In today's lecture we learned about network centrality. Centrality is a broad term that has a few different meanings based on the context in which it is used. If we know the structure of a network, then we can determine certain quantities or measures of a vertex's importance within the graph. We covered the first three of seven measures: degree centrality, betweenness centrality, and closeness centrality.
Degree centrality is the measure of how many edges are connected to a node. It is good for determining how important a node is based on its connections to other nodes. For instance, how many people you can access for information, the influence of an article in terms of citations, or the probability a computer will catch a virus based on its network connections. Degree centrality can be determined by Freeman's general formula for centralization. It is also important to normalize the centrality so that meaningful comparisons can be made between networks of different sizes.
Betweenness centrality is the measure of how many shortest paths involve a specific vertex. It is good for determining how important a node is in controlling the "flow" of a graph. Betweenness centrality can be determined by summing the number of geodesic paths connecting two vertices (j and k) that pass through the vertex in question (i) divided by all paths between j and k. If there is more than one node on a geodesic path between j and k, they will have to "share credit."
Closeness centrality is the measure of how many shortest paths a vertex has to all other vertices in the graph. It is good for determining how "close to the center" of a graph a vertex is. Closeness centrality can be determined by taking the inverse of the average geodesic distance from the vertex in question to all other vertices. Values of closeness tend to span a small range and there is little chance that a change in the graph will affect closeness to a great degree.
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