nodes and how important are the other nodes that it is directly connected to? By answering all these questions, they will be able to get some understanding to its importance in maintaining the entire network. When we're looking at the whole of a network, probably the single most important parameter is the system's overall density. The density of the network is defined as a ratio of the number of edges to the number of possible edges. As we turn up the probability of there being a link between any two nodes, we will get a more dense network, starting from zero density where no nodes are connected to complete density where all nodes are interconnected. We can then define a parameter for adding links, which is really capturing how easy is it for a node in the network to make a connection with any other. We might call this the transaction cost. When the expense of making a transaction is high, there will be few connections. As we turn it down, we will get the emergence of a dental network. For example, these transaction costs might represent trade barriers, placing a greater transaction cost on international trade. As we've reduced these trade barriers through liberalization, we've seen the emergence of globally integrated supply chains. Network density is an important parameter in that it will define the difference between a component-based system at a low level of density where the value of an element in the system is really in that node, such as a business or some technology, which is relatively isolated. The value of it is bound within the organization. When we turn up the density and the number of connections, this is no longer so. The component's value is increasingly outside of it in the network of connections it has with other nodes. In the way that a smartphone has value because we can connect it to many different services via the internet or a business has value derived from its place within a supply chain network. But networks don't always grow in a nice linear fashion, but due to the positive feedback of the network effect, we can get non-linear exponential growth as we've witnessed with the rise of the internet, which stayed relatively dormant for a number of decades before reaching a critical mass and then growing rapidly, and now there is a huge amount of value not in any one organization, but in the network of connections that gives us access to them. Thus, by reducing transaction costs low enough, this is led to a powerful network effect taking hold. A second key factor that we'll be interested in when analyzing an entire network is in asking how close are any two nodes in the network on average, what is called the average path length, which will be a function of both the number of nodes in the network, how connected they are, and the overall structure to the network. Average path length is important because it defines how close agents are to each other. Agents operating in a system where they are very far from others will create different behavior to when they have the appearance of being very close to everyone else. We might think about globalization. Through increased connectivity that has reduced the path length, we suddenly start to feel much closer to everyone else, creating a much greater sense of interdependency. Because of these shorter path lengths, externalities become much more important and immediate. So far, we've been talking about monoplex networks, meaning that with these relatively simple graphs, we're looking at just one type of network. Each node and edge in it only serve one type of function, but the real world is typically a lot more complex than this. When analyzing a large system like a metropolitan economy, a corporation, or the global commodity markets, what we're dealing with is a network that is embedded within many other networks. Our metropolitan area will be a complex system where economic interactions are embedded within sociopolitical networks, transportation and geospatial networks, financial networks and so on, all of which will strongly influence the flow and distribution of economic resources. This is clearly going to add a whole new level of complexity to our representation, but in order to do this, researchers have developed what are called multiplex networks. In a multiplex network, each type of interaction between the nodes is described by a single layer network, and the different layers of networks describe the different modes of interaction. Multiplex networks are clearly much more advanced representations of how these systems really operate through the interaction of many different functional domains. Multiplex networks lie at the forefront of contemporary research in network science, with a vast amount of untapped potential. Lastly, as we've tried to illustrate here, connectivity fundamentally changes the dynamics of an economic system. As such, it also alters how we should go about designing and managing them. At a low level of connectivity in a component-based regime, we traditionally try to intervene by directly altering the components in the system. For example, a government tries to improve its economy by starting a big infrastructure project, or we try to get people to buy things by bombarding them with advertisements. But with networks, it's all about designing and managing the connections. You get a person to buy a product by influencing their social network. Your country's economy grows by connecting it into global supply chain networks. This is economic or financial systems design and management by connecting or disconnecting things. The wealth is in the network. If you want more of something, you restructure its connections and position within the network to make it more receptive to the flow of resources, or if you want to diminish it, you disconnect it. In this video, we'll be looking at the basics of network theory as applied to economics. We talked about how connectivity is a very fundamental feature to systems, and once we reach a certain critical level of connectivity, things get flipped around and the focus becomes the structure and nature of these networks of connections. Where we start to form a description of the nodes, not in terms of their properties in isolation, but instead start asking questions like how connected is any node? How important is it to the whole network due to the volume of resources that flow through it, or its degree of irreplaceability in serving some differentiated function? We talked about the density of connections within a network being a primary factor when looking at the whole system. How this density is influenced by the cost of transaction, and when we reduce these transaction costs low enough, this can lead to a powerful network effect taking hold. Finally, we talked about multiplex networks that can give us a representation of an entire complex economic system as a set of many interacting networks and talked about how our design and management approach will change when given heightened connectivity.