gilschmidt | R Documentation |

`gilschmidt`

computes the Gil-Schmidt Power Index for all nodes in `dat`

, with or without normalization.

gilschmidt(dat, g = 1, nodes = NULL, gmode = "digraph", diag = FALSE, tmaxdev = FALSE, normalize = TRUE)

`dat` |
one or more input graphs (for best performance, sna edgelists or network objects are suggested). |

`g` |
integer indicating the index of the graph for which centralities are to be calculated (or a vector thereof). By default, |

`nodes` |
list indicating which nodes are to be included in the calculation. By default, all nodes are included. |

`gmode` |
string indicating the type of graph being evaluated. |

`diag` |
boolean indicating whether or not the diagonal should be treated as valid data. (This has no effect on this index, but is included for compatibility with |

`tmaxdev` |
boolean indicating whether or not the theoretical maximum absolute deviation from the maximum nodal centrality should be returned. By default, |

`normalize` |
logical; should the index scores be normalized? |

For graph *G=(V,E)*, let *R(v,G)* be the set of vertices reachable by *v* in *V \ v*. Then the Gil-Schmidt power index is defined as

*
C_GS(v) = sum( 1/d(v,i), i in R(v,G) )/|R(v,G)|,*

where *d(v,i)* is the geodesic distance from *v* to *i* in *G*; the index is taken to be 0 for isolates. The measure takes a value of 1 when *v* is adjacent to all reachable vertices, and approaches 0 as the distance from *v* to each vertex approaches infinity. (For finite *N=|V|*, the minimum value is 0 if *v* is an isolate, and otherwise *1/(N-1)*.)

If `normalize=FALSE`

is selected, then normalization by *|R(v,G)|* is not performed. This measure has been proposed as a better-behaved alternative to closeness (to which it is closely related).

The `closeness`

function in the sna library can also be used to compute this index.

A vector of centrality scores.

Carter T. Butts, buttsc@uci.edu

Gil, J. and Schmidt, S. (1996). “The Origin of the Mexican Network of Power”. Proceedings of the International Social Network Conference, Charleston, SC, 22-25.

Sinclair, P.A. (2009). “Network Centralization with the Gil Schmidt Power Centrality Index” *Social Networks*, 29, 81-92.

`closeness, centralization`

data(coleman) #Load Coleman friendship network gs<-gilschmidt(coleman,g=1:2) #Compute the Gil-Schmidt index #Plot G-S values in the fall, versus spring plot(gs,xlab="Fall",ylab="Spring",main="G-S Index") abline(0,1)

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