diff --git a/R/centrality.R b/R/centrality.R
index 29b1737a87..2e4f768c10 100644
--- a/R/centrality.R
+++ b/R/centrality.R
@@ -952,9 +952,8 @@ eigen_defaults <- function() {
 #' @param graph Graph to be analyzed.
 #' @param directed Logical scalar, whether to consider direction of the edges
 #'   in directed graphs. It is ignored for undirected graphs.
-#' @param scale Logical scalar, whether to scale the result to have a maximum
-#'   score of one. If no scaling is used then the result vector has unit length
-#'   in the Euclidean norm.
+#' @param scale `lifecycle::badge("deprecated")` The result is always scaled to have
+#' a maximum score of one.
 #' @param weights A numerical vector or `NULL`. This argument can be used
 #'   to give edge weights for calculating the weighted eigenvector centrality of
 #'   vertices. If this is `NULL` and the graph has a `weight` edge
@@ -990,7 +989,7 @@ eigen_defaults <- function() {
 #' @cdocs igraph_eigenvector_centrality
 eigen_centrality <- function(graph,
                              directed = FALSE,
-                             scale = TRUE,
+                             scale = deprecated(),
                              weights = NULL,
                              options = arpack_defaults()) {
 
@@ -1003,9 +1002,24 @@ eigen_centrality <- function(graph,
     options <- options()
   }
 
+  if (lifecycle::is_present(scale)) {
+    if (scale) {
+    lifecycle::deprecate_soft(
+      "2.1.1",
+      "eigen_centrality(scale)",
+      details = "eigen_centrality() will always behave as if scale=TRUE were used."
+    )
+    } else {
+      lifecycle::deprecate_warn(
+      "2.1.1",
+      "eigen_centrality(scale = 'always as if TRUE')",
+      details =  "Normalization is always performed")
+    }
+  }
+
   eigenvector_centrality_impl(graph = graph,
                               directed = directed,
-                              scale = scale,
+                              scale = TRUE,
                               weights = weights,
                               options = options)
 }
diff --git a/man/eigen_centrality.Rd b/man/eigen_centrality.Rd
index 10829ad39d..a587eae421 100644
--- a/man/eigen_centrality.Rd
+++ b/man/eigen_centrality.Rd
@@ -7,7 +7,7 @@
 eigen_centrality(
   graph,
   directed = FALSE,
-  scale = TRUE,
+  scale = deprecated(),
   weights = NULL,
   options = arpack_defaults()
 )
@@ -18,9 +18,8 @@ eigen_centrality(
 \item{directed}{Logical scalar, whether to consider direction of the edges
 in directed graphs. It is ignored for undirected graphs.}
 
-\item{scale}{Logical scalar, whether to scale the result to have a maximum
-score of one. If no scaling is used then the result vector has unit length
-in the Euclidean norm.}
+\item{scale}{\code{lifecycle::badge("deprecated")} Normalization will always take
+place.}
 
 \item{weights}{A numerical vector or \code{NULL}. This argument can be used
 to give edge weights for calculating the weighted eigenvector centrality of
diff --git a/man/evcent.Rd b/man/evcent.Rd
index 1b5d2cb337..e7fe3380e6 100644
--- a/man/evcent.Rd
+++ b/man/evcent.Rd
@@ -18,9 +18,8 @@ evcent(
 \item{directed}{Logical scalar, whether to consider direction of the edges
 in directed graphs. It is ignored for undirected graphs.}
 
-\item{scale}{Logical scalar, whether to scale the result to have a maximum
-score of one. If no scaling is used then the result vector has unit length
-in the Euclidean norm.}
+\item{scale}{\code{lifecycle::badge("deprecated")} Normalization will always take
+place.}
 
 \item{weights}{A numerical vector or \code{NULL}. This argument can be used
 to give edge weights for calculating the weighted eigenvector centrality of
diff --git a/tests/testthat/_snaps/authority.score.md b/tests/testthat/_snaps/authority.score.md
deleted file mode 100644
index 28ff138f41..0000000000
--- a/tests/testthat/_snaps/authority.score.md
+++ /dev/null
@@ -1,26 +0,0 @@
-# `authority_score()` works
-
-    Code
-      s3 <- authority_score(g2, options = arpack_defaults)$vector
-    Condition
-      Warning:
-      `authority_score()` was deprecated in igraph 2.0.4.
-      i Please use `hits_scores()` instead.
-      Warning:
-      arpack_defaults was deprecated in igraph 1.6.0.
-      i Please use `arpack_defaults()` instead.
-      i So the function arpack_defaults(), not an object called arpack_defaults.
-
-# `hub_score()` works
-
-    Code
-      s3 <- hub_score(g2, options = arpack_defaults)$vector
-    Condition
-      Warning:
-      `hub_score()` was deprecated in igraph 2.0.3.
-      i Please use `hits_scores()` instead.
-      Warning:
-      arpack_defaults was deprecated in igraph 1.6.0.
-      i Please use `arpack_defaults()` instead.
-      i So the function arpack_defaults(), not an object called arpack_defaults.
-
diff --git a/tests/testthat/_snaps/centrality.md b/tests/testthat/_snaps/centrality.md
new file mode 100644
index 0000000000..3c4f9e6a2f
--- /dev/null
+++ b/tests/testthat/_snaps/centrality.md
@@ -0,0 +1,182 @@
+# eigen_centrality() deprecated scale argument
+
+    Code
+      eigen_centrality(g, scale = TRUE)
+    Condition
+      Warning:
+      The `scale` argument of `eigen_centrality()` is deprecated as of igraph 2.1.1.
+      i eigen_centrality() will always behave as if scale=TRUE were used.
+    Output
+      $vector
+       [1] 1 1 1 1 1 1 1 1 1 1
+      
+      $value
+      [1] 2
+      
+      $options
+      $options$bmat
+      [1] "I"
+      
+      $options$n
+      [1] 10
+      
+      $options$which
+      [1] "LA"
+      
+      $options$nev
+      [1] 1
+      
+      $options$tol
+      [1] 0
+      
+      $options$ncv
+      [1] 0
+      
+      $options$ldv
+      [1] 0
+      
+      $options$ishift
+      [1] 1
+      
+      $options$maxiter
+      [1] 3000
+      
+      $options$nb
+      [1] 1
+      
+      $options$mode
+      [1] 1
+      
+      $options$start
+      [1] 1
+      
+      $options$sigma
+      [1] 0
+      
+      $options$sigmai
+      [1] 0
+      
+      $options$info
+      [1] 0
+      
+      $options$iter
+      [1] 1
+      
+      $options$nconv
+      [1] 1
+      
+      $options$numop
+      [1] 7
+      
+      $options$numopb
+      [1] 0
+      
+      $options$numreo
+      [1] 6
+      
+      
+
+---
+
+    Code
+      eigen_centrality(g, scale = FALSE)
+    Condition
+      Warning:
+      The `scale` argument of `eigen_centrality()` always as if TRUE as of igraph 2.1.1.
+      i Normalization is always performed
+    Output
+      $vector
+       [1] 1 1 1 1 1 1 1 1 1 1
+      
+      $value
+      [1] 2
+      
+      $options
+      $options$bmat
+      [1] "I"
+      
+      $options$n
+      [1] 10
+      
+      $options$which
+      [1] "LA"
+      
+      $options$nev
+      [1] 1
+      
+      $options$tol
+      [1] 0
+      
+      $options$ncv
+      [1] 0
+      
+      $options$ldv
+      [1] 0
+      
+      $options$ishift
+      [1] 1
+      
+      $options$maxiter
+      [1] 3000
+      
+      $options$nb
+      [1] 1
+      
+      $options$mode
+      [1] 1
+      
+      $options$start
+      [1] 1
+      
+      $options$sigma
+      [1] 0
+      
+      $options$sigmai
+      [1] 0
+      
+      $options$info
+      [1] 0
+      
+      $options$iter
+      [1] 1
+      
+      $options$nconv
+      [1] 1
+      
+      $options$numop
+      [1] 7
+      
+      $options$numopb
+      [1] 0
+      
+      $options$numreo
+      [1] 6
+      
+      
+
+# `authority_score()` works
+
+    Code
+      s3 <- authority_score(g2, options = arpack_defaults)$vector
+    Condition
+      Warning:
+      `authority_score()` was deprecated in igraph 2.0.4.
+      i Please use `hits_scores()` instead.
+      Warning:
+      arpack_defaults was deprecated in igraph 1.6.0.
+      i Please use `arpack_defaults()` instead.
+      i So the function arpack_defaults(), not an object called arpack_defaults.
+
+# `hub_score()` works
+
+    Code
+      s3 <- hub_score(g2, options = arpack_defaults)$vector
+    Condition
+      Warning:
+      `hub_score()` was deprecated in igraph 2.0.3.
+      i Please use `hits_scores()` instead.
+      Warning:
+      arpack_defaults was deprecated in igraph 1.6.0.
+      i Please use `arpack_defaults()` instead.
+      i So the function arpack_defaults(), not an object called arpack_defaults.
