Network Theory Topology
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Tology simply means the way in which constituent parts are interrelated or arranged. To illustrate how network topology affects the system we look at a number of simple networks each containing the same amount of nodes but each having a different overall topology owing to the way they were connected with these topologies affecting different features to the network, such as the shortest path length or how we might control the flow of information on the network.
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In the previous module, we were discussing local network metrics that referred to a single node in a graph, asking how connected it was or how influential and central it was while also building up our basic vocabulary from graph theory. In the coming set of lectures we are going to be looking at global metrics that refer to the whole of graph. A we have previously noted networks are a very informal type of structure they often simple develop without any overall top down design. 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 connects to this little networks and then more people as the network grow, until 25 years later we have a massive network of networks that is the internet.
No one planned the internet just as one really planed the global financial networks that have emerged over the past few decades, traders, investor and institutions set up connections wherever they thought there was a viable return on investment, but now that these networks are here there overall markup feeds back to effect us the user, 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 and the focus of this section to the course.
We can call this overall structure to a network its topology, where topology simply means the way in which constituent parts are interrelated or arranged:
Within the context of a network it defines the way different nodes are placed and interconnected with each other and the overall patterns that emerge out of this.
To illustrate this further here are 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. Imagine they where different transportation systems in which you are trying to get form A to B. In the star topology it would only ever take you two hops to reach your 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 rout water through a hydraulic network or electricity on a power grid.
This network could also represent the flow of information within a national society we can see how the centralized star structure or the tree structure would be much easier for some political regime to control and influence as opposed to the more decentralized fully connected or ring network. The point I are trying to make clear is simply that networks have overall structure and this overall topology to the network matters as it feedback to affect the actions and capabilities of the nodes on the local level.