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# Katz Index
#
# Similarity measure based on all paths in a graph
#
# This function counts all the paths between given pair of nodes, with shorter
# paths counting more heavily. Weigths are exponential.
#
similarity_katz <- function(graph, v1, v2, beta = 0.001, ...){
A <- igraph::get.adjacency(graph)
#I <- Diagonal(nrow(A))
I <- diag(nrow(A))
tmp <- I - beta * A
score <- solve(tmp)
diag(score) <- 0
score[v1, v2]
}
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