+
diff --git a/tests/testthat/test-alpha.centrality.R b/tests/testthat/test-alpha.centrality.R
deleted file mode 100644
index 41274c96e1..0000000000
--- a/tests/testthat/test-alpha.centrality.R
+++ /dev/null
@@ -1,70 +0,0 @@
-test_that("dense alpha_centrality works", {
-  g.1 <- make_graph(c(1, 3, 2, 3, 3, 4, 4, 5))
-  ac1 <- alpha_centrality(g.1, sparse = FALSE)
-  expect_equal(ac1, c(1, 1, 3, 4, 5))
-
-  g.2 <- make_graph(c(2, 1, 3, 1, 4, 1, 5, 1))
-  ac2 <- alpha_centrality(g.2, sparse = FALSE)
-  expect_equal(ac2, c(5, 1, 1, 1, 1))
-
-  g.3 <- make_graph(c(1, 2, 2, 3, 3, 4, 4, 1, 5, 1))
-  ac3 <- alpha_centrality(g.3, alpha = 0.5, sparse = FALSE)
-  expect_equal(ac3, c(76, 68, 64, 62, 30) / 30)
-})
-
-test_that("sparse alpha_centrality works", {
-  g.1 <- make_graph(c(1, 3, 2, 3, 3, 4, 4, 5))
-  ac1 <- alpha_centrality(g.1, sparse = TRUE)
-  expect_equal(ac1, c(1, 1, 3, 4, 5))
-
-  g.2 <- make_graph(c(2, 1, 3, 1, 4, 1, 5, 1))
-  ac2 <- alpha_centrality(g.2, sparse = TRUE)
-  expect_equal(ac2, c(5, 1, 1, 1, 1))
-
-  g.3 <- make_graph(c(1, 2, 2, 3, 3, 4, 4, 1, 5, 1))
-  ac3 <- alpha_centrality(g.3, alpha = 0.5, sparse = TRUE)
-  expect_equal(ac3, c(76, 68, 64, 62, 30) / 30)
-})
-
-##############################
-## weighted version
-
-test_that("weighted dense alpha_centrality works", {
-  star <- make_star(10)
-  E(star)$weight <- sample(ecount(star))
-
-  ac1 <- alpha_centrality(star, sparse = FALSE)
-  expect_equal(ac1, c(46, 1, 1, 1, 1, 1, 1, 1, 1, 1))
-
-  ac2 <- alpha_centrality(star, weights = "weight", sparse = FALSE)
-  expect_equal(ac2, c(46, 1, 1, 1, 1, 1, 1, 1, 1, 1))
-
-  ac3 <- alpha_centrality(star, weights = NA, sparse = FALSE)
-  expect_equal(ac3, c(vcount(star), 1, 1, 1, 1, 1, 1, 1, 1, 1))
-})
-
-test_that("weighted sparse alpha_centrality works", {
-  star <- make_star(10)
-  E(star)$weight <- sample(ecount(star))
-
-  ac1 <- alpha_centrality(star, sparse = TRUE)
-  expect_equal(ac1, c(46, 1, 1, 1, 1, 1, 1, 1, 1, 1))
-
-  ac2 <- alpha_centrality(star, weights = "weight", sparse = TRUE)
-  expect_equal(ac2, c(46, 1, 1, 1, 1, 1, 1, 1, 1, 1))
-
-  ac3 <- alpha_centrality(star, weights = NA, sparse = TRUE)
-  expect_equal(ac3, c(vcount(star), 1, 1, 1, 1, 1, 1, 1, 1, 1))
-})
-
-test_that("undirected, alpha centrality works, #653", {
-  g <- make_ring(10)
-
-  ac1 <- alpha_centrality(g, sparse = TRUE)
-  ac2 <- alpha_centrality(g, sparse = FALSE)
-  expect_equal(ac1, ac2)
-
-  g2 <- as_directed(g, mode = "mutual")
-  ac3 <- alpha_centrality(g, sparse = FALSE)
-  expect_equal(ac1, ac3)
-})
diff --git a/tests/testthat/test-arpack.R b/tests/testthat/test-arpack.R
index 384f8ea0c8..e69de29bb2 100644
--- a/tests/testthat/test-arpack.R
+++ b/tests/testthat/test-arpack.R
@@ -1,98 +0,0 @@
-test_that("arpack lifecycle warning", {
-  rlang::local_options(lifecycle_verbosity = "warning")
-
-  f <- function(x, extra = NULL) x
-  expect_warning(
-    res <- arpack(f, options = function() list(n = 10, nev = 2, ncv = 4), sym = TRUE)
-  )
-  expect_equal(res$values, c(1, 1))
-})
-
-test_that("arpack works for identity matrix", {
-  f <- function(x, extra = NULL) x
-  res <- arpack(f, options = list(n = 10, nev = 2, ncv = 4), sym = TRUE)
-  expect_equal(res$values, c(1, 1))
-})
-
-test_that("arpack works on the Laplacian of a star", {
-  f <- function(x, extra = NULL) {
-    y <- x
-    y[1] <- (length(x) - 1) * x[1] - sum(x[-1])
-    for (i in 2:length(x)) {
-      y[i] <- x[i] - x[1]
-    }
-    y
-  }
-
-  r1 <- arpack(f, options = list(n = 10, nev = 1, ncv = 3), sym = TRUE)
-  r2 <- eigen(laplacian_matrix(make_star(10, mode = "undirected")))
-
-  correctSign <- function(x) {
-    if (x[1] < 0) {
-      -x
-    } else {
-      x
-    }
-  }
-  expect_equal(r1$values, r2$values[1])
-  expect_equal(correctSign(r1$vectors), correctSign(r2$vectors[, 1]))
-})
-
-####
-# Complex case
-
-test_that("arpack works for non-symmetric matrices", {
-  A <- structure(
-    c(
-      -6, -6, 7, 6, 1, -9, -3, 2, -9, -7, 0, 1, -7, 8,
-      -7, 10, 0, 0, 1, 1, 10, 0, 8, -4, -4, -5, 8, 9, -6, 9, 3, 8,
-      6, -1, 9, -9, -6, -3, -1, -7, 8, -4, -4, 10, 0, 5, -2, 0, 7,
-      10, 1, 4, -8, 3, 5, 3, -7, -9, 10, -1, -4, -7, -1, 7, 5, -5,
-      1, -4, 9, -2, 10, 1, -7, 7, 6, 7, -3, 0, 9, -5, -8, 1, -3,
-      -3, -8, -7, -8, 10, 8, 7, 0, 6, -7, -8, 10, 10, 1, 0, -2, 6
-    ),
-    .Dim = c(10L, 10L)
-  )
-
-  f <- function(x, extra = NULL) A %*% x
-  res <- arpack(f, options = list(n = 10, nev = 3, ncv = 7, which = "LM"), sym = FALSE)
-  ## This is needed because they might return a different complex conjugate
-  expect_equal(abs(res$values / eigen(A)$values[1:3]), c(1, 1, 1))
-  expect_equal(
-    (res$values[1] * res$vectors[, 1]) / (A %*% res$vectors[, 1]),
-    cbind(rep(1 + 0i, nrow(A)))
-  )
-  expect_equal(
-    (res$values[2] * res$vectors[, 2]) / (A %*% res$vectors[, 2]),
-    cbind(rep(1 + 0i, nrow(A)))
-  )
-  expect_equal(
-    abs((res$values[3] * res$vectors[, 3]) / (A %*% res$vectors[, 3])),
-    cbind(rep(1, nrow(A)))
-  )
-
-  f <- function(x, extra = NULL) A %*% x
-  res <- arpack(f, options = list(n = 10, nev = 4, ncv = 9, which = "LM"), sym = FALSE)
-  ## This is needed because they might return a different complex conjugate
-  expect_equal(abs(res$values / eigen(A)$values[1:4]), rep(1, 4))
-  expect_equal(
-    (res$values[1] * res$vectors[, 1]) / (A %*% res$vectors[, 1]),
-    cbind(rep(1 + 0i, nrow(A)))
-  )
-  expect_equal(
-    (res$values[2] * res$vectors[, 2]) / (A %*% res$vectors[, 2]),
-    cbind(rep(1 + 0i, nrow(A)))
-  )
-  expect_equal(
-    abs((res$values[3] * res$vectors[, 3]) / (A %*% res$vectors[, 3])),
-    cbind(rep(1, nrow(A)))
-  )
-  expect_equal(
-    abs((res$values[4] * res$vectors[, 4]) / (A %*% res$vectors[, 4])),
-    cbind(rep(1, nrow(A)))
-  )
-})
-
-####
-
-# TODO: further tests for typically hard cases
diff --git a/tests/testthat/test-authority.score.R b/tests/testthat/test-authority.score.R
deleted file mode 100644
index 25d8eb4016..0000000000
--- a/tests/testthat/test-authority.score.R
+++ /dev/null
@@ -1,215 +0,0 @@
-test_that("`authority_score()` works", {
-  rlang::local_options(lifecycle_verbosity = "quiet")
-  mscale <- function(x) {
