diff --git a/R/adjacency.R b/R/adjacency.R
index c24ad085a1..930790eb47 100644
--- a/R/adjacency.R
+++ b/R/adjacency.R
@@ -1,4 +1,3 @@
-
 #' Create graphs from adjacency matrices
 #'
 #' @description
@@ -119,15 +118,15 @@ graph.adjacency <- function(adjmatrix, mode = c("directed", "undirected", "max",
 #' @examples
 #'
 #' g1 <- sample(
-#'     x = 0:1, size = 100, replace = TRUE,
-#'     prob = c(0.9, 0.1)
-#'   ) %>%
+#'   x = 0:1, size = 100, replace = TRUE,
+#'   prob = c(0.9, 0.1)
+#' ) %>%
 #'   matrix(ncol = 10) %>%
 #'   graph_from_adjacency_matrix()
 #'
 #' g2 <- sample(
-#'     x = 0:5, size = 100, replace = TRUE,
-#'     prob = c(0.9, 0.02, 0.02, 0.02, 0.02, 0.02)
+#'   x = 0:5, size = 100, replace = TRUE,
+#'   prob = c(0.9, 0.02, 0.02, 0.02, 0.02, 0.02)
 #' ) %>%
 #'   matrix(ncol = 10) %>%
 #'   graph_from_adjacency_matrix(weighted = TRUE)
@@ -193,8 +192,8 @@ graph.adjacency <- function(adjmatrix, mode = c("directed", "undirected", "max",
 #'   x
 #' }
 #' expected_g8_weights <- non_zero_sort(
-#'   halve_diag(adj_matrix + t(adj_matrix)
-#' )[lower.tri(adj_matrix, diag = TRUE)])
+#'   halve_diag(adj_matrix + t(adj_matrix))[lower.tri(adj_matrix, diag = TRUE)]
+#' )
 #' actual_g8_weights <- sort(E(g8)$weight)
 #' all(expected_g8_weights == actual_g8_weights)
 #'
@@ -229,7 +228,6 @@ graph_from_adjacency_matrix <- function(adjmatrix,
                                         ),
                                         weighted = NULL, diag = TRUE,
                                         add.colnames = NULL, add.rownames = NA) {
-
   mode <- igraph.match.arg(mode)
 
   if (!is.matrix(adjmatrix) && !inherits(adjmatrix, "Matrix")) {
@@ -377,157 +375,68 @@ mysummary <- function(x) {
   result
 }
 
+pmax_AB <- function(A,B) {
+  change <- A < B  
+  A[change] <- B[change]
+  A
+}
 
-graph.adjacency.sparse <- function(adjmatrix, mode, weighted = NULL, diag = TRUE) {
+pmin_AB <- function(A, B) {
+  change <- A > B
+  A[change] <- B[change]
+  A
+}
+
+graph.adjacency.sparse <- function(adjmatrix, mode, weighted = NULL, diag = TRUE, call = rlang::caller_env()) {
   if (!is.null(weighted)) {
     if (is.logical(weighted) && weighted) {
       weighted <- "weight"
     }
     if (!is.character(weighted)) {
-      stop("invalid value supplied for `weighted' argument, please see docs.")
+      cli::cli_abort("Invalid value supplied for `weighted' argument, please see docs.", call = call)
     }
   }
 
   if (nrow(adjmatrix) != ncol(adjmatrix)) {
-    stop("not a square matrix")
+    cli::cli_abort("Not a square matrix", call = call)
   }
 
   vc <- nrow(adjmatrix)
+  # Exit early for empty graphs
+  if (vc == 1 || Matrix::nnzero(adjmatrix) == 0) {
+    return(make_empty_graph(n = vc, directed = (mode == "directed")))
+  }
 
-  ## to remove non-redundancies that can persist in a dgtMatrix
   if (inherits(adjmatrix, "dgTMatrix")) {
     adjmatrix <- as(adjmatrix, "CsparseMatrix")
   } else if (inherits(adjmatrix, "ddiMatrix")) {
     adjmatrix <- as(adjmatrix, "CsparseMatrix")
   }
 
