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An overview of network centrality measures and metrics used to determine the importance of nodes in a network. Centrality measures include degree, betweenness, closeness, eigenvector, and others. The document also discusses the significance of centrality in various contexts and provides examples of centrality calculations.
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Measures and Metrics
various useful quantities or measures that capture particular features of the network topology.
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network centrality
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indegree
In each of the following networks, X has higher centrality than Y according to
a particular measure
outdegree betweenness closeness
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divide by the max. possible, i.e. (N-1)
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(can use other metrics, e.g. gini coefficient or standard deviation)
C (^) D =
C (^) D ( n
[ )^ −^ C^ D ( i )]
∑
[( N −1)( N − 2)]
How much variation is there in the centrality scores among the nodes?
maximum value in the network
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example financial trading networks
high centralization : one node trading with many others
low centralization : trades are more evenly distributed
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when degree isn’t everything
anywhere in the network reaches you… 14
betweenness: another centrality
measure
have to go through you in order to reach one
another in the minimum number of hops?
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Y X
j < k
'
number of pairs of vertices excluding the vertex itself
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betweenness of vertex i
paths between j and k that pass through i
all paths between j and k
betweenness on toy networks
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betweenness on toy networks
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broker