-    if (sd(x) != 0) {
-      x <- scale(x)
-    }
-    if (x[1] < 0) {
-      x <- -x
-    }
-    x
-  }
-
-  g1 <- make_graph(
-    c(1, 3, 1, 6, 1, 10, 2, 1, 3, 1, 4, 2, 4, 7, 4, 9, 5, 4, 5, 6, 5, 8, 6, 3,
-      7, 1, 7, 5, 7, 6, 7, 10, 8, 4, 9, 6, 10, 5, 10, 7),
-    directed = TRUE)
-  A <- as_adjacency_matrix(g1, sparse = FALSE)
-  s1 <- eigen(t(A) %*% A)$vectors[, 1]
-  s2 <- authority_score(g1)$vector
-  expect_equal(
-    s2,
-    c(0.519632767970952, 0.0191587307007462, 0.327572049088003,
-      0.238728053455971, 0.449690304629051, 1, 0.0966933781044594,
-      0.204851318050036, 0.0191587307007462, 0.653243552177761)
-  )
-  expect_equal(mscale(s1), mscale(s2), ignore_attr = TRUE)
-
-  g2 <- make_graph(
-    c(1, 2, 1, 4, 2, 3, 2, 4, 3, 1, 3, 5, 4, 3, 5, 1, 5, 2),
-    directed = TRUE
-  )
-  A <- as_adjacency_matrix(g2, sparse = FALSE)
-  s1 <- eigen(t(A) %*% A)$vectors[, 1]
-  s2 <- authority_score(g2)$vector
-  expect_equal(
-    s2,
-    c(0.763521118433368, 1, 0.546200349457202,
-      0.918985947228995, 0.28462967654657)
-  )
-  expect_equal(mscale(s1), mscale(s2), ignore_attr = TRUE)
-
-  rlang::with_options(lifecycle_verbosity = "warning", {
-    expect_snapshot(
-      s3 <- authority_score(g2, options = arpack_defaults)$vector
-    )
-  })
-  expect_equal(s2, s3)
-})
-
-test_that("`hub_score()` works", {
-  rlang::local_options(lifecycle_verbosity = "quiet")
-  mscale <- function(x) {
-    if (sd(x) != 0) {
-      x <- scale(x)
-    }
-    if (x[1] < 0) {
-      x <- -x
-    }
-    x
-  }
-
-  g1 <- make_graph(
-    c(1, 3, 1, 6, 1, 10, 2, 1, 3, 1, 4, 2, 4, 7, 4, 9, 5, 4, 5, 6, 5, 8, 6, 3,
-      7, 1, 7, 5, 7, 6, 7, 10, 8, 4, 9, 6, 10, 5, 10, 7),
-    directed = TRUE)
-  A <- as_adjacency_matrix(g1, sparse = FALSE)
-  s1 <- eigen(A %*% t(A))$vectors[, 1]
-  s2 <- hub_score(g1)$vector
-  expect_equal(
-    s2,
-    c(0.755296579522977, 0.198139015063149, 0.198139015063149,
-      0.0514804231207635, 0.550445261472941, 0.124905139108053,
-      1, 0.0910284037021176, 0.381305851509012, 0.208339295395331)
-  )
-  expect_equal(mscale(s1), mscale(s2), ignore_attr = TRUE)
-
-  g2 <- make_graph(
-    c(1, 2, 1, 4, 2, 3, 2, 4, 3, 1, 3, 5, 4, 3, 5, 1, 5, 2),
-    directed = TRUE
-  )
-  A <- as_adjacency_matrix(g2, sparse = FALSE)
-  s1 <- eigen(A %*% t(A))$vectors[, 1]
-  s2 <- hub_score(g2)$vector
-  expect_equal(
-    s2,
-    c(1, 0.763521118433368, 0.546200349457203,
-      0.28462967654657, 0.918985947228995)
-  )
-  expect_equal(mscale(s1), mscale(s2), ignore_attr = TRUE)
-
-  rlang::with_options(lifecycle_verbosity = "warning", {
-    expect_snapshot(
-      s3 <- hub_score(g2, options = arpack_defaults)$vector
-    )
-  })
-  expect_equal(s2, s3)
-})
-
-test_that("authority_score survives stress test", {
-  skip_on_cran()
-
-  withr::local_seed(42)
-
-  is.principal <- function(M, lambda) {
-    expect_equal(eigen(M)$values[1], lambda)
-  }
-
-  is.ev <- function(M, v, lambda) {
-    expect_equal(as.vector(M %*% v), lambda * v)
-  }
-
-  is.good <- function(M, v, lambda) {
-    is.principal(M, lambda)
-    is.ev(M, v, lambda)
-  }
-
-  for (i in 1:100) {
-    G <- sample_gnm(10, sample(1:20, 1))
-    as <- hits_scores(G)
-    M <- as_adjacency_matrix(G, sparse = FALSE)
-    is.good(t(M) %*% M, as$authority, as$value)
-  }
-
-  for (i in 1:100) {
-    G <- sample_gnm(10, sample(1:20, 1))
-    hs <- hits_scores(G)
-    M <- as_adjacency_matrix(G, sparse = FALSE)
-    is.good(M %*% t(M), hs$hub, hs$value)
-  }
-})
-
-test_that("`hits_score()` works -- authority", {
-  mscale <- function(x) {
-    if (sd(x) != 0) {
-      x <- scale(x)
-    }
-    if (x[1] < 0) {
-      x <- -x
-    }
-    x
-  }
-
-  g1 <- make_graph(
-    c(1, 3, 1, 6, 1, 10, 2, 1, 3, 1, 4, 2, 4, 7, 4, 9, 5, 4, 5, 6, 5, 8, 6, 3,
-      7, 1, 7, 5, 7, 6, 7, 10, 8, 4, 9, 6, 10, 5, 10, 7),
-    directed = TRUE)
-  A <- as_adjacency_matrix(g1, sparse = FALSE)
-  s1 <- eigen(t(A) %*% A)$vectors[, 1]
-  s2 <- hits_scores(g1)$authority
-  expect_equal(
-    s2,
-    c(0.519632767970952, 0.0191587307007462, 0.327572049088003,
-      0.238728053455971, 0.449690304629051, 1, 0.0966933781044594,
-      0.204851318050036, 0.0191587307007462, 0.653243552177761)
-  )
-  expect_equal(mscale(s1), mscale(s2), ignore_attr = TRUE)
-
-  g2 <- make_graph(
-    c(1, 2, 1, 4, 2, 3, 2, 4, 3, 1, 3, 5, 4, 3, 5, 1, 5, 2),
-    directed = TRUE
-  )
-  A <- as_adjacency_matrix(g2, sparse = FALSE)
-  s1 <- eigen(t(A) %*% A)$vectors[, 1]
-  s2 <- hits_scores(g2)$authority
-  expect_equal(
-    s2,
-    c(0.763521118433368, 1, 0.546200349457202,
-      0.918985947228995, 0.28462967654657)
-  )
-  expect_equal(mscale(s1), mscale(s2), ignore_attr = TRUE)
-
-})
-
-test_that("`hits_scores()` works -- hub", {
-  mscale <- function(x) {
-    if (sd(x) != 0) {
-      x <- scale(x)
-    }
-    if (x[1] < 0) {
-      x <- -x
-    }
-    x
-  }
-
-  g1 <- make_graph(
-    c(1, 3, 1, 6, 1, 10, 2, 1, 3, 1, 4, 2, 4, 7, 4, 9, 5, 4, 5, 6, 5, 8, 6, 3,
-      7, 1, 7, 5, 7, 6, 7, 10, 8, 4, 9, 6, 10, 5, 10, 7),
-    directed = TRUE)
-  A <- as_adjacency_matrix(g1, sparse = FALSE)
-  s1 <- eigen(A %*% t(A))$vectors[, 1]
-  s2 <- hits_scores(g1)$hub
-  expect_equal(
-    s2,
-    c(0.755296579522977, 0.198139015063149, 0.198139015063149,
-      0.0514804231207635, 0.550445261472941, 0.124905139108053,
-      1, 0.0910284037021176, 0.381305851509012, 0.208339295395331)
-  )
-  expect_equal(mscale(s1), mscale(s2), ignore_attr = TRUE)
-
-  g2 <- make_graph(
-    c(1, 2, 1, 4, 2, 3, 2, 4, 3, 1, 3, 5, 4, 3, 5, 1, 5, 2),
-    directed = TRUE
-  )
-  A <- as_adjacency_matrix(g2, sparse = FALSE)
-  s1 <- eigen(A %*% t(A))$vectors[, 1]
-  s2 <-  hits_scores(g2)$hub
-  expect_equal(
-    s2,
-    c(1, 0.763521118433368, 0.546200349457203,
-      0.28462967654657, 0.918985947228995)
-  )
-  expect_equal(mscale(s1), mscale(s2), ignore_attr = TRUE)
-
-})
-
diff --git a/tests/testthat/test-betweenness.R b/tests/testthat/test-betweenness.R
deleted file mode 100644
index 4cc849e77e..0000000000
--- a/tests/testthat/test-betweenness.R
+++ /dev/null
@@ -1,88 +0,0 @@
-test_that("betweenness works for kite graph", {
-  kite <- graph_from_literal(