-  if (mode == "directed") {
-    ## DIRECTED
-    el <- mysummary(adjmatrix)
-    if (!diag) {
-      el <- el[el[, 1] != el[, 2], ]
-    }
-  } else if (mode == "undirected") {
-    ## UNDIRECTED, must be symmetric if weighted
+  if (mode == "undirected") {
     if (!is.null(weighted) && !Matrix::isSymmetric(adjmatrix)) {
-      stop("Please supply a symmetric matrix if you want to create a weighted graph with mode=UNDIRECTED.")
-    }
-    if (diag) {
-      adjmatrix <- Matrix::tril(adjmatrix)
-    } else {
-      if (vc == 1) {
-        # Work around Matrix glitch
-        adjmatrix <- as(matrix(0), "dgCMatrix")
-      } else {
-        adjmatrix <- Matrix::tril(adjmatrix, -1)
-      }
-    }
-    el <- mysummary(adjmatrix)
-    rm(adjmatrix)
-  } else if (mode == "max") {
-    ## MAXIMUM
-    el <- mysummary(adjmatrix)
-    rm(adjmatrix)
-    if (!diag) {
-      el <- el[el[, 1] != el[, 2], ]
-    }
-    el <- el[el[, 3] != 0, ]
-    w <- el[, 3]
-    el <- el[, 1:2]
-    el <- cbind(pmin(el[, 1], el[, 2]), pmax(el[, 1], el[, 2]))
-    o <- order(el[, 1], el[, 2])
-    el <- el[o, , drop = FALSE]
-    w <- w[o]
-    if (nrow(el) > 1) {
-      dd <- el[2:nrow(el), 1] == el[1:(nrow(el) - 1), 1] &
-        el[2:nrow(el), 2] == el[1:(nrow(el) - 1), 2]
-      dd <- which(dd)
-      if (length(dd) > 0) {
-        mw <- pmax(w[dd], w[dd + 1])
-        w[dd] <- mw
-        w[dd + 1] <- mw
-        el <- el[-dd, , drop = FALSE]
-        w <- w[-dd]
-      }
-    }
-    el <- cbind(el, w)
-  } else if (mode == "upper") {
-    ## UPPER
-    if (diag) {
-      adjmatrix <- Matrix::triu(adjmatrix)
-    } else {
-      adjmatrix <- Matrix::triu(adjmatrix, 1)
-    }
-    el <- mysummary(adjmatrix)
-    rm(adjmatrix)
-    if (!diag) {
-      el <- el[el[, 1] != el[, 2], ]
+      cli::cli_abort(
+        "Please supply a symmetric matrix if you want to create a weighted graph with mode=UNDIRECTED.",
+        call = call
+      )
     }
+    adjmatrix <- Matrix::tril(adjmatrix)
   } else if (mode == "lower") {
-    ## LOWER
-    if (diag) {
-      adjmatrix <- Matrix::tril(adjmatrix)
-    } else {
-      if (vc == 1) {
-        # Work around Matrix glitch
-        adjmatrix <- as(matrix(0), "dgCMatrix")
-      } else {
-        adjmatrix <- Matrix::tril(adjmatrix, -1)
-      }
-    }
-    el <- mysummary(adjmatrix)
-    rm(adjmatrix)
-    if (!diag) {
-      el <- el[el[, 1] != el[, 2], ]
-    }
-  } else if (mode == "min") {
-    ## MINIMUM
-    adjmatrix <- sign(adjmatrix) * sign(Matrix::t(adjmatrix)) * adjmatrix
-    el <- mysummary(adjmatrix)
-    rm(adjmatrix)
-    if (!diag) {
-      el <- el[el[, 1] != el[, 2], ]
-    }
-    el <- el[el[, 3] != 0, ]
-    w <- el[, 3]
-    el <- el[, 1:2]
-    el <- cbind(pmin(el[, 1], el[, 2]), pmax(el[, 1], el[, 2]))
-    o <- order(el[, 1], el[, 2])
-    el <- el[o, ]
-    w <- w[o]
-    if (nrow(el) > 1) {
-      dd <- el[2:nrow(el), 1] == el[1:(nrow(el) - 1), 1] &
-        el[2:nrow(el), 2] == el[1:(nrow(el) - 1), 2]
-      dd <- which(dd)
-      if (length(dd) > 0) {
-        mw <- pmin(w[dd], w[dd + 1])
-        w[dd] <- mw
-        w[dd + 1] <- mw
-        el <- el[-dd, ]
-        w <- w[-dd]
-      }
-    }
-    el <- cbind(el, w)
+    adjmatrix <- Matrix::tril(adjmatrix)
+  } else if (mode == "upper") {
+    adjmatrix <- Matrix::triu(adjmatrix)
   } else if (mode == "plus") {
-    ## PLUS
     adjmatrix <- adjmatrix + Matrix::t(adjmatrix)
-    if (diag) {
-      adjmatrix <- Matrix::tril(adjmatrix)
-    } else {
-      if (vc == 1) {
-        # Work around Matrix glitch
-        adjmatrix <- as(matrix(0), "dgCMatrix")
-      } else {
-        adjmatrix <- Matrix::tril(adjmatrix, -1)
-      }
-    }
-    el <- mysummary(adjmatrix)
-    rm(adjmatrix)
-    if (diag) {
-      loop <- el[, 1] == el[, 2]
-      el[loop, 3] <- el[loop, 3] / 2
-    }
-    el <- el[el[, 3] != 0, ]
+    adjmatrix <- Matrix::tril(adjmatrix)
+  } else if (mode == "max") {
+    adjmatrix <- pmax_AB(Matrix::tril(adjmatrix), Matrix::t(Matrix::triu(adjmatrix)))
+  } else if (mode == "min") {
+    adjmatrix <- pmin_AB(Matrix::tril(adjmatrix), Matrix::t(Matrix::triu(adjmatrix)))
+    adjmatrix <- Matrix::drop0(adjmatrix)
+  }
+  el <- mysummary(adjmatrix)
+  if (!diag) {
+    el <- el[el[, 1] != el[, 2], ]
   }
 
