centralization | R Documentation |

`Centralization`

returns the centralization GLI (graph-level index) for a given graph in `dat`

, given a (node) centrality measure `FUN`

. `Centralization`

follows Freeman's (1979) generalized definition of network centralization, and can be used with any properly defined centrality measure. This measure must be implemented separately; see the references below for examples.

centralization(dat, FUN, g=NULL, mode="digraph", diag=FALSE, normalize=TRUE, ...)

`dat` |
one or more input graphs. |

`FUN` |
Function to return nodal centrality scores. |

`g` |
Integer indicating the index of the graph for which centralization should be computed. By default, all graphs are employed. |

`mode` |
String indicating the type of graph being evaluated. "digraph" indicates that edges should be interpreted as directed; "graph" indicates that edges are undirected. |

`diag` |
Boolean indicating whether or not the diagonal should be treated as valid data. Set this true if and only if the data can contain loops. |

`normalize` |
Boolean indicating whether or not the centralization score should be normalized to the theoretical maximum. (Note that this function relies on |

`...` |
Additional arguments to |

The centralization of a graph G for centrality measure *C(v)* is defined (as per Freeman (1979)) to be:

*
C^*(G) = sum( |max(C(v))-C(i)|, i in V(G) )*

Or, equivalently, the absolute deviation from the maximum of C on G. Generally, this value is normalized by the theoretical maximum centralization score, conditional on *|V(G)|*. (Here, this functionality is activated by `normalize`

.) `Centralization`

depends on the function specified by `FUN`

to return the vector of nodal centralities when called with `dat`

and `g`

, and to return the theoretical maximum value when called with the above and `tmaxdev==TRUE`

. For an example of such a centrality routine, see `degree`

.

The centralization of the specified graph.

See `cugtest`

for null hypothesis tests involving centralization scores.

Carter T. Butts buttsc@uci.edu

Freeman, L.C. (1979). “Centrality in Social Networks I: Conceptual Clarification.” *Social Networks*, 1, 215-239.

Wasserman, S., and Faust, K. (1994). *Social Network Analysis: Methods and Applications.* Cambridge: Cambridge University Press.

`cugtest`

#Generate some random graphs dat<-rgraph(5,10) #How centralized is the third one on indegree? centralization(dat,g=3,degree,cmode="indegree") #How about on total (Freeman) degree? centralization(dat,g=3,degree)

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