-    Andre - Beverly:Carol:Diane:Fernando,
-    Beverly - Andre:Diane:Ed:Garth,
-    Carol - Andre:Diane:Fernando,
-    Diane - Andre:Beverly:Carol:Ed:Fernando:Garth,
-    Ed - Beverly:Diane:Garth,
-    Fernando - Andre:Carol:Diane:Garth:Heather,
-    Garth - Beverly:Diane:Ed:Fernando:Heather,
-    Heather - Fernando:Garth:Ike,
-    Ike - Heather:Jane,
-    Jane - Ike
-  )
-  nf <- (vcount(kite) - 1) * (vcount(kite) - 2) / 2
-  bet <- structure(betweenness(kite) / nf, names = V(kite)$name)
-  bet <- round(sort(bet, decreasing = TRUE), 3)
-  expect_equal(bet, structure(c(0.389, 0.231, 0.231, 0.222, 0.102, 0.023, 0.023, 0.000, 0.000, 0.000), names = c("Heather", "Fernando", "Garth", "Ike", "Diane", "Andre", "Beverly", "Carol", "Ed", "Jane")))
-
-  bet2 <- structure(betweenness(kite, normalized = TRUE), names = V(kite)$name)
-  bet2 <- round(sort(bet2, decreasing = TRUE), 3)
-  expect_equal(bet2, bet)
-})
-
-test_that("weighted betweenness works", {
-  nontriv <- make_graph(c(
-    0, 19, 0, 16, 0, 20, 1, 19, 2, 5, 3, 7, 3, 8,
-    4, 15, 4, 11, 5, 8, 5, 19, 6, 7, 6, 10, 6, 8,
-    6, 9, 7, 20, 9, 10, 9, 20, 10, 19,
-    11, 12, 11, 20, 12, 15, 13, 15,
-    14, 18, 14, 16, 14, 17, 15, 16, 17, 18
-  ) + 1, dir = FALSE)
-
-  E(nontriv)$weight <- c(
-    0.5249, 1, 0.1934, 0.6274, 0.5249,
-    0.0029, 0.3831, 0.05, 0.6274, 0.3831,
-    0.5249, 0.0587, 0.0579, 0.0562, 0.0562,
-    0.1934, 0.6274, 0.6274, 0.6274, 0.0418,
-    0.6274, 0.3511, 0.3511, 0.1486, 1, 1,
-    0.0711, 0.2409
-  )
-
-  nontrivRes <- c(
-    20, 0, 0, 0, 0, 19, 80, 85, 32, 0, 10,
-    75, 70, 0, 36, 81, 60, 0, 19, 19, 86
-  )
-
-  bet <- betweenness(nontriv)
-  expect_equal(bet, nontrivRes)
-})
-
-test_that("normalization works well", {
-  g1 <- graph_from_literal(0 + -+1 + -+2)
-
-  b11 <- betweenness(g1, normalized = TRUE, directed = FALSE)
-  expect_equal(b11, c("0" = 0, "1" = 1, "2" = 0))
-
-  b12 <- betweenness(g1, normalized = TRUE, directed = TRUE)
-  expect_equal(b12, c("0" = 0, "1" = 1, "2" = 0))
-
-  g2 <- graph_from_literal(0 - --1 - --2)
-
-  b2 <- betweenness(g2, normalized = TRUE)
-  expect_equal(b2, c("0" = 0, "1" = 1, "2" = 0))
-})
-
-test_that("shortest paths are compared with tolerance when calculating betweenness", {
-  # The test case below is designed in a way that the paths 3-6 and 3-4-6 have the
-  # same total weight when compared with a tolerance, but they appear different
-  # if the comparison is made without an epsilon tolerance due to numeric
-  # inaccuracies.
-  #
-  # See https://github.com/igraph/rigraph/issues/314
-
-  from <- c(1, 2, 3, 3, 3, 4, 6, 7, 2, 9, 5, 7, 9, 9, 5, 8)
-  to <- c(4, 3, 6, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16)
-  edges <- cbind(from, to)
-  edges.dists <- c(
-    1.9617537, 0.9060834, 2.2165446, 1.6251956,
-    2.4473929, 0.5913490, 8.7093236, 2.8387330,
-    6.1225042, 20.7217776, 6.8027218, 16.3147479,
-    5.2605598, 6.6816853, 4.9482123, 1.8989790
-  )
-
-  g <- graph_from_data_frame(edges, directed = FALSE)
-  result <- betweenness(g, weights = edges.dists)
-
-  expect_equal(result[1:5], c("1" = 0, "2" = 44, "3" = 71, "4" = 36.5, "6" = 44))
-})
diff --git a/tests/testthat/test-bonpow.R b/tests/testthat/test-bonpow.R
deleted file mode 100644
index 5c94e10164..0000000000
--- a/tests/testthat/test-bonpow.R
+++ /dev/null
@@ -1,38 +0,0 @@
-test_that("Power centrality works", {
-  ## Generate some test data from Bonacich, 1987:
-  fig1 <- graph_from_literal(A - +B - +C:D)
-  fig1.bp <- lapply(seq(0, 0.8, by = 0.2), function(x) {
-    round(power_centrality(fig1, exponent = x), 2)
-  })
-  expect_equal(fig1.bp, list(c(A = 0.89, B = 1.79, C = 0, D = 0), c(A = 1.15, B = 1.64, C = 0, D = 0), c(A = 1.34, B = 1.49, C = 0, D = 0), c(A = 1.48, B = 1.35, C = 0, D = 0), c(A = 1.59, B = 1.22, C = 0, D = 0)))
-
-  g.c <- make_graph(c(1, 2, 1, 3, 2, 4, 3, 5), dir = FALSE)
-  bp.c <- lapply(seq(-.5, .5, by = 0.1), function(x) {
-    round(power_centrality(g.c, exponent = x), 2)[c(1, 2, 4)]
-  })
-
-  expect_equal(bp.c, list(c(0.00, 1.58, 0.00), c(0.73, 1.45, 0.36), c(0.97, 1.34, 0.49), c(1.09, 1.27, 0.54), c(1.15, 1.23, 0.58), c(1.20, 1.20, 0.60), c(1.22, 1.17, 0.61), c(1.25, 1.16, 0.62), c(1.26, 1.14, 0.63), c(1.27, 1.13, 0.64), c(1.28, 1.12, 0.64)))
-
-  g.d <- make_graph(c(1, 2, 1, 3, 1, 4, 2, 5, 3, 6, 4, 7), dir = FALSE)
-  bp.d <- lapply(seq(-.4, .4, by = 0.1), function(x) {
-    round(power_centrality(g.d, exponent = x), 2)[c(1, 2, 5)]
-  })
-  expect_equal(bp.d, list(c(1.62, 1.08, 0.54), c(1.62, 1.08, 0.54), c(1.62, 1.08, 0.54), c(1.62, 1.08, 0.54), c(1.62, 1.08, 0.54), c(1.62, 1.08, 0.54), c(1.62, 1.08, 0.54), c(1.62, 1.08, 0.54), c(1.62, 1.08, 0.54)))
-
-  g.e <- make_graph(c(1, 2, 1, 3, 1, 4, 2, 5, 2, 6, 3, 7, 3, 8, 4, 9, 4, 10), dir = FALSE)
-  bp.e <- lapply(seq(-.4, .4, by = 0.1), function(x) {
-    round(power_centrality(g.e, exponent = x), 2)[c(1, 2, 5)]
-  })
-  expect_equal(bp.e, list(c(-1.00, 1.67, -0.33), c(0.36, 1.81, 0.12), c(1.00, 1.67, 0.33), c(1.30, 1.55, 0.43), c(1.46, 1.46, 0.49), c(1.57, 1.40, 0.52), c(1.63, 1.36, 0.54), c(1.68, 1.33, 0.56), c(1.72, 1.30, 0.57)))
-
-  g.f <- make_graph(c(1, 2, 1, 3, 1, 4, 2, 5, 2, 6, 2, 7, 3, 8, 3, 9, 3, 10, 4, 11, 4, 12, 4, 13),
-    dir = FALSE
-  )
-  bp.f <- lapply(seq(-.4, .4, by = 0.1), function(x) {
-    round(power_centrality(g.f, exponent = x), 2)[c(1, 2, 5)]
-  })
-  expect_equal(
-    bp.f,
-    list(c(-1.72, 1.53, -0.57), c(-0.55, 2.03, -0.18), c(0.44, 2.05, 0.15), c(1.01, 1.91, 0.34), c(1.33, 1.78, 0.44), c(1.52, 1.67, 0.51), c(1.65, 1.59, 0.55), c(1.74, 1.53, 0.58), c(1.80, 1.48, 0.60))
-  )
-})
diff --git a/tests/testthat/test-centrality.R b/tests/testthat/test-centrality.R
index 8a6352c14d..471380cdd6 100644
--- a/tests/testthat/test-centrality.R
+++ b/tests/testthat/test-centrality.R
@@ -22,3 +22,637 @@ test_that("subgraph_centrality() ignored edge directions", {
     subgraph_centrality(as_undirected(g, mode = "each"))
   )
 })
+
+test_that("eigen_centrality() works", {
+  kite <- graph_from_literal(
+    Andre - Beverly:Carol:Diane:Fernando,
+    Beverly - Andre:Diane:Ed:Garth,
+    Carol - Andre:Diane:Fernando,
+    Diane - Andre:Beverly:Carol:Ed:Fernando:Garth,
+    Ed - Beverly:Diane:Garth,
