Network Closeness Centrality
From SONIVIS:Wiki
Network Closeness Centrality
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The Network Closeness Centrality calculates network's closeness centrality (normalized number of steps required to access every other node from a given node).
Objective
The Network Closeness Centrality calculates the mean of the Closeness Centrality of the whole network. The measure is standardized on the network size. The network closeness centrality has its maximal value if one node is linked to all other nodes in the network[1]. This network is called star network.
Calculation
![C_C= \frac{\sum_{i=1}^g [C_C (n*) - C_C(n_i)]}{[(g-2)(g-1)]/(2g-3)}\,\!](/wiki/images/math/3/7/b/37b22a08bf64e5f2b37f604b0d3a8457.png)
, where 
is the highest value of Degree Centrality of a node and 
the total number of nodes in the network. [1]
Statement
| R-example (igraph) |
| library(igraph) graph <- graph.star(10) sum(max(closeness(graph)) - closeness(graph)) /(((vcount(graph)-2)*(vcount(graph)-1))/(2*vcount(graph)-3)) |