   if (!is.null(weighted)) {
@@ -536,7 +445,12 @@ graph.adjacency.sparse <- function(adjmatrix, mode, weighted = NULL, diag = TRUE
     names(weight) <- weighted
     res <- add_edges(res, edges = t(as.matrix(el[, 1:2])), attr = weight)
   } else {
-    edges <- unlist(apply(el, 1, function(x) rep(unname(x[1:2]), x[3])))
+    if (max(el[, 3]) == 1) {
+      edges <- as.vector(t(el[, 1:2]))
+    } else {
+      row_repeats <- rep(seq_len(nrow(el)), times = el[, 3])
+      edges <- as.vector(t(el[row_repeats, 1:2]))
+    }
     res <- make_graph(n = vc, edges, directed = (mode == "directed"))
   }
   res
diff --git a/tests/testthat/test-adjacency.R b/tests/testthat/test-adjacency.R
index d29544bb49..f072b456f1 100644
--- a/tests/testthat/test-adjacency.R
+++ b/tests/testthat/test-adjacency.R
@@ -302,7 +302,7 @@ test_that("graph_from_adjacency_matrix() works", {
 })
 
 test_that("graph_from_adjacency_matrix() works -- dgCMatrix", {
-  skip_if_not_installed("Matrix")
+  skip_if_not_installed("Matrix",minimum_version = "1.6.0")
 
   M1 <- rbind(
     c(0, 0, 1, 1),
@@ -597,7 +597,7 @@ test_that("graph_from_adjacency_matrix() snapshot", {
 })
 
 test_that("graph_from_adjacency_matrix() snapshot for sparse matrices", {
-  skip_if_not_installed("Matrix")
+  skip_if_not_installed("Matrix", minimum_version = "1.6.0")
 
   rlang::local_options(lifecycle_verbosity = "warning")
 
@@ -657,3 +657,60 @@ test_that("weighted graph_from_adjacency_matrix() works on integer matrices", {
   g <- graph_from_adjacency_matrix(data, weighted = TRUE)
   expect_equal(as.matrix(g[]), data)
 })
+
+test_that("sparse/dense matrices no loops works",{
+  skip_if_not_installed("Matrix", minimum_version = "1.6.0")
+  A <- diag(1, 5)
+  A[1, 2] <- 1
+  g <- graph_from_adjacency_matrix(A, diag = FALSE)
+  expect_equal(ecount(g), 1)
+  expect_equal(get_edge_ids(g, c(1, 2)), 1)
+  
+  A <- as(A, "dgCMatrix")
+  g <- graph_from_adjacency_matrix(A, diag = FALSE)
+  expect_equal(ecount(g), 1)
+  expect_equal(get_edge_ids(g,c(1, 2)), 1)
+
+})
+
+test_that("sparse/dense matrices multiple works",{
+  skip_if_not_installed("Matrix", minimum_version = "1.6.0")
+  A <- matrix(0, 5, 5)
+  A[1, 2] <- 3
+  g <- graph_from_adjacency_matrix(A, diag = FALSE, weighted = FALSE)
+  expect_equal(ecount(g), 3)
+  expect_equal(as_edgelist(g), matrix(c(1, 2), 3, 2, byrow = TRUE))
+  
+  A <- as(A,"dgCMatrix")
+  g <- graph_from_adjacency_matrix(A,diag = FALSE)
+  expect_equal(ecount(g), 3)
+  expect_equal(as_edgelist(g), matrix(c(1, 2), 3, 2, byrow = TRUE))
+  
+})
+
+test_that("sparse/dense matrices min/max/plus",{
+  skip_if_not_installed("Matrix", minimum_version = "1.6.0")
+  A <- matrix(0, 5, 5)
+  A[1, 2] <- 3
+  A[2, 1] <- 2
+  g <- graph_from_adjacency_matrix(A, diag = FALSE, mode = "max", weighted = TRUE)
+  expect_equal(E(g)$weight[1], 3)
+  
+  g <- graph_from_adjacency_matrix(A, diag = FALSE, mode = "min", weighted = TRUE)
+  expect_equal(E(g)$weight[1], 2)
+
+  g <- graph_from_adjacency_matrix(A, diag = FALSE, mode = "plus", weighted = TRUE)
+  expect_equal(E(g)$weight[1], 5)
+
+  A <- as(A,"dgCMatrix")
+  g <- graph_from_adjacency_matrix(A, diag = FALSE, mode = "max", weighted = TRUE)
+  expect_equal(E(g)$weight[1], 3)
+  
+  g <- graph_from_adjacency_matrix(A, diag = FALSE, mode = "min", weighted = TRUE)
+  expect_equal(E(g)$weight[1], 2)
+
+  g <- graph_from_adjacency_matrix(A, diag = FALSE, mode = "plus", weighted = TRUE)
+  expect_equal(E(g)$weight[1], 5)
+  
+  
+})
\ No newline at end of file