+    Fernando - Andre:Carol:Diane:Garth:Heather,
+    Garth - Beverly:Diane:Ed:Fernando:Heather,
+    Heather - Fernando:Garth:Ike,
+    Ike - Heather:Jane,
+    Jane - Ike
+  )
+  evc <- round(eigen_centrality(kite)$vector, 3)
+  expect_equal(evc, structure(c(0.732, 0.732, 0.594, 1, 0.827, 0.594, 0.827, 0.407, 0.1, 0.023), .Names = c("Andre", "Beverly", "Carol", "Diane", "Fernando", "Ed", "Garth", "Heather", "Ike", "Jane")))
+
+
+  ## Eigenvector-centrality, small stress-test
+
+  is.principal <- function(M, lambda, eps = 1e-12) {
+    abs(eigen(M)$values[1] - lambda) < eps
+  }
+
+  is.ev <- function(M, v, lambda, eps = 1e-12) {
+    max(abs(M %*% v - lambda * v)) < eps
+  }
+
+  is.good <- function(M, v, lambda, eps = 1e-12) {
+    is.principal(M, lambda, eps) && is.ev(M, v, lambda, eps)
+  }
+
+  for (i in 1:1000) {
+    G <- sample_gnm(10, sample(1:20, 1))
+    ev <- eigen_centrality(G)
+    expect_true(is.good(as_adjacency_matrix(G, sparse = FALSE), ev$vector, ev$value))
+  }
+})
+
+test_that("eigen_centrality() deprecated scale argument", {
+  g <- make_ring(10, directed = FALSE)
+  expect_snapshot(eigen_centrality(g, scale = TRUE))
+  expect_snapshot(eigen_centrality(g, scale = FALSE))
+})
+
+test_that("betweenness works for kite graph", {
+  kite <- graph_from_literal(
+    Andre - Beverly:Carol:Diane:Fernando,
+    Beverly - Andre:Diane:Ed:Garth,
+    Carol - Andre:Diane:Fernando,
+    Diane - Andre:Beverly:Carol:Ed:Fernando:Garth,
+    Ed - Beverly:Diane:Garth,
+    Fernando - Andre:Carol:Diane:Garth:Heather,
+    Garth - Beverly:Diane:Ed:Fernando:Heather,
+    Heather - Fernando:Garth:Ike,
+    Ike - Heather:Jane,
+    Jane - Ike
+  )
+  nf <- (vcount(kite) - 1) * (vcount(kite) - 2) / 2
+  bet <- structure(betweenness(kite) / nf, names = V(kite)$name)
+  bet <- round(sort(bet, decreasing = TRUE), 3)
+  expect_equal(bet, structure(c(0.389, 0.231, 0.231, 0.222, 0.102, 0.023, 0.023, 0.000, 0.000, 0.000), names = c("Heather", "Fernando", "Garth", "Ike", "Diane", "Andre", "Beverly", "Carol", "Ed", "Jane")))
+
+  bet2 <- structure(betweenness(kite, normalized = TRUE), names = V(kite)$name)
+  bet2 <- round(sort(bet2, decreasing = TRUE), 3)
+  expect_equal(bet2, bet)
+})
+
+test_that("weighted betweenness works", {
+  nontriv <- make_graph(c(
+    0, 19, 0, 16, 0, 20, 1, 19, 2, 5, 3, 7, 3, 8,
+    4, 15, 4, 11, 5, 8, 5, 19, 6, 7, 6, 10, 6, 8,
+    6, 9, 7, 20, 9, 10, 9, 20, 10, 19,
+    11, 12, 11, 20, 12, 15, 13, 15,
+    14, 18, 14, 16, 14, 17, 15, 16, 17, 18
+  ) + 1, dir = FALSE)
+
+  E(nontriv)$weight <- c(
+    0.5249, 1, 0.1934, 0.6274, 0.5249,
+    0.0029, 0.3831, 0.05, 0.6274, 0.3831,
+    0.5249, 0.0587, 0.0579, 0.0562, 0.0562,
+    0.1934, 0.6274, 0.6274, 0.6274, 0.0418,
+    0.6274, 0.3511, 0.3511, 0.1486, 1, 1,
+    0.0711, 0.2409
+  )
+
+  nontrivRes <- c(
+    20, 0, 0, 0, 0, 19, 80, 85, 32, 0, 10,
+    75, 70, 0, 36, 81, 60, 0, 19, 19, 86
+  )
+
+  bet <- betweenness(nontriv)
+  expect_equal(bet, nontrivRes)
+})
+
+test_that("normalization works well", {
+  g1 <- graph_from_literal(0 + -+1 + -+2)
+
+  b11 <- betweenness(g1, normalized = TRUE, directed = FALSE)
+  expect_equal(b11, c("0" = 0, "1" = 1, "2" = 0))
+
+  b12 <- betweenness(g1, normalized = TRUE, directed = TRUE)
+  expect_equal(b12, c("0" = 0, "1" = 1, "2" = 0))
+
+  g2 <- graph_from_literal(0 - --1 - --2)
+
+  b2 <- betweenness(g2, normalized = TRUE)
+  expect_equal(b2, c("0" = 0, "1" = 1, "2" = 0))
+})
+
+test_that("shortest paths are compared with tolerance when calculating betweenness", {
+  # The test case below is designed in a way that the paths 3-6 and 3-4-6 have the
+  # same total weight when compared with a tolerance, but they appear different
+  # if the comparison is made without an epsilon tolerance due to numeric
+  # inaccuracies.
+  #
+  # See https://github.com/igraph/rigraph/issues/314
+
+  from <- c(1, 2, 3, 3, 3, 4, 6, 7, 2, 9, 5, 7, 9, 9, 5, 8)
+  to <- c(4, 3, 6, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16)
+  edges <- cbind(from, to)
+  edges.dists <- c(
+    1.9617537, 0.9060834, 2.2165446, 1.6251956,
+    2.4473929, 0.5913490, 8.7093236, 2.8387330,
+    6.1225042, 20.7217776, 6.8027218, 16.3147479,
+    5.2605598, 6.6816853, 4.9482123, 1.8989790
+  )
+
+  g <- graph_from_data_frame(edges, directed = FALSE)
+  result <- betweenness(g, weights = edges.dists)
+
+  expect_equal(result[1:5], c("1" = 0, "2" = 44, "3" = 71, "4" = 36.5, "6" = 44))
+})
+
+test_that("closeness works", {
+  kite <- graph_from_literal(
+    Andre - Beverly:Carol:Diane:Fernando,
+    Beverly - Andre:Diane:Ed:Garth,
+    Carol - Andre:Diane:Fernando,
+    Diane - Andre:Beverly:Carol:Ed:Fernando:Garth,
+    Ed - Beverly:Diane:Garth,
+    Fernando - Andre:Carol:Diane:Garth:Heather,
+    Garth - Beverly:Diane:Ed:Fernando:Heather,
+    Heather - Fernando:Garth:Ike,
+    Ike - Heather:Jane,
+    Jane - Ike
+  )
+
+  clo <- closeness(kite) * (vcount(kite) - 1)
+  expect_equal(
+    round(sort(clo, decreasing = TRUE), 3),
+    c(Fernando = 0.643, Garth = 0.643, Diane = 0.600, Heather = 0.600, Andre = 0.529, Beverly = 0.529, Carol = 0.500, Ed = 0.500, Ike = 0.429, Jane = 0.310)
+  )
+
+  clo2 <- closeness(kite, normalized = TRUE)
+  expect_equal(clo, clo2)
+})
+
+## TODO: weighted closeness
+
+test_that("closeness centralization works", {
+  kite <- graph_from_literal(
+    Andre - Beverly:Carol:Diane:Fernando,
+    Beverly - Andre:Diane:Ed:Garth,
+    Carol - Andre:Diane:Fernando,
+    Diane - Andre:Beverly:Carol:Ed:Fernando:Garth,
+    Ed - Beverly:Diane:Garth,
+    Fernando - Andre:Carol:Diane:Garth:Heather,
+    Garth - Beverly:Diane:Ed:Fernando:Heather,
+    Heather - Fernando:Garth:Ike,
+    Ike - Heather:Jane,
+    Jane - Ike
+  )
+
+  c1 <- closeness(kite, normalized = TRUE)
+  c2 <- centr_clo(kite)
+  expect_equal(unname(c1), c2$res)
+  expect_equal(c2$centralization, 0.270374931581828)
+  expect_equal(c2$theoretical_max, 4.23529411764706)
+})
+test_that("arpack lifecycle warning", {
+  rlang::local_options(lifecycle_verbosity = "warning")
+
+  f <- function(x, extra = NULL) x
+  expect_warning(
+    res <- arpack(f, options = function() list(n = 10, nev = 2, ncv = 4), sym = TRUE)
+  )
