diff --git a/benchmark/benchmarks.jl b/benchmark/benchmarks.jl
index abff6d2b..e77fad58 100644
--- a/benchmark/benchmarks.jl
+++ b/benchmark/benchmarks.jl
@@ -1,6 +1,7 @@
 using BenchmarkTools
 using LinearAlgebra
 using SparseMatrixColorings
+import SparseMatrixColorings as SMC
 using SparseArrays
 using StableRNGs
 
@@ -29,13 +30,13 @@ for structure in [:nonsymmetric, :symmetric],
     results = [coloring(A, problem, algo; decompression_eltype=Float64) for A in As]
     Bs = [compress(Float64.(A), result) for (A, result) in zip(As, results)]
 
-    SUITE[:coloring][structure][partition][decompression]["n=$n"]["p=$p"] = @benchmarkable begin
+    bench_col = @benchmarkable begin
         for A in $As
             coloring(A, $problem, $algo)
         end
     end
 
-    SUITE[:decompress][structure][partition][decompression]["n=$n"]["p=$p"] = @benchmarkable begin
+    bench_dec = @benchmarkable begin
         for (B, result) in zip($Bs, $results)
             if B isa AbstractMatrix
                 decompress(B, result)
@@ -44,4 +45,34 @@ for structure in [:nonsymmetric, :symmetric],
             end
         end
     end
+
+    SUITE[:coloring][structure][partition][decompression]["n=$n"]["p=$p"] = bench_col
+    SUITE[:decompress][structure][partition][decompression]["n=$n"]["p=$p"] = bench_dec
+end
+
+for structure in [:nonsymmetric, :symmetric],
+    partition in (structure == :nonsymmetric ? [:column, :row] : [:column]),
+    order in [LargestFirst(), SmallestLast(), IncidenceDegree(), DynamicLargestFirst()],
+    n in [10^3, 10^5],
+    p in [2 / n, 5 / n, 10 / n]
+
+    nb_samples = 5
+    As = [sparse(Symmetric(sprand(StableRNG(i), Bool, n, n, p))) for i in 1:nb_samples]
+    if structure == :symmetric
+        gs = [SMC.AdjacencyGraph(A) for A in As]
+        bench_ord = @benchmarkable begin
+            for g in $gs
+                SMC.vertices(g, $order)
+            end
+        end
+    else
+        gs = [SMC.BipartiteGraph(A) for A in As]
+        valside = partition == :row ? Val(1) : Val(2)
+        bench_ord = @benchmarkable begin
+            for g in $gs
+                SMC.vertices(g, $valside, $order)
+            end
+        end
+    end
+    SUITE[:order][structure][partition][string(order)]["n=$n"]["p=$p"] = bench_ord
 end