The hyperbolic index is an index that considers all closed walks of even or odd length on induced neighborhoods of a vertex.

hyperbolic_index(g, type = "odd")

g | igraph object. |
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type | string. 'even' if only even length walks should be considered. 'odd' (Default) if only odd length walks should be used. |

A vector containing centrality scores.

The hyperbolic index is an illustrative index that should not be used for any serious analysis. Its purpose is to show that with enough mathematical trickery, any desired result can be obtained when centrality indices are used.

library(igraph) g <- graph.empty(n=11,directed = FALSE) g <- add_edges(g,c(1,11,2,4,3,5,3,11,4,8,5,9,5,11,6,7,6,8, 6,10,6,11,7,9,7,10,7,11,8,9,8,10,9,10)) hyperbolic_index(g,type = "odd")#> [1] 0.000000e+00 0.000000e+00 1.276458e+00 4.218847e-15 9.186479e-01 #> [6] 3.554977e+00 3.554977e+00 1.925897e+00 1.925897e+00 5.995581e+00 #> [11] 1.501126e+00hyperbolic_index(g,type = "even")#> [1] 3.086161 3.086161 6.848357 3.570911 6.227501 11.664512 11.664512 #> [8] 8.585124 8.585124 16.291922 7.755459