+  expect_equal(res$values, c(1, 1))
+})
+
+test_that("arpack works for identity matrix", {
+  f <- function(x, extra = NULL) x
+  res <- arpack(f, options = list(n = 10, nev = 2, ncv = 4), sym = TRUE)
+  expect_equal(res$values, c(1, 1))
+})
+
+test_that("arpack works on the Laplacian of a star", {
+  f <- function(x, extra = NULL) {
+    y <- x
+    y[1] <- (length(x) - 1) * x[1] - sum(x[-1])
+    for (i in 2:length(x)) {
+      y[i] <- x[i] - x[1]
+    }
+    y
+  }
+
+  r1 <- arpack(f, options = list(n = 10, nev = 1, ncv = 3), sym = TRUE)
+  r2 <- eigen(laplacian_matrix(make_star(10, mode = "undirected")))
+
+  correctSign <- function(x) {
+    if (x[1] < 0) {
+      -x
+    } else {
+      x
+    }
+  }
+  expect_equal(r1$values, r2$values[1])
+  expect_equal(correctSign(r1$vectors), correctSign(r2$vectors[, 1]))
+})
+
+####
+# Complex case
+
+test_that("arpack works for non-symmetric matrices", {
+  A <- structure(
+    c(
+      -6, -6, 7, 6, 1, -9, -3, 2, -9, -7, 0, 1, -7, 8,
+      -7, 10, 0, 0, 1, 1, 10, 0, 8, -4, -4, -5, 8, 9, -6, 9, 3, 8,
+      6, -1, 9, -9, -6, -3, -1, -7, 8, -4, -4, 10, 0, 5, -2, 0, 7,
+      10, 1, 4, -8, 3, 5, 3, -7, -9, 10, -1, -4, -7, -1, 7, 5, -5,
+      1, -4, 9, -2, 10, 1, -7, 7, 6, 7, -3, 0, 9, -5, -8, 1, -3,
+      -3, -8, -7, -8, 10, 8, 7, 0, 6, -7, -8, 10, 10, 1, 0, -2, 6
+    ),
+    .Dim = c(10L, 10L)
+  )
+
+  f <- function(x, extra = NULL) A %*% x
+  res <- arpack(f, options = list(n = 10, nev = 3, ncv = 7, which = "LM"), sym = FALSE)
+  ## This is needed because they might return a different complex conjugate
+  expect_equal(abs(res$values / eigen(A)$values[1:3]), c(1, 1, 1))
+  expect_equal(
+    (res$values[1] * res$vectors[, 1]) / (A %*% res$vectors[, 1]),
+    cbind(rep(1 + 0i, nrow(A)))
+  )
+  expect_equal(
+    (res$values[2] * res$vectors[, 2]) / (A %*% res$vectors[, 2]),
+    cbind(rep(1 + 0i, nrow(A)))
+  )
+  expect_equal(
+    abs((res$values[3] * res$vectors[, 3]) / (A %*% res$vectors[, 3])),
+    cbind(rep(1, nrow(A)))
+  )
+
+  f <- function(x, extra = NULL) A %*% x
+  res <- arpack(f, options = list(n = 10, nev = 4, ncv = 9, which = "LM"), sym = FALSE)
+  ## This is needed because they might return a different complex conjugate
+  expect_equal(abs(res$values / eigen(A)$values[1:4]), rep(1, 4))
+  expect_equal(
+    (res$values[1] * res$vectors[, 1]) / (A %*% res$vectors[, 1]),
+    cbind(rep(1 + 0i, nrow(A)))
+  )
+  expect_equal(
+    (res$values[2] * res$vectors[, 2]) / (A %*% res$vectors[, 2]),
+    cbind(rep(1 + 0i, nrow(A)))
+  )
+  expect_equal(
+    abs((res$values[3] * res$vectors[, 3]) / (A %*% res$vectors[, 3])),
+    cbind(rep(1, nrow(A)))
+  )
+  expect_equal(
+    abs((res$values[4] * res$vectors[, 4]) / (A %*% res$vectors[, 4])),
+    cbind(rep(1, nrow(A)))
+  )
+})
+
+####
+
+# TODO: further tests for typically hard cases
+
+test_that("Power centrality works", {
+  ## Generate some test data from Bonacich, 1987:
+  fig1 <- graph_from_literal(A - +B - +C:D)
+  fig1.bp <- lapply(seq(0, 0.8, by = 0.2), function(x) {
+    round(power_centrality(fig1, exponent = x), 2)
+  })
+  expect_equal(fig1.bp, list(c(A = 0.89, B = 1.79, C = 0, D = 0), c(A = 1.15, B = 1.64, C = 0, D = 0), c(A = 1.34, B = 1.49, C = 0, D = 0), c(A = 1.48, B = 1.35, C = 0, D = 0), c(A = 1.59, B = 1.22, C = 0, D = 0)))
+
+  g.c <- make_graph(c(1, 2, 1, 3, 2, 4, 3, 5), dir = FALSE)
+  bp.c <- lapply(seq(-.5, .5, by = 0.1), function(x) {
+    round(power_centrality(g.c, exponent = x), 2)[c(1, 2, 4)]
+  })
+
+  expect_equal(bp.c, list(c(0.00, 1.58, 0.00), c(0.73, 1.45, 0.36), c(0.97, 1.34, 0.49), c(1.09, 1.27, 0.54), c(1.15, 1.23, 0.58), c(1.20, 1.20, 0.60), c(1.22, 1.17, 0.61), c(1.25, 1.16, 0.62), c(1.26, 1.14, 0.63), c(1.27, 1.13, 0.64), c(1.28, 1.12, 0.64)))
+
+  g.d <- make_graph(c(1, 2, 1, 3, 1, 4, 2, 5, 3, 6, 4, 7), dir = FALSE)
+  bp.d <- lapply(seq(-.4, .4, by = 0.1), function(x) {
+    round(power_centrality(g.d, exponent = x), 2)[c(1, 2, 5)]
+  })
+  expect_equal(bp.d, list(c(1.62, 1.08, 0.54), c(1.62, 1.08, 0.54), c(1.62, 1.08, 0.54), c(1.62, 1.08, 0.54), c(1.62, 1.08, 0.54), c(1.62, 1.08, 0.54), c(1.62, 1.08, 0.54), c(1.62, 1.08, 0.54), c(1.62, 1.08, 0.54)))
+
+  g.e <- make_graph(c(1, 2, 1, 3, 1, 4, 2, 5, 2, 6, 3, 7, 3, 8, 4, 9, 4, 10), dir = FALSE)
+  bp.e <- lapply(seq(-.4, .4, by = 0.1), function(x) {
+    round(power_centrality(g.e, exponent = x), 2)[c(1, 2, 5)]
+  })
+  expect_equal(bp.e, list(c(-1.00, 1.67, -0.33), c(0.36, 1.81, 0.12), c(1.00, 1.67, 0.33), c(1.30, 1.55, 0.43), c(1.46, 1.46, 0.49), c(1.57, 1.40, 0.52), c(1.63, 1.36, 0.54), c(1.68, 1.33, 0.56), c(1.72, 1.30, 0.57)))
+
+  g.f <- make_graph(c(1, 2, 1, 3, 1, 4, 2, 5, 2, 6, 2, 7, 3, 8, 3, 9, 3, 10, 4, 11, 4, 12, 4, 13),
+    dir = FALSE
+  )
+  bp.f <- lapply(seq(-.4, .4, by = 0.1), function(x) {
+    round(power_centrality(g.f, exponent = x), 2)[c(1, 2, 5)]
+  })
+  expect_equal(
+    bp.f,
+    list(c(-1.72, 1.53, -0.57), c(-0.55, 2.03, -0.18), c(0.44, 2.05, 0.15), c(1.01, 1.91, 0.34), c(1.33, 1.78, 0.44), c(1.52, 1.67, 0.51), c(1.65, 1.59, 0.55), c(1.74, 1.53, 0.58), c(1.80, 1.48, 0.60))
+  )
+})
+
+test_that("dense alpha_centrality works", {
+  g.1 <- make_graph(c(1, 3, 2, 3, 3, 4, 4, 5))
+  ac1 <- alpha_centrality(g.1, sparse = FALSE)
+  expect_equal(ac1, c(1, 1, 3, 4, 5))
+
+  g.2 <- make_graph(c(2, 1, 3, 1, 4, 1, 5, 1))
+  ac2 <- alpha_centrality(g.2, sparse = FALSE)
+  expect_equal(ac2, c(5, 1, 1, 1, 1))
+
+  g.3 <- make_graph(c(1, 2, 2, 3, 3, 4, 4, 1, 5, 1))
+  ac3 <- alpha_centrality(g.3, alpha = 0.5, sparse = FALSE)
+  expect_equal(ac3, c(76, 68, 64, 62, 30) / 30)
+})
+
+test_that("sparse alpha_centrality works", {
+  g.1 <- make_graph(c(1, 3, 2, 3, 3, 4, 4, 5))
+  ac1 <- alpha_centrality(g.1, sparse = TRUE)
+  expect_equal(ac1, c(1, 1, 3, 4, 5))
+
+  g.2 <- make_graph(c(2, 1, 3, 1, 4, 1, 5, 1))
+  ac2 <- alpha_centrality(g.2, sparse = TRUE)
+  expect_equal(ac2, c(5, 1, 1, 1, 1))
+
+  g.3 <- make_graph(c(1, 2, 2, 3, 3, 4, 4, 1, 5, 1))
+  ac3 <- alpha_centrality(g.3, alpha = 0.5, sparse = TRUE)
+  expect_equal(ac3, c(76, 68, 64, 62, 30) / 30)
+})
+
+##############################
+## weighted version
+
+test_that("weighted dense alpha_centrality works", {
