diff --git a/R/centrality.R b/R/centrality.R
index ffbb5e76d5..e116ec96c8 100644
--- a/R/centrality.R
+++ b/R/centrality.R
@@ -1112,7 +1112,8 @@ diversity <- diversity_impl
 #'   [arpack()] for details.
 #' @inheritParams rlang::args_dots_empty
 #' @return A named list with members:
-#'   \item{vector}{The hub or authority scores of the vertices.}
+#'   \item{hub}{The hub score of the vertices.}
+#'   \item{authority}{The authority score of the vertices.}
 #'   \item{value}{The corresponding eigenvalue of the calculated
 #'     principal eigenvector.}
 #'   \item{options}{Some information about the ARPACK computation, it has
diff --git a/man/hits_scores.Rd b/man/hits_scores.Rd
index 63e7a564d1..78ab35bfe5 100644
--- a/man/hits_scores.Rd
+++ b/man/hits_scores.Rd
@@ -33,7 +33,8 @@ selected by the surfer.}
 }
 \value{
 A named list with members:
-\item{vector}{The hub or authority scores of the vertices.}
+\item{hub}{The hub score of the vertices.}
+\item{authority}{The authority score of the vertices.}
 \item{value}{The corresponding eigenvalue of the calculated
 principal eigenvector.}
 \item{options}{Some information about the ARPACK computation, it has
diff --git a/tests/testthat/_snaps/authority.score.md b/tests/testthat/_snaps/authority.score.md
new file mode 100644
index 0000000000..28ff138f41
--- /dev/null
+++ b/tests/testthat/_snaps/authority.score.md
@@ -0,0 +1,26 @@
+# `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-authority.score.R b/tests/testthat/test-authority.score.R
index e228f1c166..6d3946430a 100644
--- a/tests/testthat/test-authority.score.R
+++ b/tests/testthat/test-authority.score.R
@@ -1,4 +1,5 @@
 test_that("`authority_score()` works", {
+  rlang::local_options(lifecycle_verbosity = "quiet")
   mscale <- function(x) {
     if (sd(x) != 0) {
       x <- scale(x)
@@ -21,14 +22,16 @@ test_that("`authority_score()` works", {
   s2 <- authority_score(g2)$vector
   expect_equal(mscale(s1), mscale(s2), ignore_attr = TRUE)
 
-  rlang::local_options(lifecycle_verbosity = "warning")
-  expect_warning(
-    s3 <- authority_score(g2, options = arpack_defaults)$vector
-  )
+  rlang::with_options(lifecycle_verbosity = "warning", {
+    expect_snapshot(
+      s3 <- authority_score(g2, options = arpack_defaults)$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)
@@ -51,10 +54,11 @@ test_that("`hub_score()` works", {
   s2 <- hub_score(g2)$vector
   expect_equal(mscale(s1), mscale(s2), ignore_attr = TRUE)
 
-  rlang::local_options(lifecycle_verbosity = "warning")
-  expect_warning(
-    s3 <- hub_score(g2, options = arpack_defaults)$vector
-  )
+  rlang::with_options(lifecycle_verbosity = "warning", {
+    expect_snapshot(
+      s3 <- hub_score(g2, options = arpack_defaults)$vector
+    )
+  })
   expect_equal(s2, s3)
 })
 
@@ -64,9 +68,10 @@ test_that("`hub_score()` works", {
 # and any vector with alternating values (a, b, a, b, ...) is a valid
 # solution, not just all-ones.
 test_that("authority scores of a ring are all one", {
+  rlang::local_options(lifecycle_verbosity = "quiet")
   g3 <- make_ring(99)
-  expect_equal(authority_score(g3)$vector, rep(1, vcount(g3)))
-  expect_equal(hub_score(g3)$vector, rep(1, vcount(g3)))
+  expect_equal(hits_scores(g3)$authority, rep(1, vcount(g3)))
+  expect_equal(hits_scores(g3)$hub, rep(1, vcount(g3)))
 })
 
 test_that("authority_score survives stress test", {
@@ -89,15 +94,66 @@ test_that("authority_score survives stress test", {
 
   for (i in 1:100) {
     G <- sample_gnm(10, sample(1:20, 1))
-    as <- authority_score(G)
+    as <- hits_scores(G)
     M <- as_adj(G, sparse = FALSE)
-    is.good(t(M) %*% M, as$vector, as$value)
+    is.good(t(M) %*% M, as$authority, as$value)
   }
 
   for (i in 1:100) {
     G <- sample_gnm(10, sample(1:20, 1))
-    hs <- hub_score(G)
+    hs <- hits_scores(G)
     M <- as_adj(G, sparse = FALSE)
-    is.good(M %*% t(M), hs$vector, hs$value)
+    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 <- sample_pa(100, m = 10)
+  A <- as_adj(g1, sparse = FALSE)
+  s1 <- eigen(t(A) %*% A)$vectors[, 1]
+  s2 <- hits_scores(g1)$authority
+  expect_equal(mscale(s1), mscale(s2), ignore_attr = TRUE)
+
+  g2 <- sample_gnp(100, 2 / 100)
+  A <- as_adj(g2, sparse = FALSE)
+  s1 <- eigen(t(A) %*% A)$vectors[, 1]
+  s2 <- hits_scores(g2)$authority
+  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 <- sample_pa(100, m = 10)
+  A <- as_adj(g1, sparse = FALSE)
+  s1 <- eigen(A %*% t(A))$vectors[, 1]
+  s2 <- hits_scores(g1)$hub
+  expect_equal(mscale(s1), mscale(s2), ignore_attr = TRUE)
+
+  g2 <- sample_gnp(100, 2 / 100)
+  A <- as_adj(g2, sparse = FALSE)
+  s1 <- eigen(A %*% t(A))$vectors[, 1]
+  s2 <-  hits_scores(g2)$hub
+  expect_equal(mscale(s1), mscale(s2), ignore_attr = TRUE)
+
+})
+