Network topology refers to the overall make-up and structure to a network, with the word topology meaning the way in which constituent parts are interrelated or arranged. Within the context of network theory, it defines the way different nodes are placed and interconnected with respect to each other and the overall patterns that emerge out of this. The network diagram on the right illustrates a set of simple networks, each containing the same amount of nodes but each having a different overall topology owing to the way it is connected. We can see how these different network topologies would, in turn, have very different features and properties to them. The networks illustrated may be different transportation systems in which one is trying to get from A to B. In the star topology, it would only ever take one or two hops to reach the destination, but in the ring, it might take 3, the tree structure possibly 4. And this same influence from the topology would apply if we were trying to route water through a hydraulic network or electricity on a power grid, likewise, these networks could also represent the flow of information within a national society.
The overall topology of a network is often a product of the local interactions between the nodes. For example, someone builds a protocol for two computers to exchange information over a network and shares it with a colleague. Other people see the utility of it and connect to this little network, and then more people as the network grows, until 25 years later we have a massive network of networks that is the internet. No one planned the internet just as one really planned the global financial networks that have emerged over the past few decades. Traders, investors, and institutions set up connections wherever they thought there was a viable return on investment. But now that these networks are here, their overall markup feeds back to affect us the users. Networks may start out quite random but they often develop into some stable overall structure, and understanding the patterns to this overall structure is of central importance in network theory.
Some of the most important factors influencing the overall topology to a network include; its degree of connectivity, the number of nodes in the network, and its overall pattern of connectivity, i.e. how centralized or distributed it is. With connectivity, we are really talking about the density of the connections in the system. The degree of connectivity will largely be a product of how easy or difficult it is for any two nodes to form a connection. As we reduce the barriers to interaction, we will see the network become denser, integrated and increasingly defined by the structure and make-up of the network, as opposed to the components in isolation. Another macro-scale property to the network that is of importance with respect to its overall topology is its size. By size, we simply mean the number of nodes. This may sound like a trivial factor but scale can matter, as sometimes more is not just more – it can, in fact, be different. Think about living in a small rural community where everyone knows everyone by just one or two degrees of separation vs. living in a large urban metropolis where the anonymity of much longer path lengths between people creates new types of social dynamics. Lastly, the network’s overall pattern of connectedness is an important factor. The way in which a network is connected plays a large part in how networks are analyzed and interpreted. Due to some common set of properties shared by a subset of the system, we often get subsystems forming within networks. These subsystems are called clusters and often have a significant effect on the networks makeup. For example, we might think here about the clustering in the different cultural groups around the world. Although two cultures like that of France and Italy are different, they share a common Greco-Roman heritage that gives them and other European countries a set of common features through which they form a cultural cluster within the network of global cultures.
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