+  star <- make_star(10)
+  E(star)$weight <- sample(ecount(star))
+
+  ac1 <- alpha_centrality(star, sparse = FALSE)
+  expect_equal(ac1, c(46, 1, 1, 1, 1, 1, 1, 1, 1, 1))
+
+  ac2 <- alpha_centrality(star, weights = "weight", sparse = FALSE)
+  expect_equal(ac2, c(46, 1, 1, 1, 1, 1, 1, 1, 1, 1))
+
+  ac3 <- alpha_centrality(star, weights = NA, sparse = FALSE)
+  expect_equal(ac3, c(vcount(star), 1, 1, 1, 1, 1, 1, 1, 1, 1))
+})
+
+test_that("weighted sparse alpha_centrality works", {
+  star <- make_star(10)
+  E(star)$weight <- sample(ecount(star))
+
+  ac1 <- alpha_centrality(star, sparse = TRUE)
+  expect_equal(ac1, c(46, 1, 1, 1, 1, 1, 1, 1, 1, 1))
+
+  ac2 <- alpha_centrality(star, weights = "weight", sparse = TRUE)
+  expect_equal(ac2, c(46, 1, 1, 1, 1, 1, 1, 1, 1, 1))
+
+  ac3 <- alpha_centrality(star, weights = NA, sparse = TRUE)
+  expect_equal(ac3, c(vcount(star), 1, 1, 1, 1, 1, 1, 1, 1, 1))
+})
+
+test_that("undirected, alpha centrality works, #653", {
+  g <- make_ring(10)
+
+  ac1 <- alpha_centrality(g, sparse = TRUE)
+  ac2 <- alpha_centrality(g, sparse = FALSE)
+  expect_equal(ac1, ac2)
+
+  g2 <- as_directed(g, mode = "mutual")
+  ac3 <- alpha_centrality(g, sparse = FALSE)
+  expect_equal(ac1, ac3)
+})
+
+test_that("`authority_score()` works", {
+  rlang::local_options(lifecycle_verbosity = "quiet")
+  mscale <- function(x) {
+    if (sd(x) != 0) {
+      x <- scale(x)
+    }
+    if (x[1] < 0) {
+      x <- -x
+    }
+    x
+  }
+
+  g1 <- make_graph(
+    c(1, 3, 1, 6, 1, 10, 2, 1, 3, 1, 4, 2, 4, 7, 4, 9, 5, 4, 5, 6, 5, 8, 6, 3,
+      7, 1, 7, 5, 7, 6, 7, 10, 8, 4, 9, 6, 10, 5, 10, 7),
+    directed = TRUE)
+  A <- as_adjacency_matrix(g1, sparse = FALSE)
+  s1 <- eigen(t(A) %*% A)$vectors[, 1]
+  s2 <- authority_score(g1)$vector
+  expect_equal(
+    s2,
+    c(0.519632767970952, 0.0191587307007462, 0.327572049088003,
+      0.238728053455971, 0.449690304629051, 1, 0.0966933781044594,
+      0.204851318050036, 0.0191587307007462, 0.653243552177761)
+  )
+  expect_equal(mscale(s1), mscale(s2), ignore_attr = TRUE)
+
+  g2 <- make_graph(
+    c(1, 2, 1, 4, 2, 3, 2, 4, 3, 1, 3, 5, 4, 3, 5, 1, 5, 2),
+    directed = TRUE
+  )
+  A <- as_adjacency_matrix(g2, sparse = FALSE)
+  s1 <- eigen(t(A) %*% A)$vectors[, 1]
+  s2 <- authority_score(g2)$vector
+  expect_equal(
+    s2,
+    c(0.763521118433368, 1, 0.546200349457202,
+      0.918985947228995, 0.28462967654657)
+  )
+  expect_equal(mscale(s1), mscale(s2), ignore_attr = TRUE)
+
+  rlang::with_options(lifecycle_verbosity = "warning", {
+    expect_snapshot(
+      s3 <- authority_score(g2, options = arpack_defaults)$vector
+    )
+  })
+  expect_equal(s2, s3)
+})
+
+test_that("`hub_score()` works", {
+  rlang::local_options(lifecycle_verbosity = "quiet")
+  mscale <- function(x) {
+    if (sd(x) != 0) {
+      x <- scale(x)
+    }
+    if (x[1] < 0) {
+      x <- -x
+    }
+    x
+  }
+
+  g1 <- make_graph(
+    c(1, 3, 1, 6, 1, 10, 2, 1, 3, 1, 4, 2, 4, 7, 4, 9, 5, 4, 5, 6, 5, 8, 6, 3,
+      7, 1, 7, 5, 7, 6, 7, 10, 8, 4, 9, 6, 10, 5, 10, 7),
+    directed = TRUE)
+  A <- as_adjacency_matrix(g1, sparse = FALSE)
+  s1 <- eigen(A %*% t(A))$vectors[, 1]
+  s2 <- hub_score(g1)$vector
+  expect_equal(
+    s2,
+    c(0.755296579522977, 0.198139015063149, 0.198139015063149,
+      0.0514804231207635, 0.550445261472941, 0.124905139108053,
+      1, 0.0910284037021176, 0.381305851509012, 0.208339295395331)
+  )
+  expect_equal(mscale(s1), mscale(s2), ignore_attr = TRUE)
+
+  g2 <- make_graph(
+    c(1, 2, 1, 4, 2, 3, 2, 4, 3, 1, 3, 5, 4, 3, 5, 1, 5, 2),
+    directed = TRUE
+  )
+  A <- as_adjacency_matrix(g2, sparse = FALSE)
+  s1 <- eigen(A %*% t(A))$vectors[, 1]
+  s2 <- hub_score(g2)$vector
+  expect_equal(
+    s2,
+    c(1, 0.763521118433368, 0.546200349457203,
+      0.28462967654657, 0.918985947228995)
+  )
+  expect_equal(mscale(s1), mscale(s2), ignore_attr = TRUE)
+
+  rlang::with_options(lifecycle_verbosity = "warning", {
+    expect_snapshot(
+      s3 <- hub_score(g2, options = arpack_defaults)$vector
+    )
+  })
+  expect_equal(s2, s3)
+})
+
+test_that("authority_score survives stress test", {
+  skip_on_cran()
+
+  withr::local_seed(42)
+
+  is.principal <- function(M, lambda) {
+    expect_equal(eigen(M)$values[1], lambda)
+  }
+
+  is.ev <- function(M, v, lambda) {
+    expect_equal(as.vector(M %*% v), lambda * v)
+  }
+
+  is.good <- function(M, v, lambda) {
+    is.principal(M, lambda)
+    is.ev(M, v, lambda)
+  }
+
+  for (i in 1:100) {
+    G <- sample_gnm(10, sample(1:20, 1))
+    as <- hits_scores(G)
+    M <- as_adjacency_matrix(G, sparse = FALSE)
+    is.good(t(M) %*% M, as$authority, as$value)
+  }
+
+  for (i in 1:100) {
+    G <- sample_gnm(10, sample(1:20, 1))
+    hs <- hits_scores(G)
+    M <- as_adjacency_matrix(G, sparse = FALSE)
+    is.good(M %*% t(M), hs$hub, hs$value)
+  }
+})
+
+test_that("`hits_score()` works -- authority", {
+  mscale <- function(x) {
+    if (sd(x) != 0) {
+      x <- scale(x)
+    }
+    if (x[1] < 0) {
+      x <- -x
+    }
+    x
+  }
+
+  g1 <- make_graph(
+    c(1, 3, 1, 6, 1, 10, 2, 1, 3, 1, 4, 2, 4, 7, 4, 9, 5, 4, 5, 6, 5, 8, 6, 3,
+      7, 1, 7, 5, 7, 6, 7, 10, 8, 4, 9, 6, 10, 5, 10, 7),
+    directed = TRUE)
+  A <- as_adjacency_matrix(g1, sparse = FALSE)
+  s1 <- eigen(t(A) %*% A)$vectors[, 1]
+  s2 <- hits_scores(g1)$authority
+  expect_equal(
+    s2,
+    c(0.519632767970952, 0.0191587307007462, 0.327572049088003,
+      0.238728053455971, 0.449690304629051, 1, 0.0966933781044594,
+      0.204851318050036, 0.0191587307007462, 0.653243552177761)
+  )
+  expect_equal(mscale(s1), mscale(s2), ignore_attr = TRUE)
+
+  g2 <- make_graph(
+    c(1, 2, 1, 4, 2, 3, 2, 4, 3, 1, 3, 5, 4, 3, 5, 1, 5, 2),
+    directed = TRUE
+  )
+  A <- as_adjacency_matrix(g2, sparse = FALSE)
+  s1 <- eigen(t(A) %*% A)$vectors[, 1]
+  s2 <- hits_scores(g2)$authority
+  expect_equal(
+    s2,
+    c(0.763521118433368, 1, 0.546200349457202,
+      0.918985947228995, 0.28462967654657)
+  )
+  expect_equal(mscale(s1), mscale(s2), ignore_attr = TRUE)
+
+})
+
+test_that("`hits_scores()` works -- hub", {
+  mscale <- function(x) {
+    if (sd(x) != 0) {
+      x <- scale(x)
