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In this module, we talk about one of the key concepts in network theory, centrality. Centrality gives us some idea of the node’s position within the overall network and it is also a measure that tells us how influential or significant a node is within a network although this concept of significance will have different meanings depending on the context.

Transcription:

In the previous module we talked about the degree of connectivity of a given node in a network and this leads us to the broader concept of centrality. Centrality is really a measure that tells us how influential or significant a node is within the overall network, this concept of significance will have different meanings depending on the type of network we are analyzing, so in some ways centrality indices are answers to the question “What characterizes an important node?”

From this measurement of centrality we can get some idea of the nodes position within the overall network. The degree of a node’s connectivity that we previously looked at is probably the simples and most basic measure of centrality. We can measure the degree of a node by looking at the number of other nodes it is connected to vs. the total it could possibly be connected to. But this measurement of degree only really captures what is happening locally around that node it don’t really tell us where the node lies in the network, which is needed to get a proper understanding of its degree centrality and influence.

This concept of centrality is quite a bit more complex than that of degree and may often depend on the context, but we will present some of the most important parameters for trying to capture the significance of any given node within a network. The significance of a node can be thought of in two ways, firstly how much of the networks recourses flow through the node and secondly how critical is the node to that flow, as in can it be replaced, so a bridge within a nations transpiration network may be very significant because it carries a very large percentage of the traffic or because it is the only bridge between two important locations. So this helps us understand significance on a conceptual level but we now need to define some concrete parameters to capture and quantify this intuition.

We will present four of the most significant metric for doing this here;

Firstly as we have already discussed a nodes degree of connectivity is a primary metric that defined its degree of significance within its local environment. Secondly, we have what are called closeness centrality measures that try to capture how close a node is to any other node in the network that is how quickly or easily can the node reach other nodes. Betweenness is a third metric we might use, which is trying to capture the nodes role as a connector or bridge between other groups of nodes. Lastly we have prestige measures that are trying to describe how significant you are based upon how significant the nodes you are connect to are. Again which one of these works best will be context dependent.

￼So to talk about closeness then; closeness maybe defined as the reciprocal of farness where the farness of a given node is defined as the sum of its distances to all other nodes. Thus, the more central a node is the lower its total distance to all other nodes. Closeness can be regarded as a measure of how long it will take to spread something such as information from the node of interest to all other nodes sequentially; we can understand how this correlates to the node’s significance in that it is a measurement of the nodes capacity to effect all the other elements in the network.