+    }
+    if (x[1] < 0) {
+      x <- -x
+    }
+    x
+  }
+
+  g1 <- make_graph(
+    c(1, 3, 1, 6, 1, 10, 2, 1, 3, 1, 4, 2, 4, 7, 4, 9, 5, 4, 5, 6, 5, 8, 6, 3,
+      7, 1, 7, 5, 7, 6, 7, 10, 8, 4, 9, 6, 10, 5, 10, 7),
+    directed = TRUE)
+  A <- as_adjacency_matrix(g1, sparse = FALSE)
+  s1 <- eigen(A %*% t(A))$vectors[, 1]
+  s2 <- hits_scores(g1)$hub
+  expect_equal(
+    s2,
+    c(0.755296579522977, 0.198139015063149, 0.198139015063149,
+      0.0514804231207635, 0.550445261472941, 0.124905139108053,
+      1, 0.0910284037021176, 0.381305851509012, 0.208339295395331)
+  )
+  expect_equal(mscale(s1), mscale(s2), ignore_attr = TRUE)
+
+  g2 <- make_graph(
+    c(1, 2, 1, 4, 2, 3, 2, 4, 3, 1, 3, 5, 4, 3, 5, 1, 5, 2),
+    directed = TRUE
+  )
+  A <- as_adjacency_matrix(g2, sparse = FALSE)
+  s1 <- eigen(A %*% t(A))$vectors[, 1]
+  s2 <-  hits_scores(g2)$hub
+  expect_equal(
+    s2,
+    c(1, 0.763521118433368, 0.546200349457203,
+      0.28462967654657, 0.918985947228995)
+  )
+  expect_equal(mscale(s1), mscale(s2), ignore_attr = TRUE)
+
+})
+
+test_that("spectrum works for symmetric matrices", {
+  withr::local_seed(42)
+
+  std <- function(x) {
+    x <- zapsmall(x)
+    apply(x, 2, function(col) {
+      if (any(col < 0) && col[which(col != 0)[1]] < 0) {
+        -col
+      } else {
+        col
+      }
+    })
+  }
+
+  g <- sample_gnp(50, 5 / 50)
+  e0 <- eigen(as_adjacency_matrix(g, sparse = FALSE))
+
+  e1 <- spectrum(g, which = list(howmany = 4, pos = "LA"))
+  expect_equal(e0$values[1:4], e1$values)
+  expect_equal(std(e0$vectors[, 1:4]), std(e1$vectors))
+
+  e2 <- spectrum(g, which = list(howmany = 4, pos = "SA"))
+  expect_equal(e0$values[50:47], e2$values)
+  expect_equal(std(e0$vectors[, 50:47]), std(e2$vectors))
+
+  rlang::local_options(lifecycle_verbosity = "warning")
+  expect_warning(
+    e3 <- spectrum(g, which = list(howmany = 4, pos = "SA"), options = arpack_defaults)
+  )
+})
diff --git a/tests/testthat/test-closeness.R b/tests/testthat/test-closeness.R
deleted file mode 100644
index 6684310d16..0000000000
--- a/tests/testthat/test-closeness.R
+++ /dev/null
@@ -1,46 +0,0 @@
-test_that("closeness works", {
-  kite <- graph_from_literal(
-    Andre - Beverly:Carol:Diane:Fernando,
-    Beverly - Andre:Diane:Ed:Garth,
-    Carol - Andre:Diane:Fernando,
-    Diane - Andre:Beverly:Carol:Ed:Fernando:Garth,
-    Ed - Beverly:Diane:Garth,
-    Fernando - Andre:Carol:Diane:Garth:Heather,
-    Garth - Beverly:Diane:Ed:Fernando:Heather,
-    Heather - Fernando:Garth:Ike,
-    Ike - Heather:Jane,
-    Jane - Ike
-  )
-
-  clo <- closeness(kite) * (vcount(kite) - 1)
-  expect_equal(
-    round(sort(clo, decreasing = TRUE), 3),
-    c(Fernando = 0.643, Garth = 0.643, Diane = 0.600, Heather = 0.600, Andre = 0.529, Beverly = 0.529, Carol = 0.500, Ed = 0.500, Ike = 0.429, Jane = 0.310)
-  )
-
-  clo2 <- closeness(kite, normalized = TRUE)
-  expect_equal(clo, clo2)
-})
-
-## TODO: weighted closeness
-
-test_that("closeness centralization works", {
-  kite <- graph_from_literal(
-    Andre - Beverly:Carol:Diane:Fernando,
-    Beverly - Andre:Diane:Ed:Garth,
-    Carol - Andre:Diane:Fernando,
-    Diane - Andre:Beverly:Carol:Ed:Fernando:Garth,
-    Ed - Beverly:Diane:Garth,
-    Fernando - Andre:Carol:Diane:Garth:Heather,
-    Garth - Beverly:Diane:Ed:Fernando:Heather,
-    Heather - Fernando:Garth:Ike,
-    Ike - Heather:Jane,
-    Jane - Ike
-  )
-
-  c1 <- closeness(kite, normalized = TRUE)
-  c2 <- centr_clo(kite)
-  expect_equal(unname(c1), c2$res)
-  expect_equal(c2$centralization, 0.270374931581828)
-  expect_equal(c2$theoretical_max, 4.23529411764706)
-})
diff --git a/tests/testthat/test-evcent.R b/tests/testthat/test-evcent.R
deleted file mode 100644
index f4d79444f0..0000000000
--- a/tests/testthat/test-evcent.R
+++ /dev/null
@@ -1,37 +0,0 @@
-test_that("eigen_centrality works", {
-  kite <- graph_from_literal(
-    Andre - Beverly:Carol:Diane:Fernando,
-    Beverly - Andre:Diane:Ed:Garth,
-    Carol - Andre:Diane:Fernando,
-    Diane - Andre:Beverly:Carol:Ed:Fernando:Garth,
-    Ed - Beverly:Diane:Garth,
-    Fernando - Andre:Carol:Diane:Garth:Heather,
-    Garth - Beverly:Diane:Ed:Fernando:Heather,
-    Heather - Fernando:Garth:Ike,
-    Ike - Heather:Jane,
-    Jane - Ike
-  )
-  evc <- round(eigen_centrality(kite)$vector, 3)
-  expect_equal(evc, structure(c(0.732, 0.732, 0.594, 1, 0.827, 0.594, 0.827, 0.407, 0.1, 0.023), .Names = c("Andre", "Beverly", "Carol", "Diane", "Fernando", "Ed", "Garth", "Heather", "Ike", "Jane")))
-
-
-  ## Eigenvector-centrality, small stress-test
-
-  is.principal <- function(M, lambda, eps = 1e-12) {
-    abs(eigen(M)$values[1] - lambda) < eps
-  }
-
-  is.ev <- function(M, v, lambda, eps = 1e-12) {
-    max(abs(M %*% v - lambda * v)) < eps
-  }
-
-  is.good <- function(M, v, lambda, eps = 1e-12) {
-    is.principal(M, lambda, eps) && is.ev(M, v, lambda, eps)
-  }
-
-  for (i in 1:1000) {
-    G <- sample_gnm(10, sample(1:20, 1))
-    ev <- eigen_centrality(G)
-    expect_true(is.good(as_adjacency_matrix(G, sparse = FALSE), ev$vector, ev$value))
-  }
-})
diff --git a/tests/testthat/test-graph.eigen.R b/tests/testthat/test-graph.eigen.R
deleted file mode 100644
index 5bac0a6ced..0000000000
--- a/tests/testthat/test-graph.eigen.R
+++ /dev/null
@@ -1,30 +0,0 @@
-test_that("spectrum works for symmetric matrices", {
-  withr::local_seed(42)
-
-  std <- function(x) {
-    x <- zapsmall(x)
-    apply(x, 2, function(col) {
-      if (any(col < 0) && col[which(col != 0)[1]] < 0) {
-        -col
-      } else {
-        col
-      }
-    })
-  }
-
-  g <- sample_gnp(50, 5 / 50)
-  e0 <- eigen(as_adjacency_matrix(g, sparse = FALSE))
-
-  e1 <- spectrum(g, which = list(howmany = 4, pos = "LA"))
-  expect_equal(e0$values[1:4], e1$values)
-  expect_equal(std(e0$vectors[, 1:4]), std(e1$vectors))
-
-  e2 <- spectrum(g, which = list(howmany = 4, pos = "SA"))
-  expect_equal(e0$values[50:47], e2$values)
-  expect_equal(std(e0$vectors[, 50:47]), std(e2$vectors))
-
-  rlang::local_options(lifecycle_verbosity = "warning")
-  expect_warning(
-    e3 <- spectrum(g, which = list(howmany = 4, pos = "SA"), options = arpack_defaults)
-  )
-})